JPWO2001081821A1 - Folded line structure, folded line forming die, and folded line forming method - Google Patents

Abstract

A linear folding line M having a plurality of polygonal parts P and a linear part connecting part connecting outer sides of the parts P to each other, and being foldable along the linear part connecting part; A fold line structure (for example, a PET bottle) A provided with V, wherein the fold lines M and V are a plurality of mountain fold lines whose one surface side is mountain fold when viewed from one surface side of the fold line structure. The said structure A with a fold line which has M and one or more valley fold lines V which become a valley fold, and each fold line satisfies a folding condition. A novel folding method in which a wall-shaped structure is divided into polygonal flat parts P by a number of folding lines, and folding lines M and V at boundaries between the divided flat plate parts P can be folded. And a novel folding line forming die and a folding line forming method.

Description

次に図１８９Ａの各要素の展開図を２Ｎ等分（Ｎ；整数）する。この時、螺旋状の折り線になるよう図のように半径方向と角φをなすような角度で展開図上に分割線を描く。図１８９Ａは各展開図を１６等分したものである。分割された小要素を半径方向に積上げ新たに扇形要素を作る。積上げて構成された扇形要素を図１８９Ｂに示し、これは湾曲した形状の扇形要素を表す。この湾曲形状の扇形要素を１６個接合し、接合線を交互に山、谷折り線とすると、螺旋形折り線を持つ放物面形状殻（図１８３参照）が得られる。図１８３の放物面形状殻の頂点を通る中心軸回りに巻取ったものは図１８４、図１８５に示されている。
（実施例３０）
図１９０は本発明の実施例３０の折り線付構造物としての巻取式のテントの斜視図である。
図１９１は前記図１９０の巻取式のテントの折り畳み途中の状態の斜視図である。
図１９２は前記図１９０の状態から更に折り畳んだ状態のテントの斜視図である。
図１９０において、巻取式のテントＨは、山折り線Ｍおよび谷折り線Ｖが等角螺旋（ベルヌーイの螺旋）に沿って形成されており、前記折り線Ｍ，Ｖにより形成された扇形のパーツを、折り線Ｍ，Ｖに沿って折り畳みながら巻き取ることができる。テントＨは伸長状態ではドーム型となり、その外側面の外周部および半径方向の中央部にはそれぞれ円周方向に延びるリング状のフレキシブルチューブＨ１およびＨ２が固着されている。前記テントＨは、前記フレキシブルチューブＨ１，Ｈ２にエアを供給して膨らますことにより、図１９０の伸長状態に保持される。
この実施例３０では、殻を構成する膜厚が大きい時には中央部分で巻き取りが窮屈になる場合があるので、これを避けるため前記図１８９Ａを分割する際、最初８等分し、次にこれを適当に不等分に分割する。
すなわち８等分した後、これを更に中心角比０．４７５：０．５２５で２分割して構成した時の湾曲形状の扇形要素の組８個（１６要素）を交互に接合して構成した曲面は図１９０に示されている。ここで中心角の小さな要素の左方を谷折り、右方を山折りとすると中心軸回りに下方にずれながら巻き取られる。これを図１９１、図１９２に示す。この巻取り法は上述の窮屈度合いを緩和させる利点がある。
これ等のモデルは巻取り／展開可能な大型のテント以外に、パラボラアンテナのパラボラ面を形成するのに利用可能である。
産業上の利用可能性
以上、本発明の実施例を詳述したが、本発明は、前記実施例に限定されるものではなく、特許請求の範囲に記載された本発明の要旨の範囲内で、種々の変更を行うことが可能である。本発明の変更実施例を下記に例示する。
（１）前記実施例１、図２では、折り線形成用型は、一対の折り畳み可能な折り線形成部材（ｆｌｅｘｉｂｌｅ金型）を有し、前記一対の折り線形成部材によりシート状部材を挟んだ状態で一対の折り線形成部材を同時に折り畳むことにより、シート状部材に折り線を形成するように構成したが、折り畳み可能な折り線形成部材（ｆｌｅｘｉｂｌｅ金型）は一対ではなく、１枚だけでもよい。折り線形成部材を１枚とした場合には、その一面側にシート状部材を吸着した状態で折り畳めばよい。前記シート状部材を吸着する方法としては、例えば、折り線形成部材のパーツに通気孔を開けておいて、他面側を低圧にすることにより一面側にシート状部材を吸着することが可能となる。
また、磁化した材料製のパーツを使用した折り線形成部材と、柔軟な磁性ラバーシートとの間にシート状部材を挟んだ状態で折り線形成部材を折り畳むことにより折り線を形成することが可能となる。
（２）前記本発明者の研究結果および各実施例の説明から分かるように、本発明は新規な折り畳み可能な折り線により種々の形状の折り線およびパーツを使用可能となったので、多種多様な折り線付の折り畳み可能構造物を得ることが可能である。したがって、本発明は、種々の形状の伸長、収縮可能な宇宙空間構造物を構成することが可能である。
【図面の簡単な説明】
図１は折り紙や折り畳み構造物の折りたたまれる直線である折り線と複数の折り線の交点である節点との代表例を示す折り線説明図である。
図２は三浦によって宇宙用構造物の展開用に考案された、いわゆる“Ｍｉｕｒａ ｏｒｉ”とよばれる折り畳み構造の説明図である。
図３は前記図２に示す水平の折り線を等角でジグザグにした図である。
図４は頂角２Θの６個の扇型要素により形成される円板の一部（扇形部分）の折り畳み可能な折り線の例を示す図である。
図５は前記図２に示す水平の折り線群を任意の傾きに取った図で、折り線（１）〜（６）に対して折り線（７）〜（９）を全ての節点で等角・対称に作図した図である。
図６は前記図５の折り畳み法の周期性を考慮に入れた折り線の例を示す図である。
図７は１節点４折り線法および１節点６折り線法による平面折りを示す図で本発明者が考えた折り畳み方法の１例を示す図である。
図８は前記図７に示す節点のうちの６本の折り線が交わる１つの節点とその周囲の６本の折り線（１節点６折り線）の折り畳み条件を示す図である。
図９は帯板を折り線に沿って折りたたんだときに帯板の両端部が接合されて円筒となる条件を説明する図であり、図９Ａは帯板と折り線および折り線の角度を示す図、図９Ｂは図９Ａに示す折り線に沿って折りたたんだときの基準軸の向きを変化を示す図である。
図１０は前記式（５）を満たし且つ折り畳み方向が同一方向（山折りまたは谷折りのいずれか一方）の折り線により正４角形に折り畳む例の説明図で、図１０Ａは展開された状態の帯板の折り線（１），（２），（３），（４）を示す図、図１０Ｂは折り畳み途中の状態を示す図、図１０Ｃは折り畳んだ状態を示す図である。
図１１は前記式（５）を満たし且つ折り畳み方向が同一方向（山折りまたは谷折りのいずれか一方）の折り線により正６角形に折り畳む例の説明図で、図１１Ａは展開された状態の帯板の折り線（１），（２），（３），（４），（５），（６）を示す図、図１１Ｂは折り畳み途中の状態を示す図、図１１Ｃは折り畳んだ状態を示す図である。
図１２は前記式（５）を満たし且つ折り畳み方向が同一方向の折り線により正８角形に折り畳む例の説明図で、図１２Ａは展開された状態の帯板の折り線（１），（２），…，（８）を示す図、図１２Ｂは折り畳み途中の状態を示す図、図１２Ｃは折り畳んだ状態を示す図である。
図１３は前記式（５）を満たし且つ折り畳み方向が交互に反転する（山折り方向と谷折り方向とに反転する）折り線により正６角形に折り畳む例の説明図で、図１３Ａは展開された状態の帯板の折り線（１）〜（１２）を示す図、図１３Ｂ〜図１３Ｆは折り畳み途中の状態を示す図、図１３Ｇは折り畳んだ状態を示す図である。
図１４は前記図９Ａに示す帯状の板をπ・（Ｎ−２）／Ｎだけ等間隔に同方向に折り曲げて正Ｎ角形を構成する場合で且つＮ＝６の場合の代表的な展開図を示す図である。
図１５は前記図１４の山折り線と水平の折線の角度の２倍（π／３）をα＝２π／９とβ＝π／９のように分解して不等辺の台形要素で構成される疑似円筒の展開図である。
図１６は前記図１４のＹ軸方向の山折り線をα＝π／３の山折り線Ｉとβ＝π／６の谷折り線ＩＩに分解した折り線の組を６個導入することによって製作される円筒の説明図で、図１６Ａは展開図、図１６Ｂは前記図１６Ａの展開図の両端を接合したときに製作される折り畳み円筒の半折り状態を示す図、図１６Ｃは前記図１６Ｂと同じものの異なる方向から見た斜視図である。
図１７は前記図１４の点ＡとＢを合致させ、水平の折り線から山折り部分をなくした図で、水平方向に底角π／６の２等辺三角形からなるダイヤモンド模様（（１）〜（３））の展開図である。
図１８は不等辺三角形要素で構成される変形ダイヤモンド模様による展開図である。
図１９は水平の折り線に対して１つ飛びに対称で且つ折り畳みが可能な展開図を有する疑似円筒体の説明図で、図１９Ａは展開図、図１９Ｂは前記図１９の展開図の両端を接合したときに製作される折り畳み円筒の半折り状態を示す図、図１９Ｃは前記図１９Ｂと同じものを異なる方向から見た図である。
図２０は前記図１９の点Ｂと同様の折り線だけで構成した折り畳みの展開図の例を示す図である。
図２１は折り畳み線により形成された複数の形状の多角形のパーツ（平板壁）を有する折り畳み可能な円筒壁の展開図である。
図２２はＧｕｅｓｔ等が検討した３角形状の分割平板で作られた分割平板の連結部が螺旋状になり、それ等が一周する毎に螺旋（１）が１段上昇する時の円筒構造物を本発明者が展開図で表したものである。
図２３は図１７の全体をψ＝π／６だけ傾斜させたものに対応し、斜め方向の３個のダイヤモンド模様が構成されている。
図２４は前記図２３と等価の展開図を有する疑似円筒体の説明図で、図２４Ａは展開図、図２４Ｂは前記図２３、図２４Ａの展開図の両端を接合したときに製作される折り畳み円筒の半折り状態を示す図である。
図２５は前記図１４をπ／６傾斜させた展開図を有する疑似円筒体ｋ説明図で、図２５Ａは展開図、図２５Ｂは前記図２５Ａの展開図の両端を接合したときに製作される折り畳み円筒の半折り状態を示す図である。
図２６は前記図１５をπ／６傾斜させた展開図を有する疑似円筒体の説明図で、図２６Ａは展開図、図２６Ｂは前記図２６Ａの展開図の両端を接合したときに製作される折り畳み円筒の半折り状態を示す図である。
図２７は前記図１６をπ／６傾斜させた展開図である。
図２８は図１９の螺旋型であり、図中の点Ａ，Ｄを結ぶ直線で切断して得たものである。図２８中に記載の角（〜０．１９３π）はこの切断線と水平線のなす角を示し、この場合には三角形要素の形状が与えられているため谷折り線の角度は限定されたものになる。
図２９は前記図２４を一般化した折り線を有する螺旋型の折り畳み円筒体の説明図で、図２９Ａは展開図、図２９Ｂは前記図２９Ａの展開図の両端を接合したときに製作される折り畳み円筒の半折り状態を示す図である。
図３０は前記図２９の６段の展開図を３段して１段毎にβの値を変えた場合の展開図である。
図３１は図２９の螺旋状の山折り線および谷折り線を１段毎に逆転させて得られる反復螺旋型の展開図である。この展開図はまた図１６の点ＡとＢを一致させることによっても得られる。
図３２は、前記図２１に示す円筒体の展開図の平行な２本の直線ＡＢ′、Ｃ′Ｄにより切り取られた部分を示す図であり、ＡとＢ′およびＤとＣ′が重なるように図３２の左右の両端縁を接続することにより折り畳み可能な円筒体となるものの展開図である。
図３３は任意形状の４角形要素（パーツ）を有するり畳み可能な円筒体の展開図である。
図３４は展開図の両端を接合したときの連続性を保つ方法の説明図である。
図３５は１節点６折り線の場合で谷折り線が対称に挿入される場合の折り畳み条件を満たす折り線間の角度関係を示す図で、後述の図５１Ｂ、図５２の場合の折り畳み条件の説明図である。
図３６は山折り線（２）、（３）、（５）間に谷折り線（４）、（６）が交互に挿入される場合の折り畳み条件を満たす折り線間の角度関係を示す図で、後述の図５６Ｂ、図５７の場合の折り畳み条件の説明図である。
図３７は１節点４折り線の場合を示す。折りたたみ条件式を上と同様の手順で求められる。
図３８は主折り線が展開図の外辺に平行な円錐における展開図が頂角２ΘのＮ個の二等辺三角形で構成される場合の展開図の要部拡大図である。
図３９は式（１４）で得られる値を用いて求めた折り線付疑似円錐壁の展開図を有する疑似円錐壁の説明図で、図３９Ａは展開図、図３９Ｂは前記図３９Ａの展開図を有する折り線付円錐壁の半折り状態の斜視図である。
図４０は折り線により不等辺三角形要素に分割される場合の折り線付円錐壁の展開図の要部拡大図である。
図４１は折り線により不等辺三角形要素に分割される場合の折り線付円錐壁の展開図で、Ｎ＝３、２Θ＝π／９、α＝π／９、δ＝π／６とした時の展開図（θ^＊＝約０．０６８８π）である。
図４２は前記図４０の点Ｆで右上方に角度α、左上方に角度δを取った折り線により不等辺三角形要素に分割される場合の折り線付円錐壁の展開図で、Θ，α，δ値を図４１と同じ値とした場合の展開図である。
図４３は前記図３８の二等辺三角形要素による分割の代わりに、台形要素により分割した場合の折り線付円錐壁の展開図の要部拡大図である。
図４４は折り線により等脚台形に分割され且つ正Ｎ角錐に折り畳まれる折り線付円錐壁の、Ｎ＝６、前記図４３のφ^＊＝π／３６、２Θ＝π／１２の場合の展開図を有する疑似円錐壁の説明図で、図４４Ａは展開図、図４４Ｂは前記図４４Ａの展開図を有する折り線付円錐壁を半折りにした状態の斜視図である。
図４５は二等辺三角形要素（頂角２Θ）がＮ個からなる折り線付円錐壁の展開図を考え、その一段だけを湾曲した帯状部分として書き出した図である。
図４６は３個の二等辺三角形要素からなる簡単な、螺旋型の展開図を有する折り線付円錐壁の展開図である。
図４７は前記図４６の展開図を折りたたんだ時の上面図である。
図４８は前記図４５および図４６で説明したモデルを変形した実用的モデルの説明図で、図４８Ａは変形方法の説明図、図４８Ｂは図４８Ａの要部拡大図である。
図４９は前記図４８Ａの折り線により形成される図形ＡＢＧＨＦＥを折り線ＡＦ，ＢＦで順次折り畳んだときの様子を示す図で、図４９ＡはＡＦを谷折りしたた後の矩形ＡＢＦＥとＢＧＨＦの状態を示す（薄墨部；裏面）図、図４９Ｂは前記図４９Ａの状態で更にＢ’Ｆ（元の線分ＢＦ）で山折りを行った後の状態を示す図である。
図５０は図４８Ａに示す１段目の帯板に相当する部分および２段目に相当する部分を示す図である。
図５１は前記図４８〜図５０に示す折り線を有する折り線付円錐壁においてＮ＝６、γ＋ψ^＊＝π／３、ψ^＊＝π／６、γ＝π／６とした場合の展開図（２Θ＝π／１８）を有する疑似円錐壁の説明図で、図５１Ａは展開図、図５１Ｂは前記図５１の展開図を有する折り線付円錐壁を半折りにした状態の斜視図である。
図５２は前記図４８〜図５０に示す折り線を有する折り線付円錐壁においてＮ＝６、γ＋ψ^＊＝π／３、ψ^＊＝π／４，γ＝π／１２とした場合の展開図（２Θ＝π／６）である。
図５３は前記図５１の展開図の段数を少なくして１段毎にψ^＊の値を大きくした場合の展開図である。
図５４は前記図５３の展開図を有する折り畳み円錐壁と同じ円錐壁を形成する展開図である。
図５５は前記図５０で２段目の谷折り線を１段目のそれと角度γで逆方向に取った場合の図である。
図５６は前記図５１を反復螺旋型にした展開図を有する疑似円錐体の説明図で、図５６Ａは展開図、図５６Ｂは前記図５６の展開図を有する折り線付円錐壁を半折りにした状態の斜視図である。
図５７は２Θ＝π／６，ψ^＊＝π／６，γ＝π／６として得た反復螺旋型の展開図（Ｎ＝６）である。
図５８は等角螺旋に沿った折り線を有する折り畳み可能な折り線付円錐壁の展開図の説明図で、図５８Ａは全体説明図、図５８Ｂは前記図５８Ａの要部拡大図である。
図５９は前記図５８の螺旋を反転させる場合の折り線付円錐壁の展開図の説明図である。
図６０は前記図４４の展開図の描き方の説明図である。
図６１は前記図４４を等角螺旋型にした展開図を有する疑似円錐体の説明図で、図６１Ａは展開図、図６１Ｂは前記図６１Ａの展開図を有する折り線付円錐壁を半折りにした状態の斜視図である。
図６２は図５１Ａの円周方向の螺旋を右端で１段上昇するようにした折り線付きの折り畳み円錐壁の展開図である。
図６３は折り紙における最も簡単な折りたたみ法の説明図である。
図６４は折り線付円板状折り畳み構造物の展開図の説明図で、図６４Ａは折り畳み条件を説明するための要部拡大図、図６４Ｂは全体図である。
図６５は前記図６４Ｂに示す折り線付円板状折り畳み構造物の展開図の拡大図である。
図６６は前記図６５の展開図を有する折り線付円板状折り畳み構造物の半折り状態で且つ折り畳み量が少ない状態の斜視図である。
図６７は前記図６５の展開図を有する折り線付円板状折り畳み構造物の半折り状態で且つ折り畳み量が多い状態の斜視図である。
図６８は前記図６５の展開図を有する折り線付円板状折り畳み構造物を完全に折り畳んだ状態の斜視図である。
図６９は半径方向のＺｉｇ／Ｚａｇの折り線の振り角を中心に近づく程大きくした場合の折り線付円板状折り畳み構造物の展開図の説明図で、図６９Ａは折り畳み条件を説明するための要部拡大図、図６９Ｂは全体図である。
図７０は半径方向のＺｉｇ／Ｚａｇの折り線の振り角を中心に近づく程大きくし且つ円周方向の折り線もＺｉｇ／Ｚａｇにした場合の折り線付円板状折り畳み構造物の展開図の説明図で、図７０Ａは折り畳み条件を説明するための要部拡大図、図７０Ｂは全体図である。
図７１は螺旋状の折り線の交点がアルキメデスの螺旋上にある従来公知の巻取り法の説明図である。
図７２は本発明者の考えた新しい折り線を示す図で、図７２Ａは前記図７１において、半径方向の折り線（１）が１つの屈曲点を持ち、この屈曲点で螺旋が反転する折り線を示す図、図７２Ｂは、前記図７２Ａの屈曲点の外側を半径方向に折りたたむ方法で置き換えた図である。
図７３は円形膜、または部分円形膜（扇形膜）等を半径方向および円周方向に折り畳む折り線を等角螺旋に沿って形成する際の折り線の説明図である。
図７４は円形膜、または部分円形膜（扇形膜）等を半径方向および円周方向に折り畳む折り線を等角螺旋に沿って形成する際の折り線の説明図である。
図７５は前記図７４の要部拡大図である。
図７６は円形膜、または部分円形膜（扇形膜）等を半径方向および円周方向に折り畳む折り線を等角螺旋に沿って形成する際の折り畳み条件の説明図である。
図７７は主折り線が放射線に対して等角で折り曲げられる場合の折り畳み条件の説明図である。
図７８は２本のジグザグ状の螺旋（ｍ＝２）を折り線として、中心回りに折りたたむ例を示したもので、ｎ＝４、２等辺３角形要素数Ｎ＝（２ｎ＋１）ｍ＝１８、γ＝２０°の場合の折り畳み展開図の例を示す図である。
図７９は２本のジグザグ状の螺旋（ｍ＝２）を折り線として、中心回りに折りたたむ例を示したもので、ｎ＝４、２等辺３角形要素数Ｎ＝（２ｎ＋１）ｍ＝１８、γ＝０°の場合の折り畳み展開図の例で前記図７８とは放射線に対する折り線の角度が異なる例を示す図である。
図８０は２本のジグザグ状の螺旋（ｍ＝２）を折り線として、中心回りに折りたたむ例を示したもので、ｎ＝１０、２等辺３角形要素数Ｎ＝（２ｎ＋１）ｍ＝４２、γ＝０°の場合の折り畳み展開図の例を示す図である。
図８１は２本のジグザグ状の螺旋（ｍ＝２）を折り線として、中心回りに折りたたむ例を示したもので、ｎ＝４、２等辺３角形要素数Ｎ＝（２ｎ＋１）ｍ＝１８、γ＝０°の場合の折り線付円板状折り畳み構造物の展開図の例を示す図である。
図８２は前記図８１の展開図を有する折り線付円板状折り畳み構造物の半折り状態で且つ折り畳み量が少ない状態の斜視図である。
図８３は前記図８１の展開図を有する折り線付円板状折り畳み構造物の半折り状態で且つ折り畳み量が多い状態の斜視図である。
図８４は前記図８１の展開図を有する折り線付円板状折り畳み構造物を完全に折り畳んだ状態の斜視図である。
図８５は４本のジグザグ状の螺旋（ｍ＝４）を折り線として、中心回りに折りたたむ例を示したもので、ｎ＝７、２等辺３角形要素数Ｎ＝（２ｎ＋１）ｍ＝６０、γ＝０°の場合の折り畳み展開図の例を示す図である。
図８６は３本のジグザグ状の螺旋（ｍ＝３）を折り線として、中心回りに折りたたむ例を示したもので、ｎ＝８、２等辺３角形要素数Ｎ＝（２ｎ＋１）ｍ＝５１、γ＝０°の場合の折り畳み展開図の例を示す図である。
図８７は１本のジグザグ状の螺旋（ｍ＝１）を折り線として、中心回りに折りたたむ例を示したもので、ｎ＝１０、２等辺３角形要素数Ｎ＝（２ｎ＋１）ｍ＝２１、γ＝０°の場合の折り畳み展開図の例を示す図である。
図８８は４本のジグザグ状の螺旋（ｍ＝４）を折り線として、中心回りに折りたたむ例を示したもので、ｎ＝７、２等辺３角形要素数Ｎ＝（２ｎ＋１）ｍ＝６０、γ＝０°の場合の折り線付円板状折り畳み構造物の展開図の例を示す図である。
図８９は前記図８８の展開図を有する折り線付円板状折り畳み構造物の半折り状態で且つ折り畳み量が少ない状態の斜視図である。
図９０は前記図８８の展開図を有する折り線付円板状折り畳み構造物の半折り状態で且つ折り畳み量が多い状態の斜視図である。
図９１は前記図８８の展開図を有する折り線付円板状折り畳み構造物を完全に折り畳んだ状態の斜視図である。
図９２は、主折り線とする螺旋を多数（ｍ＝１２）にした場合の展開図である。
図９３は前記図７７に基づいて、２種の等角の螺旋で構成された展開図である。分割数Ｎ＝１２，θ_１＝π／１８０，θ_２＝２９π／１８０であり、φは、およそπ／１８である。図９３の展開図を折り畳むと、上下対称に中心回りに良好に巻取られる。図９３のものは、副折り線が微細であるため巻取時にこれ等の折り線が弾性変形で置き換えられることを示唆する。
図９４は山折り線と谷折り線とを交互に設けた円形薄板の展開図である。
図９５は山折り線と谷折り線とを交互に設け且つ谷折り線とその左右両側の山折り線との円周方向の長さが左右で異なる折り線付円板状折り畳み構造物の展開図である。
図９６は前記図９５の隣接する山折り線の間の扇形部分を除去した図である。
図９７はシート状部材の折り畳み条件の説明図で、図９７Ａは折り畳む前の展開図、図９７Ｂは図９７Ａの折り線で折り畳んだ状態を示す図である。
図９８はＤＣＣ（ｄｕｏｕｂｌｅ ｃｏｒｒｕｇａｔｅｄ ｃｏｒｅ）の説明図で、図９８ＡはＤＣＣの展開図、図９８Ｂはその半たたみ状態の外観図である。
図９９は前記図９８の垂直の折り線群をｚｉｇ／ｚａｇにしたものの説明図で、図９９Ａはその展開図、図９９Ｂはその半たたみ状態の外観図である。
図１００は新たに考案した接合部のあるコアのモデルの説明図で、図１００Ａは展開図、図１００Ｂは図１００Ａの展開図を半折り状態にしたものの平面図、図１００Ｃは図１００Ａの展開図を折り畳んで３次元化したものの外観図である。
図１０１は新たに考案した接合部のあるコアの別のモデルの説明図で、図１０１Ａは展開図、図１０１Ｂは図１０１Ａの展開図を半折り状態にしたものの平面図、図１０１Ｃは図１０１Ａの展開図を折り畳んで３次元化したものの外観図である。
図１０２は本発明者が考案した接合部のあるコアの別の折りたたみ条件を満たさないモデルの説明図で、図１０２Ａは展開図、図１０２Ｂは図１０２Ａの要部拡大図である。
図１０３は前記図１０２Ａの展開図を折り畳んで作成するコアの説明図で、図１０３Ａは折り畳んだコアの斜視図、図１０３Ｂは前記図１０３Ａのコアの下面にシートを接着したものの斜視図である。
図１０４は本発明者が考案した接合部のあるコアの別の折りたたみ条件を満たさないモデルの説明図で、図１０４Ａは展開図、図１０４Ｂは図１０４Ａの要部拡大図である。
図１０５は１枚の板からハニカムコアを製造する方法の説明図で、図１０５Ａは展開図、図１０５Ｂは前記図１０５Ａの展開図を有する板から製造したハニカムコアの図である。
図１０６は前記図１０３Ａに示すコア材料を製造する折畳み金型を示す図である。
図１０７は製作したアルミニュウムコアの説明図で、図１０７Ａは斜視図、図１０７Ｂは展開図で前記図１０３Ａに示す紙の展開図と同じ形状ある。
図１０８は円筒状折り線付構造物の応用例の説明図で、図１０８Ａは展開図である。
図１０９は螺旋型の円筒状折り線付構造物の応用例の説明図で、図１０９Ａは展開図、図１０９Ｂは前記図１０９Ａを基に構成された伸縮可能なｉｎｆｌａｔａｂｌｅ構造を示す図である。
図１１０は本発明の実施例１の折り線形成用型の平面図である。
図１１１は前記図１１０の折り線形成用型を使用して折り線を形成したシート状部材の斜視図である。
図１１２は本発明の実施例２の折り線形成用型の説明図であり、折り線を形成するシート状部材の両面を挟むための一対のフレキシブル金型のうちの一方のフレキシブル金型の斜視図である。
図１１３は本発明の実施例３の折り線形成用型の平面図である。
図１１４は前記図１１３の折り線形成用型の使用状態の説明図で、図１１４Ａは折り線形成用型を２つ折りにした状態を示す図、図１１４Ｂは前記図１１４Ａに示す２つ折りにした折り線形成用型を折り畳んだ状態を示す図である。
図１１５は前記図１１３、図１１４に示す折り線形成用型を使用して折り線を形成したシート状部材の説明図で、図１１５Ａは半折り状態のシート状部材の平面図、図１１５Ｂは完全に折り畳んだ状態の平面図である。
図１１６は前記図１１５Ｂに示す折り畳んだシート状部材の説明図で、図１１６Ａは斜視図、図１１６Ｂは前記図１１６Ａに示す折り畳んだシート状部材の１面（下面）に平面状のシート状部材を接着したものの斜視図である。
図１１７は本発明の実施例４の折り線付構造物としてのペットボトルの側面図である。
図１１８は同実施例４のペットボトルの側断面図である。
図１１９は前記図１１７のペットボトルを軸方向に圧縮した状態（半折り畳み状態）の説明図で、図１１９Ａは半折り畳み状態を示す図、図１１９Ｂはほぼ完全に折り畳んだ状態で開口部に蓋をした状態の側面図である。
図１２０は前記ペットボトルＡの製造方法の説明図で、金型（折り線形成面を有する金型）が開いた状態を示す図である。
図１２１は前記ペットボトルＡの製造方法の説明図で、金型が閉じ且つ管状または袋状の素管（パリソン）を金型内で延伸させた状態を示す図である。
図１２２は前記図１２１の素管内部に圧搾空気を吹き込んで膨張させる状態を示す図である。
図１２３は本発明の折り線付構造物の実施例５としてのペットボトルの説明図で、螺旋に沿って形成された折り線付構造物（ペットボトル）を示す図である。
図１２４は本発明の折り線付構造物の実施例６としてのペットボトルの説明図で、螺旋に沿って形成された円筒壁を有する折り線付構造物（ペットボトル）を示す図である。
図１２５は本発明の実施例７の折り線付構造物としてのコーヒー缶の側面図である。
図１２６は同実施例７のコーヒー缶の側断面図である。
図１２７は前記図１２６のコーヒー缶を軸方向に圧縮した状態（半折り畳み状態）の説明図で、図１２７Ａは半折り畳み状態の側面図、図１２７Ｂはほぼ完全に折り畳んだ状態の側面図である。
図１２８は前記コーヒー缶Ａの製造方法の説明図で、円筒部材の内面に配置する内側金型（折り線形成面を有する金型）の説明図で、図１２８Ａは対向して配置された一対の内側第１金型が円筒部材内部に挿入された平断面図、図１２８Ｂは前記図１２８Ａの一対の内側第１金型の間に一対の内側第２金型が挿入された平断面図、図１２８Ｃは前記図１２８Ｂの内側第１および第２金型の中央部にカムロッドを挿入した状態の平断面図、図１２８Ｄは前記図１２８Ｃのカムロッドを回転させて内側第２金型を外方に押し出すことにより内側第１および第２金型を外方に押し出した状態を示す図である。
図１２９は前記コーヒー缶Ａの製造方法の説明図で、図１２９Ａは円筒部材の内面に内側金型（折り線形成面を有する金型）をセットした状態で外側金型Ｋ２を型締めしする前の状態を示す図、図１２９Ｂは前記図１２９Ａの状態から型締めした状態を示す図である。
図１３０は本発明の折り線付構造物の実施例８としてのコーヒー缶の説明図で、螺旋に沿って形成された円筒壁を有する折り線付構造物（コーヒー缶）を示す図である。
図１３１は、前記コーヒー缶Ａの製造方法の他の実施例の説明図である。
図１３２は本発明の実施例９の折り線付構造物としての小型容器の説明図で、図１３２Ａは小型容器の蓋の斜視図、図１３２Ｂは小型容器の伸長した状態の斜視図である。
図１３３は同実施例９の小型容器の説明図で、図１３３Ａは小型容器を折り畳んだ状態の斜視図、図１３３Ｂは前記図１３３Ａの１０９Ｂ−１０９Ｂ線断面図、図１３３Ｃは前記図１３３Ｂの小型容器に蓋をした状態の断面図である。
図１３４は前記小型容器Ｂの製造方法の説明図で、金型（折り線形成面を有する金型）が閉じた状態を示す図である。
図１３５は本発明の実施例１０の折り線付構造物としての紙パックの説明図で、紙パックが伸長した使用状態の斜視図である。
図１３６は前記図１３５の紙パックを折り畳む途中の状態を示す図である。
図１３７は前記図１３６の紙パックをさらに折り畳んだ状態を示す図である。
図１３８は前記図１３５〜図１３７に示す紙パックの展開図である。
図１３９は本発明の実施例１１の折り線付構造物としての紙パックの説明図で、紙パックが伸長した使用状態の斜視図である。
図１４０は前記図１３９の紙パックを折り畳む途中の状態を示す図である。
図１４１は前記図１４０の紙パックをさらに折り畳んだ状態を示す図である。
図１４２は前記図１３９〜図１４１に示す紙パックの展開図である。
図１４３は本発明の実施例１２の折り線付構造物としての紙パックの説明図で、紙パックが伸長した使用状態の斜視図である。
図１４４は前記図１４３の紙パックを折り畳む途中の状態を示す図である。
図１４５は前記図１４４の紙パックをさらに折り畳んだ状態を示す図である。
図１４６は前記図１４３〜図１４５に示す紙パックの展開図である。
図１４７は本発明の実施例１３の折り線付構造物としての紙パックの説明図で、紙パックが伸長した使用状態の斜視図である。
図１４８前記図１４７の紙パックを折り畳む途中の状態を示す図である。
図１４９は前記図１４８の紙パックをさらに折り畳んだ状態を示す図である。
図１５０は前記図１４７〜図１４９に示す紙パックの展開図である。
図１５１は本発明の実施例１４の折り線付構造物としてのポンプの説明図である。
図１５２は本発明の実施例１５の折り線付構造物としてのごみ箱の説明図で、図１５２Ａは側面図、図１５２Ｂは側断面図である。
図１５３は本発明の実施例１６の折り線付構造物としての鉛筆立ての説明図で、図１５３Ａは側面図、図１５３Ｂは側断面図である。
図１５４は本発明の実施例１７の折り線付構造物としてのゲス（箱内部仕切り部材）の説明図で、ゲスが紙箱内に収容されている状態を示す斜視図である。
図１５５は前記図１５４のゲスの斜視図である。
図１５６は前記図１５５のゲスの展開図である。
図１５７は本発明の実施例１８の折り線付構造物としてのゲス（箱内部仕切り部材）の説明図で、紙箱内から取り出されたゲスの斜視図である。
図１５８は前記図１５７のゲスの展開図である。
図１５９は本発明の実施例１９の折り線付構造物としてのゲス（箱内部仕切り部材）の説明図で、ゲスが紙箱内に収容されている状態を示す斜視図である。
図１６０は前記図１５９のゲスの斜視図である。
図１６１は前記図１５９のゲスの展開図である。
図１６２は本発明の実施例２０の折り線付構造物としてのゲス（箱内部仕切り部材）の説明図で、ゲスが紙箱内に収容されている状態を示す斜視図である。
図１６３は前記図１６２のゲスの斜視図である。
図１６４は前記図１６３のゲスの展開図である。
図１６５は本発明の実施例２１の折り線付構造物としてのゲス（箱内部仕切り部材）の説明図で、ゲスが紙箱内に収容されている状態を示す斜視図である。
図１６６は前記図１６５のゲスの斜視図である。
図１６７は前記図１６６のゲスの展開図である。
図１６８は折り畳み式通路カバーの説明図で、図１６８Ａは半折り状態の斜視図、図１６８Ｂは完全に折り畳んだ状態の斜視図である。
図１６９は本発明の実施例２２の折り線付構造物としての折り畳み式通路カバーの展開図である。
図１７０は前記図１７１の展開図を有する折り畳み式通路カバーの説明図で、図１７０Ａは半折り状態の斜視図、図１７０Ｂは完全に折り畳んだ状態の斜視図である。
図１７１は本発明の実施例２３の折り線付構造物としての折り畳み式通路カバーの展開図である。
図１７２は本発明の実施例２４の折り線付構造物としてのランプシェードの説明図で、図１７２はランプシェードを製作する素材であるシート状部材の展開図、図１７２Ｂは前記図１７２Ａのシート状部材の左右の両側辺を接合して疑似円錐を製作して構成したランプシェードを半折り状態にしたものの斜視図である。
図１７３は本発明の実施例２５の折り線付構造物としてのクリスマスカードの説明図で、図１７３Ａはクリスマスカードを折り畳んだ状態の平面図、図１７３Ｂは前記図１７３Ａを開いた状態の平面図、図１７３Ｃは前記図１７３Ｂの矢印１７３Ｃの斜め上方から見た図である。
図１７４は本発明の実施例２６の折り線付構造物としての帽子の説明図で、図１７４Ａは帽子の斜視図、図１７４Ｂは前記図１７４Ａの１１１Ｂ−１１１Ｂ線断面図、図１７４Ｃは前記図１７４Ｂの矢印１１１Ｃから見た図である。
図１７５は同実施例２６の帽子の説明図で、図１７５Ａは帽子を折り畳んだ状態の平面図、図１７５Ｂは前記図１７５Ａの矢印１１２Ｂから見た図である。
図１７６は本発明の実施例２７の折り線付構造物としての帽子の説明図で、図１７６Ａは帽子の斜視図、図１７６Ｂは前記図１７６Ａの１１３Ｂ−１１３Ｂ線断面図、図１７６Ｃは前記図１７６Ｂの矢印１１３Ｃから見た図である。
図１７７は同実施例２７の帽子の説明図で、図１７７Ａは帽子を折り畳んだ状態の平面図、図１７７Ｂは前記図１７７Ａの矢印１１４Ｂから見た図である。
図１７８は本発明の実施例２８の折り線付構造物としての巻取式の帽子の斜視図である。
図１７９は前記図１７８の巻取式の帽子の折り畳み途中の状態の斜視図である。
図１８０は前記図１７９の状態から更に折り畳んだ状態の巻取式の帽子の斜視図である。
図１８１は前記図１７８〜図１８０に示す巻取式の帽子の製造方法の説明図で、図１８１Ａは図１７８鍔部Ａの展開図、図１８１Ｂは側頭部Ｂの展開図、図１８１Ｃは頭頂部Ｃの展開図である。
図１８２は前記図１７８〜図１８１に示す巻取式の帽子の他の製造方法の説明図である。
図１８３は本発明の実施例２９の折り線付構造物としての巻取式のテントの斜視図である。
図１８４は前記図１８３の巻取式のテントの折り畳み途中の状態の斜視図である。
図１８５は前記図１８３の状態から更に折り畳んだ状態のテントの斜視図である。
図１８６は前記図１８３〜図１８５に示す巻取式のテントの製造方法の説明図で、図１８６Ａは伸長状態で放物曲面状のドーム型となる巻取式テントを、円周方向に分割したときに形成されるパーツの１つを展開した図、図１８６Ｂは前記図１８６Ａのパーツの端部ＡＢとＣＤとを接続したときに形成されるた円錐壁を示す図である。
図１８７は前記図１８３〜図１８５に示す巻取式のテントの製造方法の説明図で、図１８７は伸長状態で半径ｒ１のドーム型となる巻取式テントを、ドーム型の中心位置の座標をｒ＝０、ｊ＝１，２，…，１０として、半径方向に１０等分した位置の座標ｒｊ（ｒｊ＝ｒ１×（１１−ｊ）／１０）を半径とする円により１０分割したときに形成されるパーツ（円錐壁）（ｊ）の形状を示す図である。
図１８８は前記図１８７のパーツ番号（ｊ）と、母線の形状および長さＬｊと、傾きθｊとを示す図である。
図１８９は前記図１８７、図１８８に示すパーツ（１），（２），…，（１０）の展開図を円周方向に１６分割したときの分割パーツ（Ｊ：Ｊ＝１，２，…，１０）の形状の説明図で、図１８９Ａは各パーツ（ｊ）がそれぞれ１６個の分割パーツ（Ｊ）により構成されることを示す図、図１８９Ｂは分割パーツ（Ｊ）を半径方向に接続したものを示す図である。
図１９０は本発明の実施例３０の折り線付構造物としての巻取式のテントの斜視図である。
図１９１は前記図１９０の巻取式のテントの折り畳み途中の状態の斜視図である。
図１９２は前記図１９０の状態から更に折り畳んだ状態のテントの斜視図である。Technical field
The present invention relates to a folded line structure, a folding line forming die, and a folding line forming method that can be folded so as to be deformed between a folded state in which the outer shape is reduced and an expanded state in which the outer shape is increased, and in particular, A plate-shaped, cylindrical-shaped, or conical-walled structure is divided into polygonal parts (flat walls) such as triangles or quadrilaterals by a large number of folding lines, and the boundary between the divided parts (flat walls) is folded. The present invention relates to a folding structure with a folding line, in which a line can be folded.
The present invention is applicable to plate-shaped objects with fold lines, and cylindrical and conical objects with fold lines that can be folded in the axial direction, for example, plate members such as rigid floors and bottom walls, It can be used for various containers having a cylindrical wall such as a PET bottle, an object having a conical wall such as a lamp shade, a space structure, and a building structure.
Background art
Research related to the development of folding and unfolding structures has been technically developed in connection with the construction of antennas and solar cell structures to be deployed in outer space, or, conversely, the study of plastic buckling using the folding method. did. In addition, these studies have also been applied to studies aimed at elucidating the growth and motor functions of living things, such as the mechanism of folding of feathers and leaves of insects and the like.
A planar folding structure and a cylindrical folding structure having a foldable fold line are conventionally known (see (J01) and (J02) below), but a conical foldable structure having a foldable fold line is not known. Not previously known.
Conventional foldable structures with folding lines are mainly designed for deployment of space structures, and the following technologies (J01) and (J02) are known.
(J01) Planar folding structure
As the planar folded structure, Miura ori using folding lines of origami (an idea of a developed space structure [Kiyo Miura, Journal of the Japan Society of Mechanical Engineers, Vol. 90, No. 828, published in November 1987, P1394] To 1400]) are conventionally known. Miura ori divides a planar structure into a number of parallelograms formed by fold lines, and has a flat plate shape whose outer shape is enlarged in a developed state where the fold line is extended, and has a reduced outer shape and thickness in a folded state. In the form of a flat plate with increased irregularities.
(J02) Cylindrical folding structure
As a conventional cylindrical folding structure, a folding cylinder having a triangular folding line is described in the following document.
(A) The Folding of Triangulated Cylinders, Part I: Geometric Considations (SD Guest, S. Pellegrio, Journal of Applied Mechanics, DECE VER 77/94;
(B) The Folding of Triangulated Cylinders, Part II: The Folding Process (SD Guest, S. Pellegrio, Journal of Applied Mechanics, DECEMBER 1994/78, 1994).
(C) The Folding of Triangulated Cylinders, Part III: Experiments (SD Guest, S. Pellegri, Journal of Applied Technologies, MARCH 1996, Vol. 63/77).
S. D. Guest, S.M. In the above-mentioned documents (a) to (c) by Pellegrio et al., A cylindrical wall is divided into a large number of triangular flat plate walls by a large number of folding lines including a folding line formed along a spiral, and each triangular flat plate is divided. It is described that a foldable cylindrical wall can be formed by foldably connecting a boundary portion of the wall. Further, in the above document, the length of a side of a triangle at which a folding structure can be folded is shown by numerical calculation. Judging from the length of the sides of the triangle indicated by the numerical calculation, the shape of the foldable triangle is like a triangle approximated to an isosceles triangle with a base angle of about 30 °.
The cylindrical folding structures described in the above-mentioned documents (a) to (c) are cylindrical in the expanded state where the folding line is extended, and are cylindrical bodies contracted in the axial direction in the folded state.
(Problems of conventional technology)
In the above-mentioned conventional planar folding structure and cylindrical folding structure, the condition of the fold line that can be folded is not known, and the fold line used is used within a range that is empirically known. . That is, the flat wall formed by the fold lines used is limited to a parallelogram in a planar folding structure, and is limited to a triangle in a cylindrical folding structure.
Further, the conventional foldable cylindrical folding structure is premised on having a fold line along a spiral, and the shape of the flat wall formed by the fold line has a base angle of about 30 °. Is only a triangle similar to the isosceles triangle.
In such a narrow range that is empirically known, even if a study on the use of a folding structure such as the planar folding structure and the cylindrical folding structure is performed, a new folding line of the folding structure can be obtained. It may not be easy to find and find folded structures using new folding lines.
The inventor of the present invention can easily find a new method of folding a folded structure, and can easily invent and use a new folded structure when the conditions of the foldable folding line of the folded structure formed with the folding line become clear. I thought it would be.
Therefore, the present inventor conducted a study (study on a folding method) for finding a condition of a foldable line of a folding structure (a structure with a folding line) to which a folding line was previously attached.
Research on folding structures that can be folded along conventional folding lines is often performed using an origami model using origami, but the folding lines that can be folded are complicated. Therefore, it takes time to form a foldable fold line. In particular, it takes time to form a fold line on a sheet having greater rigidity than origami.
Therefore, the present inventor has studied on a method of easily forming a folding line on a sheet-like member such as paper, metal foil, and plastic sheet.
What has been learned from the study of the folding method and the folding line forming method described above will be described below.
(Research results of folding method and folding line forming method)
The present inventor has found the following as a result of research on a method of folding a folded structure and a method of forming a fold line of a sheet-shaped member.
(A) The plane wall and the quasi-cylindrical wall and the conical wall formed by a large number of divided plane walls can be formed by a large number of divided plane walls of a predetermined shape divided by a large number of linear folding lines. it can. In that case, the flat wall, the cylindrical wall, and the conical wall can be folded when the folding line satisfies a predetermined folding condition.
(B) The inventor has clarified all the folding conditions of the flat wall, the cylindrical wall, and the conical wall. According to the folding condition, the shape of a large number of divided flat walls obtained by dividing a flat wall or a cylindrical wall by a fold line is a conventionally studied shape (a parallelogram or a cylindrical wall in the case of a flat wall). Various shapes other than isosceles triangles and isosceles trapezoids are possible.
(C) A folding line is easily formed on the sheet-like member by half-folding or completely folding the plate with the folding line in a state where the sheet-like member is sandwiched by two plates with the same folding line that can be folded. It is possible to form.
Next, the details of the research results will be described.
Here, we focus on clarifying the possibility of folding from a geometrical point of view. First, we discuss a general method of folding using an origami model, and then describe a foldable cylindrical structural model. After that, the folding performance of the cylinder manufactured using the polymer sheet will be described.
In addition, a model for fabricating a foldable conical structure, which has not been reported so far, was geometrically determined using the idea of origami, and these models were developed by combining equiangular spirals. Analytically clarify that the figure is represented.
(1) Planar folding structure with folding line
1. How to fold
FIG. 1 is a fold line explanatory diagram showing a representative example of a fold line, which is a straight line to be folded of an origami or a folded structure, and a node, which is an intersection of a plurality of fold lines.
In FIG. 1, fold lines formed by mountain folds are represented by solid lines (M1, M2, and M3), and valley fold lines are represented by broken lines (V1). The numbers of the mountain fold and valley fold lines joining the nodes are denoted by NM and NV, respectively. . It is well known that the following equation holds between NM and NV at a node.
| NM−NV | = 2 ………………………………… (1)
When the total number of folding lines is set to NT, NT = NM + NV. If Equation (1) is, for example, NM-NV = 2, NT = 2 (1 + NV), and it can be seen that the number of fold lines forming the node is "even". The total number of folding lines NT is NT ≧ 4, and NT = 4 is the minimum number of folding lines for forming a node.
As shown in FIG. 1, when the X axis is aligned with the mountain fold line (M3) and the mountain folds (M1) and (M2) are performed, a valley fold (V1) occurs. If the angles between the mountain folds (M1) and (M2) and the X axis are α and β, respectively, the angle γ between the fold lines (V1) and (M2) is
γ = α …………………………………………… (2)
Given by Expression (2) is a relational expression of the angle when completely folded along the folding lines (1) to (4) in the Y-axis direction.
By this operation, the band-shaped paper is folded in half, and the axial direction to the right of the node is folded by 2α (when α <β) or 2β (when α> β).
When α = β, the axial direction is not bent in the Y-axis direction. At this time, it is easily presumed that the band-shaped paper bends in a zigzag manner when the mountain fold and the valley fold are alternately performed, and that when the mountain fold (or the valley fold) is continuously performed, the paper becomes cylindrical.
In the present specification, the term “planar fold” refers to folding plane paper in a zigzag manner and folding it into a new plane in this manner, and the term “cylindrical” refers to a method of folding a sheet in the same direction to produce a cylindrical structure that can be folded in the Y-axis direction. Ori ".
2 flat fold
2.1 Miura ori (prior art)
In order to consider the possibility of the structure of the structure, consider the simplest case of "one-node four-fold line".
FIG. 2 is an explanatory view of a so-called “Miura ori” folding structure devised by Miura for deployment of a space structure.
In FIG. 2, the fold lines of the folded structure are three horizontal fold lines ((1) to (3)) and three zigzag fold lines (peak, valley, peak fold, respectively). To (6)). The fold lines (1) to (3) are alternately subjected to mountain folds and valley folds so as to satisfy the expression (1), and each of the fold lines (4) to (6) corresponds to the fold lines (1) to (3). It is "symmetric" for all. Therefore, at each node (black dot), the folding condition of Expression (2) is automatically satisfied at an arbitrary angle α in the drawing, and the node can be completely folded in the Y-axis direction in the drawing.
At this time, it also contracts in the X-axis direction depending on the angle α, and the contraction amount increases as the folding angle α increases. Also, as can be seen from FIG. 2, the horizontal fold line alternates from a mountain fold to a valley fold and from a valley fold to a mountain fold at the left and right of the node. The characteristic of the 4-fold line method enables the flat paper to be periodically folded from Y = + ∞ to −∞.
FIG. 3 is a view in which the horizontal fold line shown in FIG. 2 is zigzag at an equal angle.
In FIG. 2, at each node, the folding lines (4) to (6) are symmetrical with respect to the horizontal folding lines (1) to (3), but the horizontal folding is zigzag at an equal angle as shown in FIG. 3, the folding condition in the Y-axis direction in Expression (2) is satisfied, and the plane paper in FIG. 3 is completely folded in a new shape. It can be seen that when the fold is in a half-folded state, the flat paper can be made three-dimensional, that is, in a state having an “apparent” thickness, and a flat plate with high rigidity and light weight can be manufactured.
2.2 Generalization of plane folding
If the horizontal folding lines provided in zigzag in FIG. 3 are continued in the same direction, the fan-shaped or circular plate can be folded in the radial direction.
FIG. 4 is a view showing an example of a foldable line of a part (sector-shaped portion) of a disk formed by six sector-shaped elements having a vertex angle of 2 °.
In FIG. 4, the circumferential folding lines (1) to (5) are bent by 2 °. The radial fold lines (7), (8), (9)... Are provided in a zigzag manner within the angle 、, and the outer sides A, B, C.
At this time, since the angle β in FIG. 4 is α0 + か ら due to the periodicity of these fold lines, the angle α1 between the circumferential fold line (1) and the radial fold line is taken as α−Θ. The folding conditional expression, Expression (2), is satisfied. That is, if the angle between the radial fold line and the circumferential fold line is selected from time to time as shown in the figure, α-Θ, α-2Θ... An exploded view can be created in which the board can be folded radially.
In addition, similarly to the fan-shaped plate, it is possible to draw a development view in which the circular plate can be folded in the radial direction.
FIG. 5 is a diagram in which the horizontal fold lines shown in FIG. 2 are taken at an arbitrary inclination. The fold lines (7) to (9) are equal at all the nodes with respect to the fold lines (1) to (6). It is the figure drawn in angle and symmetry.
As shown in FIG. 5, when folding lines (7) to (9) are plotted at all nodes at equal angles and symmetrically with respect to folding lines (1) to (6), the folding condition is satisfied at each node, It can be folded in the Y-axis direction.
Here, α1 and β1 (initial values) can be freely selected.
FIG. 6 is a diagram showing an example of a folding line in which the periodicity of the folding method of FIG. 5 is taken into consideration.
In FIG. 6, horizontal fold lines (1) to (6) show fold lines having a small angle ± θ alternately with the horizontal direction. The zigzag of the vertical folding line groups (7), (8),.
FIG. 7 is a view showing plane folding by the one-node four-fold line method and the one-node six-fold line method, showing an example of the folding method considered by the present inventors.
In FIG. 7, even when a 6-fold line method and a 4-fold line method of symmetrical folding lines are combined with a horizontal folding line, flat paper can be folded in a zigzag manner as in the case of Miura ori shown in FIG. .
FIG. 8 is a view showing a folding condition of one node where six folding lines of the nodes shown in FIG. 7 intersect and six folding lines (one node and six folding lines) around the node.
As shown in FIG. 8, there is a combination in which two valley fold lines are inserted at symmetrical positions of four mountain fold lines at the time of one node and six fold lines. The angle relationship that satisfies the folding condition by the folding line method frequently used in this specification is shown below.
The mountain fold line is (M1), (M2), (M3), (M4), the valley fold line is (V1), (V2), and the extension of the fold line (V1) is the X axis. The angles formed by the folding lines (M1) and (V1), (M2) and (V1) are α and β, the angles formed by (M3) and (V2), and the angles formed by (M4) and (V2) are γ and δ. Assuming that the angle between V2) and the X axis is θ, the folding condition is expressed by the following equation (3).
β-α = δ-γ + θ ………………………………… (3)
The establishment of the above equation (3) is proved as follows using the following equation (4).
In the case of the 6-fold line method shown in FIG. 8, conditions for folding in the Y-axis direction at the node A are derived. The XY axis is taken as shown in FIG. The angles formed by the folding lines (M1), (V1), (M2) and the vertical line (P) to the X axis are p1, p2, p3, and the vertical line (Q) and the folding lines (M4), (V2), (V Assuming that angles formed by M3) are q1, q2, and q3, p1 = π / 2-α, p2 = π / 2, p3 = π / 2 + β, q1 = π / 2 + δ + θ, q2 = π / 2 + θ, and q3 = π / 2-γ + θ.
Equation (4) is used for a vector pointing in the same direction based on the symmetric position (points A and B) of the X axis in the region of X <0 by the mountain fold (M1), (M2), and valley fold (V1). And an angle of PL = (− α + β + π / 2) after folding.
In the region of X> 0, the vectors in the same direction starting from the points C and D by the mountain fold (M3), (M4) and the valley fold (V2) are folded, and then QR = (δ−θ−γ + π). / 2). The points A and C and the points B and D are on the same plane, and their vectors are oriented in the same direction. Therefore, if PL = QR, equation (3) is obtained.
When (V2) matches the X axis, θ = 0 is satisfied, and the following equation (3 ′) is satisfied.
β-α = δ-γ ………………………… (3 ′)
In the case of the 6-fold line method, a mountain fold (or a valley fold) is always formed on both sides of the central node. When this folding method is repeated, the sheet is folded in the same direction, and the flat paper automatically becomes cylindrical. On the other hand, in order to perform planar zigzag folding using the six-fold line method, it is indispensable to combine this fold line method with the preceding four-fold line method (see FIG. 2) (see FIG. 7).
(2) Cylindrical folding structure with folding line
It is easily inferred that a cylinder that can be folded in the vertical direction can be manufactured by continuously performing equiangular mountain folding. Hereinafter, it is considered that a foldable cylinder is manufactured by such an operation.
1. Strip with expanded cylinder
FIG. 9 is a view for explaining the condition in which both ends of the band plate are joined to form a cylinder when the band plate is folded along the folding line, and FIG. 9A shows the band plate, the folding line, and the angle of the folding line. FIG. 9B is a diagram showing a change in the direction of the reference axis when folded along the folding line shown in FIG. 9A.
Consider a case where the strip is folded alternately between mountain folds and valley folds as shown in FIG. 9A or N times in the same direction (N: even number). The angles between the N fold lines (1), (2),... And the X axis are θ1, θ2,..., Θn, and the axial directions after the folding are X1, X2,. By the first folding operation (folding line (1)), the right side of (1) becomes the back surface.
With this operation, the new axis (X1) forms an angle of 2θ1 = Θ2 with the X0 axis (see FIG. 9B). When the second folding is performed at the folding line (2), the X2 axis forms an angle Θ2 = 2θ1-2θ2 with the reference axis X0. By folding (3), the X3 axis becomes an angle of X0 and Θ3 = 2 (θ1−θ2 + θ3). By these series of folding operations, the front and back surfaces appear alternately, and the angle ΔN (in the case of N = even number) formed by the XN axis with the reference axis is represented by the following expression by the folding operation N times.
{N = 2 ｛θ1−θ2 + θ3 −−− θN} (4)
When this strip is folded, the condition for joining (closing) the left and right ends of the strip without gap is given by the following equation (5) when n is an integer other than 0.
ΘN / 2π = n …………………………………… (5)
Next, an example in which the left and right ends of the band plate folded so as to satisfy the expression (5) will be described with reference to FIGS.
FIG. 10 is an explanatory view of an example in which the above formula (5) is satisfied and the folding direction is folded in a regular quadrangle by a fold line in the same direction (either mountain fold or valley fold). FIG. FIG. 10B is a diagram showing folding lines (1), (2), (3), and (4) of the band plate, FIG. 10B is a diagram showing a state of being folded, and FIG. 10C is a diagram showing a folded state.
In FIG. 10A, fold lines (1), (2), (3), and (4) that are folded in the same direction (either mountain fold or valley fold) of the strip extending in the X-axis direction as the reference axis are respectively The angles are θ1, θ2, θ3, and θ4 with respect to the X axis, and θ1 = θ3 = 135 ° and θ2 = θ4 = 45 °. That is, the fold lines (1), (2), (3), and (4) are formed zigzag at 45 ° (= π / 4) with respect to the X axis. Also, the left portion of the fold line (1) of the X axis is the X0 axis, and the X axis portion of the right side of each fold line (n) when n = 1, 2, 3, 4 is the Xn axis (n = 1). To 4).
In FIG. 10C, the angle Θ2 formed by the axis X2 and the axis X0 is Θ2 = 2 (θ1−θ2) = 2 (135 ° −45 °) = 2 × 90 ° = 180 ° = π.
The angle Θ4 formed by the axis X4 and the axis X0 is Θ4 = 2 (θ1−θ2 + θ3−θ4) = 2 (135 ° −45 ° + 135 ° −45 °) = 2π. Therefore, n in equation (5) is n = (Θ4 / 2π) = 1, and the axis X4 overlaps the axis X0. In this case, both ends of the strip are joined without any gap.
FIG. 11 is an explanatory view of an example in which the expression (5) is satisfied and the folding direction is a regular hexagonal folding line along a folding line in the same direction (either mountain fold or valley fold). FIG. FIG. 11B is a diagram showing the folding lines (1), (2), (3), (4), (5), and (6) of the band plate, FIG. 11B is a diagram showing a state in the middle of folding, and FIG. FIG.
In FIG. 11A, the folding lines (1) to (6) of the strip extending in the X-axis direction, which is the reference axis, form angles θ1 to θ6 with respect to the X-axis, respectively, and θ1 = θ3 = θ5. = 135 ° and θ2 = θ4 = θ6 = 45 °. That is, the fold lines (1) to (6) are formed zigzag at 30 ° (= π / 6) with respect to the X axis.
In FIG. 11, the angle Θ6 formed by the axis X6 with the axis X0 is Θ6 = 2 (θ1−θ2 + θ3−θ4 + θ5−θ6) = 2 (150 ° −30 ° + 150 ° −30 ° + 150 ° −30 °) = 2 × 2π. . Therefore, n in equation (5) is n = (Θ6 / 2π) = 2, and the axis X6 overlaps the axis X0. In this case, both ends of the strip are joined without any gap.
FIG. 12 is an explanatory view of an example in which the above-mentioned expression (5) is satisfied and the folding direction is folded in a regular octagonal shape by a folding line in the same direction. FIG. 12A shows folding lines (1) and (2) of the strip in a developed state. ),..., (8), FIG. 12B is a view showing a state in which the sheet is being folded, and FIG. 12C is a view showing a state in which the sheet is folded.
In FIG. 12A, fold lines (1) to (8) of the strip extending in the X-axis direction which is the reference axis form angles θ1 to θ8 with respect to the X-axis, respectively, and θ1 = θ3 = θ5. = Θ7 = 157.5 °, θ2 = θ4 = θ6 = θ8 = 22.5 °. That is, the fold lines (1) to (8) are formed zigzag at 22.5 ° (= π / 8) with respect to the X axis.
In FIG. 12, the angle Θ8 formed by the axis X8 with the axis X0 is Θ8 = 2 (θ1−θ2 + θ3−θ4 + θ5−θ6 + θ7−θ8) = 2 (157.5 ° −22, 5 ° +... + 157.5 ° −22.5 °) ) = 3 × 2π. Therefore, n in the equation (5) is n = (Θ8 / 2π) = 3, and the axis X8 overlaps the axis X0. In this case, both ends of the strip are joined without any gap.
From the description of FIGS. 10 to 12, when the folding direction is the same direction (either mountain fold or valley fold), the band plate is folded in the same direction and folded into a regular N-gon (N is an even number). It can be seen that the folding lines (1), (2),..., (N) at an angle θ = π / N with respect to the reference axis X should be formed in a zigzag manner at equal intervals.
FIG. 13 is an explanatory diagram of an example of folding into a regular hexagon by a fold line that satisfies the expression (5) and the folding direction is alternately reversed (reversed in the mountain fold direction and the valley fold direction), and FIG. 13A is expanded. FIGS. 13B to 13F are views showing a state in the middle of folding, and FIG. 13G is a view showing a folded state.
In FIG. 13A, the fold lines (1), (3),... .., Θ11, and θ1 = θ3 =... = Θ11 = 60 °. The fold lines (2), (4),..., (12) indicated by dotted lines that are folded in the opposite direction (for example, the valley fold direction) to the fold lines (1), (3),. .., Θ12 with respect to the X axis, and θ2 = θ4 =.
The imaginary line (13) shown in FIG. 13 is a line that overlaps the fold line (1) when the band plate is folded.
In FIG. 13, the angle Θ12 formed by the axis X12 and the axis X0 as a solid line is Θ12 = 2 (θ1−θ2 + θ3−... + Θ11−θ12) = 2 (60 ° −30 ° + 60 ° −... + 60 ° −30 °) = 2 × π It is. Therefore, n in equation (5) is n = (Θ12 / 2π) = 1, and the axis X12 overlaps the axis X0. In this case, both ends of the strip are joined without any gap.
2. Folded cylinder with main fold line consisting of horizontal fold lines
The upper and lower ends of the band-shaped paper (FIG. 9A) are considered to be horizontal folding lines, and some of these steps are assumed in the Y-axis direction. The parallel horizontal fold lines (group) are named main fold lines.
FIGS. 14 to 16 are development views of a model for manufacturing a cylinder that can be folded in the Y-axis direction, in which the main folding line using the 4-fold line method and the 6-fold line method is a horizontal fold line group. .
As is well known (as can be seen from the description of FIGS. 9A and 9B), when a cylinder that is folded in a regular N-gonal cross-sectional shape by the one-node four-fold line method is used, a band-like plate is formed by π · (N−2) / A regular N-sided polygon can be formed by bending in the same direction by N at equal intervals. Note that π · (N−2) / N is the size of the interior angle of the regular N-sided polygon.
FIG. 14 is a typical development view in the case where the belt-like plate shown in FIG. 9A is bent in the same direction at equal intervals by π · (N−2) / N to form a regular N-gon and N = 6. FIG.
Here, in consideration of the fact that when the folding angle is θ in the above equation (4), it is possible to bend by 2θ, six zigzag mountain fold lines (1) to (6) forming an angle π / 6 with the horizontal folding line. Are introduced at equal intervals. At each mountain fold line, a cylindrical structure that is folded by π / 3 and finally folded in a hexagonal cross-sectional shape is manufactured.
FIG. 15 shows a trapezoidal element having unequal sides obtained by decomposing twice (π / 3) the angle between the mountain fold line and the horizontal fold line in FIG. 14 into α = 2π / 9 and β = π / 9. FIG.
In the case of folding into a regular hexagon, the division of the angles can be arbitrarily selected as long as the sum is π / 3.
FIG. 16 shows a case where six sets of fold lines obtained by decomposing the mountain fold line in the Y-axis direction of FIG. 14 into a mountain fold line I of α = π / 3 and a valley fold line II of β = π / 6 are introduced. 16A is an exploded view of a manufactured cylinder, FIG. 16A is a developed view, FIG. 16B is a view showing a half-folded state of a folded cylinder manufactured when both ends of the developed view of FIG. 16A are joined, and FIG. FIG. 4 is a perspective view of the same thing as seen from a different direction.
In FIG. 16A, the values of α and β can be freely selected as long as α−β = π / 6 here.
FIG. 17 is a diagram in which the points A and B in FIG. 14 are matched and the mountain fold is removed from the horizontal fold line. The diamond pattern ((1) to (1) to (6)) is a horizontal isosceles triangle having a base angle π / 6. It is a development view of (3)).
At this time, the cross-sectional shape at the horizontal folding line portion becomes an equilateral triangle, which corresponds to a model of diamond buckling in plastic buckling of a thin-walled cylinder.
FIG. 18 is a developed view of a deformed diamond pattern composed of scalene triangular elements.
19 is an explanatory view of a pseudo-cylindrical body having a development view symmetrical and foldable one by one with respect to a horizontal folding line, FIG. 19A is a development view, and FIG. 19B is both ends of the development view of FIG. 19C is a view showing a half-folded state of a folding cylinder manufactured when the above is joined, and FIG. 19C is a view of the same thing as FIG. 19B seen from a different direction. The five types of developed views shown in FIGS. 14 to 17 are applicable to all horizontal folding lines, but can also be folded in the developed view shown in FIG.
In FIG. 19, at the point A, the folding condition expression, Expression (3) is, of course, satisfied due to the symmetry, but the expression (3) also holds at the point B.
FIG. 20 is a diagram showing an example of a developed development of a fold constituted by only fold lines similar to the point B in FIG.
FIG. 21 is a development view of a foldable cylindrical wall having a plurality of polygonal parts (flat walls) formed by folding lines.
The cylindrical wall having the developed view of FIG. 21 can create a collapsible cylinder having a plurality of polygonal parts.
3. Cylinder with fold line when the main fold line has a slope (spiral type)
Consider a case where the horizontal folding lines in FIGS. 14 to 21 are inclined.
In the above-mentioned documents (a) to (c), Guest et al. Consider a cylinder formed by a triangular divided flat plate, and it is possible to manufacture a cylindrical folded structure. The appropriate shape of the triangle was examined by numerical calculation.
FIG. 22 shows a cylindrical structure in which a connecting portion of a divided flat plate made of a triangular divided flat plate examined by Guest et al. Has a spiral shape, and the spiral (1) rises one step every time it goes around. Is a development view of the present inventor. They analyzed the characteristics of the cylinder shown in the developed view of FIG. 22 when folded, using the angles (α, β) between the spirals as variables, but could not show the complete folding conditions. Did not.
FIG. 23 is a development view of a foldable cylindrical structure which corresponds to the above-described FIG. 17 in which the entirety is inclined by ψ = π / 6 and has three diagonal diamond patterns.
24 is an explanatory view of a pseudo cylindrical body having a development view equivalent to that of FIG. 23. FIG. 24A is a development view, and FIG. 24B is a fold manufactured when both ends of the development views of FIGS. 23 and 24A are joined. It is a figure showing the half-fold state of a cylinder.
In the example shown in FIGS. 23 to 24B, when the left end L and the right end R of the developed view are joined to produce a cylinder, the pattern formed by the folding lines is continuous.
FIG. 25 is an explanatory view of a pseudo cylindrical body k having a development view obtained by inclining FIG. 14 by π / 6. FIG. 25A is a development view, and FIG. 25B is manufactured when both ends of the development view of FIG. 25A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 25A corresponds to a view obtained by cutting FIG. 14 along a horizontal line GH inclined by π / 6 with respect to a horizontal line, and setting the cut line as a horizontal lower end.
FIG. 26 is an explanatory view of a pseudo-cylindrical body having a development view in which FIG. 15 is inclined by π / 6. FIG. 26A is a development view, and FIG. 26B is manufactured when both ends of the development view of FIG. 26A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 27 is a developed view obtained by tilting FIG. 16 by π / 6.
In the examples shown in FIGS. 25 to 27, when the left end L and the right end R of the developed view are joined to form a cylinder, the pattern formed by the folding lines is generally not continuous. Details of the continuity of the development view will be described later.
FIG. 28 is a spiral type shown in FIG. 19, which is obtained by cutting along a straight line connecting points A and D in the figure. The angle (up to 0.193π) shown in FIG. 28 indicates the angle between the cutting line and the horizontal line. In this case, the angle of the valley fold line is limited because the shape of the triangular element is given. Become.
FIG. 29 is an explanatory view of a spiral-shaped folding cylinder having a folding line generalized from FIG. 24, FIG. 29A is a developed view, and FIG. 29B is manufactured when both ends of the developed view of FIG. 29A are joined. It is a figure which shows the half-fold state of a folding cylinder.
The folding condition does not depend on the value of β in FIG. 29A (described later).
FIG. 30 is a developed view when the developed view of the six steps in FIG. 29A is changed to three steps, α is set to 30 °, and the value of β is changed for each step.
As shown in FIG. 30, the folding condition can be satisfied even if the value of β is set independently for each stage.
FIG. 31 is a developed view of a repetitive spiral type obtained by inverting the spiral mountain fold line and the valley fold line of FIG. 29A step by step. This development can also be obtained by matching points A and B in FIG.
FIG. 32 is a view showing a portion cut by two parallel straight lines AB 'and C'D of the developed view of the cylindrical body shown in FIG. 21 so that A and B' and D and C 'overlap. FIG. 33 is a developed view of a foldable cylinder formed by connecting left and right edges of FIG.
The cylindrical wall having the development shown in FIG. 32 can create a collapsible cylinder having a plurality of polygonal parts.
FIG. 33 is an exploded view of a collapsible cylinder having an arbitrary-shaped quadrilateral element (part).
In FIG. 33, when a straight line obtained by extending AF is AE, the folding condition is ∠BAE = ∠DAC = α. The value of α can be arbitrarily determined as α = 180 ° / N (N is a positive integer). For example, when N = 8, α = 180 ° / 8 = 22.5 °. Therefore, by setting ∠BAE = ∠DAC = α = 22.5 ° and setting the length of the AE to an appropriate arbitrary value, a foldable cylinder having an arbitrary-shaped part can be created.
4. Continuity of fold lines in spiral development
As described above, when the left and right ends of the spiral developed view are joined, the continuity of the folding line is not always satisfied at both ends of the developed view. When a developed view is given by a trapezoidal element as in the case of FIGS. 25 to 27, continuity can be maintained by appropriately selecting the upper base length Lu of the trapezoid in FIG.
FIG. 34 is an explanatory diagram of a method for maintaining continuity when both ends of a developed view are joined.
In FIG. 34, a point A is determined by drawing N trapezoidal elements in the direction of the main fold line (angle ψ) from the origin O as a base point. Assuming that the height of the trapezoid is h, the length OA = N {(h / tan θ) + Lu} for a regular N-gon. Draw m (even number) elements below the N-th trapezoidal element, and determine point B as shown in the figure. In order that the developed view is continuous for an arbitrary ψ, the point B needs to be on the X axis. Since AB = mh, the following equation (6) is obtained from tanψ = OA / OB.
Lu = {2N-m-tan} / tanθ {h / tan} (6)
That is, when Lu is properly determined by the equation (6), continuity of the left and right ends of the developed view in these cases can be obtained.
5. Verification of folding condition of cylinder with fold line
A typical example verifies whether or not the condition for closing in the circumferential direction when the cylinder having the folding line described above is folded (see Equation (5)) is satisfied.
In the cylinder given in FIG. 25, consider the folding line of the strip portion (small width D) at the lowermost end of this developed view. Here, there are 18 fold lines, and fold lines having the same inclination repeatedly appear every 6 lines from the left side. Therefore, they are formed of three sets of 6 fold lines. Using equation (4), the rotation angle of the axis by these fold lines is expressed by ψ (= π / 6) as the inclination angle.
ΘN = 2 ｛(α + ψ) -ψ + ψ-ψ + (α + ψ) -ψ｝ × 3 = 12α (7)
It becomes. Since α = π / 6, ΔT = 2π in equation (4), which satisfies equation (5). Thus, it can be seen that the closing condition is satisfied after folding.
In the case of FIG. 29A, the following equation is obtained by considering the rotation angles of the lowermost six parallelogram portions by the folding lines.
{T = 2} (α + β) −β} × 6 = 12α (8)
If α = π / 6 is used, ΔT = 2π, and the closing condition (see equation (5)) is satisfied. As can be seen from equation (8), it can be seen that ΔT does not depend on the β value.
That is, in the models of FIGS. 29 to 31, the condition for folding into a regular N-gon shape is α = π / N, and the angle β in the figures can be freely selected.
In the spiral model shown in FIGS. 23 to 31 described above, except for FIG. 28 (considering hexagonal folding), the inclination angle の of the valley fold line is all π / N. However, as seen in the example of FIG. 25, the inclination angle の of the main folding line is not limited to π / N as long as the continuity of the developed view can be satisfied.
6. Fabrication of foldable pseudo cylinder
The present inventor has examined the folding characteristics in the axial direction with a pseudo cylinder made of a polypropylene sheet having a thickness of 0.2 mm according to the above development view, and has confirmed that it is possible. When the spiral type folding model shown in FIGS. 25 and 27 is pressed by the material testing machine, the upper part of the cylinder is folded while the lower part stops while rotating.
Observation of the progress of these folding shows that the proposed model is capable of good folding and that the load required for complete folding is extremely low, 20-40N. (Diameter of the cylinder before folding; about 100 mm).
7. Summary of research on cylinders with fold lines
In the above description, a method of manufacturing a pseudo-cylinder that divides a developed view into triangular elements, trapezoidal elements, or quadrangles of an arbitrary shape and folds it into a regular N-gon shape, taking N = 6 (partly N = 3, 8) as an example Was explained. Unless the main fold line, which is difficult to satisfy the continuity of the left and right ends of the developed view, is composed of an odd number of trapezoidal elements, the fold angle at one node is (N−2) / N · By setting it to π, a folded structure can be manufactured for an arbitrary N value (N ≧ 3, an integer).
If the angle of the fold line is selected so as to satisfy the expression (5) and the length of the fold line is appropriately selected, it is also possible to manufacture a folded structure that is not a regular N-sided shape.
When the cylinder is made of a thin polymer sheet, it seems easy to mold it into a shape as shown in FIGS. 16B and 24B. Therefore, it is considered that a container such as a foldable PET bottle can be manufactured by molding in such a shape.
When the valley fold line forms a spiral shape, it is generally easier to expand and contract in the axial direction than that of the horizontal type. This seems to have to be considered in improving the folding structure.
(3) Conical folding structure with folding line
1. Basic relations for folding
When the conical wall constituting the foldable conical folding structure with a folding line is a one-contact six-fold line and a one-node four-fold line, the angle relationship between the folding lines to be folded at these nodes is shown in FIGS. 37.
FIG. 35 is a diagram showing the angular relationship between the folding lines satisfying the folding condition when the valley fold line is symmetrically inserted in the case of one node 6 fold line, and shows the folding condition in the case of FIGS. FIG.
If the angle between the inserted valley fold lines is defined as θ and the angles α to δ are defined as shown in FIG. 35, the following equation (3) is established.
β-α = δ-γ + θ ………………………………… (3)
FIG. 36 is a diagram showing an angle relationship between folding lines satisfying the folding condition when the valley folding lines (V1) and (V2) are alternately inserted between the mountain folding lines (M1), (M2) and (M3). 58 is an explanatory diagram of folding conditions in the case of FIGS. 56B and 57 described later.
In FIG. 36, the angle between the X axis, which is an extension of the mountain fold line (M4), and (M1) and (M3) is α^*, Β^*And the angle between each folding line is θ₁~ Θ₄And The XY axis is set as shown in FIG. 36 with the node O as the origin.
The condition for folding in the Y-axis direction at the node O is derived in the same manner as described above. In the region where X <0, the vector in the same direction at the symmetric position of the X axis (points B and C) has the angle π (= Q) after being folded by the mountain fold (M4).₂) And turn in the opposite direction.
Next, consider vectors of points D and E in an area where X> 0. The angle between the perpendicular (Q) to the X axis and the fold lines (M1), (V1), (M2), (V2), (M3) is q as shown in FIG.₁~ Q₅Then
q₁= Π / 2 + α^*,
q₂= Π / 2 + α^*−θ₁,
q₃= Π / 2 + α^*− (Θ₁+ Θ₂),
q₄= Π / 2-β^*+ Θ₄,
q₅= Π / 2-β^*
It becomes. The angle Q between these vectors due to this folding₂Is given by the following equation (9).
Q₂/ 2
= Q₁-Q₂+ Q₃-Q₄+ Q₅
= Π / 2 + α^*− (Θ₂+ Θ₄) ……………………… (9)
After folding, points B and D are still on the same plane, and the vector at this point points in the same direction.₂Value and Q of negative area₁= Π equal, then
α^*= Θ₂+ Θ₄
Get.
α^*+ Β^*= Θ₁+ ... + θ₄
With,
β^*= Θ₁+ Θ₃
Therefore, the folding condition in this case is expressed by the following equation (10).
α^*= Θ₂+ Θ₄, Β^*= Θ₁+ Θ₃          ............ (10)
FIG. 37 shows the case of one node 4-fold line. The folding conditional expression is obtained by the same procedure as above.
Q₂/ 2 = q₁-Q₂+ Q₃= Π / 2 + α-γ
Because
Q₂= Q₁= Π
And put
α = γ.
That is, when the mountain fold lines (M1) to (M3) are given, a valley fold (V1) occurs at a position of a γ value equal to an angle α formed between the X axis, which is an extension of (M3), and (M1).
2. Conical wall with fold line whose main fold line is parallel to the outside of the development
FIG. 38 is an enlarged view of a main part of a development view in a case where a development view of a cone whose main fold line is parallel to the outer side of the development view is composed of N isosceles triangles having a vertex angle of 2 °.
The valley fold line (dashed line) in FIG. 38 is called a main fold line. The vertex is 0, the points on the outer side are A, B, C, and D. A straight line is formed from these points at an angle α with the outer side, and the intersections are E, F, and G.
Lines that form angles α with the line segments EF and FG are drawn from the points E, F and G in the same manner as above, and their intersections are defined as H and I. With this drawing, the development view is divided by two types of isosceles triangle elements. O, H, B and O, I, C form a straight line from the symmetry, and a diamond pattern symmetrical to the left and right of the straight line OF is obtained. The straight line OF forms a right angle with the outer side BC. The folding line forming the node F corresponds to that in FIG.
∠CFG = ∠BFE = β, and in consideration of the symmetry at the node F, δ in FIG. Since the angle between the valley fold line EF and FG is 2 °, when θ = 2 °, the equation (10) becomes
β-α = Θ ………………………………… (11)
It becomes. Since ΔOFE and ΔOFG are isosceles triangles with a vertex angle of 2 ° (base angle π / 2 °), ΔHFI = γ^*Then, the following equation (12) is obtained.
γ^*+ 2α = π-2Θ …………………………… (12)
When folded at node F, the angle between the valley fold lines EF and FG is γ^*-2α. If the valley fold line is folded in a regular N-gon shape, the angle formed by the valley fold line is (N−2) / N · π.
γ^*−2α = (N−2) / N · π (13)
The α and β values satisfying the folding condition from the above equations (11) to (13) are given by the following equations (14).
α = π / 2N−Θ / 2, β = α + Θ = π / 2N + Θ / 2 (14)
Considering the case of N = 3, 2Θ = π / 6, α = π / 8 and β = 5π / 24 are obtained from Expression (14).
FIG. 39 is an explanatory view of a pseudo-cone wall having a development view of a pseudo-cone wall with a folding line obtained by using the value obtained by Expression (14). FIG. 39A is a development view, and FIG. 39B is a development view of FIG. 39A. It is a perspective view of the half-fold state of the conical wall with a folding line which has a.
FIG. 40 is an enlarged view of a main part of a development view of a conical wall with a fold line when divided into inequilateral triangular elements by a fold line.
In FIG. 40, points on the outer side are represented by A, B, C, D,..., And a line forming an angle α with the outer side at each point is drawn on the upper right, and a line forming an angle δ is drawn on the upper left. Are E, F, and G (∠BOF = θ^*). From these points, straight lines are drawn on the line segments EF, FG and the upper left at an angle α, and on the upper right at an angle δ, and their intersections are designated as H and I.
Points O, H, B and O, I, C form a straight line. An asymmetric diamond pattern is obtained on the left and right of the straight line OF. ∠BFE = β, ∠CFG = γ, and the intersection of EF and BC is J. ＯOBC and △ OCD and ＦOEF and △ OFG are isosceles triangles each having an apex angle of 2Θ, ∠DCJ = ∠GFJ = 2Θ, and ∠OFJ = ∠OCJ is obtained.
That is, points O, F, C, and J are on the same circle, and {CJF = {FOC = 2} −θ^*It becomes. Focusing on ΔBFJ, the following equation is obtained.
β-α = 2Θ-θ^*      ………………………………… (15)
{CFJ = γ−2} obtained from the angular relation around the point F is converted to δ = {CFJ + (2} −θ) obtained from the angular relation of {CFJ.^*) Yields the following equation (16).
δ−γ = −θ^*          …………………………… (16)
Θ in equation (16)^*Is substituted into Expression (15), and considering that the angle between the valley fold lines EF and FG is 2 °, the following folding condition expression (17 ′) is satisfied.
β-α = δ-γ + 2Θ ........................ (17 ')
As before, ∠HFI = γ^*In other words, the angle formed by the valley fold lines EF and FG when folded at the node F is γ^*− (Α + δ). Considering the folding of a regular N-gon, this value is equalized with (N−2) / N · π, and γ obtained from a geometric relationship^*By using + (α + δ) = π−2Θ, the following folding condition expression (17) is obtained.
(Α + δ) = π / N−Θ ………………………… (17)
When α and δ satisfying the expression (17) are selected, a foldable development view composed of scalene triangular elements is obtained.
FIG. 41 is a development view of a conical wall with a fold line when divided into inequilateral triangular elements by a fold line, where N = 3, 2Θ = π / 9, α = π / 9, and δ = π / 6. Of development (θ^*= About 0.0688π).
FIG. 42 is a development view of a conical wall with a fold line when it is divided into a trapezoidal triangular element by a fold line having an angle α at the upper right and an angle δ at the upper left at the point F in FIG. , Δ values are the same as those in FIG. 41.
Even if the angle α is set to the upper right and the angle δ is set to the upper left at the point F in FIG. 40, a developed view that can be folded is obtained. The rectangle obtained here is a dashed parallelogram, and points F, I,...^*Rotate with. The folding condition at the node is established in the same manner as in FIG.
FIG. 43 is an enlarged view of a main part of a development view of a conical wall with a fold line in the case of dividing by a trapezoidal element instead of dividing by the isosceles triangular element of FIG.
In FIG. 43, two straight lines (AC, BD) forming an angle α with AB from points A and B on the outer side are drawn symmetrically with respect to a straight line OI, and an apex angle φ^*Points C and D are determined so that
∠DCE = r^*And ∠DCB = ∠DCO + ∠OCF, ∠DCO = π / 2−φ^*/ 2, {OCF = (π / 2−Θ) −α}^*Is represented by the following equation (18).
Γ^*= Π- (φ^*/ 2 + Θ + α) ………………………… (18)
Since the line segment CF is a valley fold line, the angle between the mountain fold DC and the valley fold CF after folding by folding at the node C becomes Γ^*This value is given by the following equation (19) using the equation (18).
Γ^*−α = π− (φ^*/ 2 + Θ + 2α) .................. (19)
Considering the case of folding in a regular N-gon, (Γ^*−α) and (N−2) / N · π are equalized to obtain the following equation (20-1).
α = π / N- (φ^*/ 2 + Θ) / 2 ………………… (20-1)
Since {HCF = 2} and AB and CD are parallel, ΔACH = α, and β = ΔACF is expressed by the following equation (20-2).
β = α + φ^*/ 2 + Θ
= Π / N + (φ^*/ 2 + Θ) / 2 ………………… (20-2)
At the point C, ∠ACH = ∠EAF = α, so that the folding conditional expression (17) is satisfied.
FIG. 44 is a view of a conical wall with a fold line, which is divided into an equilateral trapezoidal shape by a fold line and folded into a regular N pyramid, where N = 6, φ in FIG.^*= Π / 36, 2Θ = π / 12 is an explanatory view of a pseudo-conical wall having a development view, FIG. 44A is a development view, and FIG. 44B is a half-fold of a conical wall with a folding line having the development view of FIG. 44A. FIG.
3. Conical wall with fold line where the main fold line is spiral
2. In the section, a development view in which a valley fold line is parallel to a bottom surface when a cone is formed has been described. Here, the folding in the case where the valley fold line serving as the main fold line has a spiral shape will be considered.
FIG. 45 is a view showing a development view of a conical wall with a folding line composed of N isosceles triangular elements (vertical angle 2 °), in which only one step is written out as a curved strip portion.
Here, it is assumed that the mountain fold and the valley fold are periodically introduced, and the angles formed by the fold lines with the outer sides AB,... Are ζ, η (0 ≦ (ζ, η) ≦ π / 2).
When this strip is bent along these folding lines, it is bent in the circumferential direction by φ = 2 (ζ−η) N. Originally, the band plate was bent at an angle ψ = 2NΘ. Therefore, in order to join both ends of the band plate without gaps after folding, it is necessary that φ + ψ = 2π. This corresponds to the circumferential folding condition, which is expressed by the following equation (21).
φ + ψ = 2 (ζ−η + Θ) N = 2π (21)
FIG. 46 is an exploded view of a conical wall with a fold line having a simple, spiral exploded view consisting of three isosceles triangular elements. FIG. 47 is a top view when the development view of FIG. 46 is folded.
In FIG. 46, three radiations ((1) to (3)) and a group of lines ((4), (5)...) Parallel to the outer side are mountain fold lines. The valley fold line forms an angle α with the outer side. Considering that the angles β to δ in FIG. 46 are isosceles triangular elements (vertical angle 2 °), the following expression holds.
β = π / 2 + Θ-α
γ = π / 2 + Θ + α
δ = π / 2-Θ-α
The valley fold line forming the spiral is bent by 2 ° every time it passes through one triangular element. When θ = 2Θ is set in the folding condition expression (17) and α to δ are substituted, it can be seen that expression (17) holds for an arbitrary α.
The α value is obtained under the condition of closing in the circumferential direction after folding, and in the case of folding in a regular N-gon shape, using ζ = α, η = π / 2-Θ in Expression (21), the following expression (22 can get.
α = {(N−2) / 2N} · π ………………………… (22)
In FIG. 46, three spirals (1) to (3) emerging from points A, F, and G are formed by the radial mountain fold lines in FIG.
Although this model gives a typical spiral pattern, it is folded down to the center in FIG. 46 without any gap, and thus it is difficult to practically use it as a method for folding a thin plate or film having a thickness.
48 is an explanatory diagram of a practical model obtained by modifying the model described in FIGS. 45 and 46. FIG. 48A is an explanatory diagram of a modification method, and FIG. 48B is an enlarged view of a main part of FIG. 48A.
In FIG. 48A, the points C and D are set at an angle 2θ around the center O on the circumference.^*, And move to points E and F, respectively. Then, ∠CAE = ∠BDF = ... = ψ^*And put.
By this operation, the congruent rectangles ABFE, BGHF,... Are periodically drawn on the same circumference.
In FIG. 48B, the valley fold line is set to AF, and angles α to δ and p and q are given as shown in the figure.
∠OAB = ∠OBA = π / 2ΘΘ
Is obtained, the following equation is obtained.
p = π / 2 − {+}^*, Β = π / 2 + Θ−γ−ψ^*,
δ = π / 2−Θ− (γ + ψ)^*) ………………………… (23)
∠ACE = π / 2-θ^*Therefore, paying attention to △ AEC, ∠AEC = π / 2−θ^*−ψ)^*Get. Considering that ＯOCE and △ OEF are isosceles triangles, and using ∠AEF = q = π- (∠OEC + ∠OEF + ∠AEC) obtained from the angular relationship around point E, the following equation (24) is obtained. .
q = π / 2 + 2θ^*+ Ψ− + Θ, α = γ-2θ^*
……………………… (24)
FIG. 49 is a view showing a state in which the figure ABGHFE formed by the folding line in FIG. 48A is sequentially folded along folding lines AF and BF. FIG. FIG. 49B is a view showing a state after the mountain fold is further performed at B′F (original line segment BF) in the state of FIG. 49A.
When each point is determined as shown in Fig. 49B, ∠AFB '= β, ブ ロ ッ ク FB'H "= δ.The two blocks are divided into the straight line AF in FIG. And B′H ″. Assuming that this angle is ψ as shown in the figure, ψ = π-2 (γ + ψ^*). Β + δ = π−2 (γ + ψ) obtained from equation (23)^*), The following equation (25) is obtained.
ψ = 2 (γ + ψ^*) ……………………………… (25)
Considering the folding in a regular N-gonal shape, one of the inner angles is (N−2) π / N.
(Γ + ψ^*) = (N−2) π / 2N (26)
Get.
FIG. 50 is a view showing a portion corresponding to the first-stage band plate and a portion corresponding to the second-stage band shown in FIG. 48A.
In FIG. 50, the second-stage drawing can be newly performed based on points E, F, and H in the same procedure as that performed in FIG. The rectangle groups in the second row are similar to those in the first row.
Next, the folding condition is examined by taking the point F in FIG. 50 as an example. From equations (23) and (24), β−α = π / 2 + Θ−ψ^*+ 2θ^*-2γ and δ-γ = π / 2-Θ-ψ^*-2γ is obtained. That is, the following equation (27) is obtained.
β−α = δ−γ + (p−q) = δ−γ + 2 (Θ + θ^*) ............ (27)
The angle between the fold lines (1) and (2) in FIG. 50 is 2 ° due to the periodicity, and similarly, the angle between the fold lines (2) and (3) is 2θ.^*It is. That is, (1) and (3) are 2 (Θ + θ^*Considering the angle of (), equation (27) shows that the folding conditional expression at the node F is satisfied.
FIG. 51 shows N = 6, γ + ψ in the fold line-shaped conical wall having the fold lines shown in FIGS.^*= Π / 3, ψ^*51A is an explanatory view of a pseudo-cone wall having a development view (2Θ = π / 18) when γ / 6 and γ = π / 6, FIG. 51A is a development view, and FIG. 51B is a development view of FIG. It is a perspective view of the state where the conical wall with a fold line was folded in half.
FIG. 52 shows N = 6, γ + ψ in the conical wall with a fold line having the fold lines shown in FIGS.^*= Π / 3, ψ^*= Π / 4, γ = π / 12 (2１２ = π / 6).
FIG. 53 shows an example in which the number of stages in the developed view of FIG.^*FIG. 6 is a development view when the value of “” is increased.
In FIG. 53, in the case of a conical wall, ψ^*+ Γ = 60 °. ψ^*Under + γ = 60 ° ψ^*And γ are divided. For each stage 各^*And γ can be arbitrarily divided. In the conformal spiral, the pattern becomes smaller toward the center.^*Is smaller.
FIG. 54 is a developed view showing the same conical wall as the folded conical wall having the developed view of FIG. 53.
FIG. 54 is a developed view of a conical wall having the same shape as that of FIG. In FIG. 54, the joining of both side edges is easier than in FIG.
FIG. 55 is a view when the second valley fold line in FIG. 50 is taken in an opposite direction to that of the first tier at an angle γ.
If the intersection of this valley fold line and OA (O; center) is K, then {KEO is}^*And the newly obtained rectangle EFIK is similar to that of the first stage. The state of the folding line at the point F corresponds to FIG. When the mountain fold line (1) in FIG. 37 corresponds to the mountain fold line FH, θ in FIG.₁~ Θ₄Is θ₁= Δ, θ₂= Γ, θ₃= Α, θ₄= Β.
Since the line segments FH and FE in FIG. 55 form an angle of 2 °, α in FIG.^*And β^*Is shown in FIG.
α^*= Δ + γ + 2Θ, β^*= Α + β + 2Θ (28-1)
It becomes.
Using equations (23) and (24), α in the above equation^*, Β^*Is
α^*= Π / 2-ψ^*−Θ = β + γ
β^*= Π / 2-ψ^*−Θ−2θ^*= Α + δ
.................. (28-2)
It becomes. These equations give θ₁= Δ, θ₂= Γ, θ₃= Α, θ₄Using = β, equation (10) is obtained, and the folding condition is satisfied.
Drawing a valley fold line in the opposite direction for each stage in this manner creates a repetitive spiral-shaped folding structure.
FIG. 56 is an explanatory view of a pseudo-cone having a development view in which the FIG. 51 is made into a repetitive spiral type. FIG. 56A is a development view, and FIG. 56B is a half-fold of a conical wall with a folding line having the development view of FIG. It is a perspective view of the state which carried out.
FIG. 57 shows 2Θ = π / 6, ψ^*= [Pi] / 6, [gamma] = [pi] / 6;
4. Analytical study using conformal spirals
The two types of patterns formed by the folding lines in the above-described developed view are similar and become smaller toward the center.
58 is an explanatory view of a development view of a foldable conical wall with a folding line having a folding line along an equiangular spiral, FIG. 58A is an overall explanatory view, and FIG. 58B is an enlarged view of a main part of FIG. 58A.
The developed views shown in FIGS. 39A and 42 are generally expressed in a form as shown in FIG. 58A, where the angle formed by one pattern with respect to the center O is 2 °, similarly to the above-described geometrical treatment. You. This FIG. 58A is drawn as follows. First, line segments (1) and (2) are drawn in the upper right direction so as to form an angle ψ with the radiations OA and OI from the center O starting from the points A and I.
Next, line segments (4) and (5) are drawn from the points A and M in the upper left direction so as to form an angle φ with the radiation (ψ and φ values are α and δ in FIGS. 40 and 42, and ψ = π / 2). −Θ−α, φ = π / 2−Θ−δ). Assuming that the intersections of (1) and (5) and (2) and (4) are F and B, respectively, the points B and F are on concentric circles.
Similarly, when the above operation is performed at points B and F, points C, J and G are determined, and points D, K and H are sequentially determined. That is, the rows F, G, H,... Of points taken in the upper right direction from the point A always form an angle ψ with the radial direction, and the points A, B, C, D, E form an angle φ with the radial direction. It is drawn as follows. Point A. Assuming that a line connecting F, G, and H is a new curve (1) and a line connecting points A, B, C, and D is a new curve (4), these two curves are equiangular with the radial direction. It becomes a line going to the center.
That is, each of these points is on a conformal spiral emanating from the center O. 58A, (1), (2), and (3) are counterclockwise spirals, and (4), (5), and (6) are clockwise spirals.
As shown in FIG. 58A, when the angle formed by the line segments AB, BC,... With respect to the central angle is set to 2Θ ′, the angle formed by the line segments AF, FG, GH is 2 (Θ−Θ ′). The folding condition is examined using an enlarged view of two rectangles on the left and right of the point F (FIG. 58B). These rectangles are congruent, and the line segments BF and FG form a corner 2 °. The relationship between お よ び, φ and α to δ is as shown in the figure. Since {OBF in FIG. 58A is an isosceles triangle having a vertex angle of 2 °, α + φ = π / 2−Θ and δ + ψ = π / 2−Θ, and
α + δ = π- (φ + ψ) -2Θ …………………… (29)
Get. From the inner angle relation of △ ABF or △ MFN,
β + γ = π− (φ + ψ) …………………… (30)
Get. The following equations hold from equations (22) and (23).
β−α = δ−γ + 2Θ .................. (31)
Considering that the line segments BF and FG form an angle of 2 °, the above equation (3) holds.
That is, it is understood that the folding condition is automatically established when the folding line is drawn by the equiangular spiral.
When φ = ψ is FIG. 39A and φ φ, FIG. 42 corresponds. Radius R of points B and F₁Is the radius of the development₀Is given by the following equation using the sine law.
R₁/ R₀= Sin ｛2 (Θ-Θ ') + ψ｝ = p (32)
The radius of the point (C, J, G...) Of the second step from the outer circumference and the point (D, K, H.², P³Given by ...
FIG. 59 is an explanatory view of a development view of the conical wall with a folding line when the spiral of FIG. 58 is reversed.
In FIG. 59, as in FIG. 58, the radial direction and the angle ψ are taken upward from the point A to the right and the angle φ is taken upward to the left. These are (1) and (2), respectively. From point J, draw (3) in the same way as (1) and from point K, draw (4) in the same way as (2). Intersection of (1) and (4) is point C, intersection of (2) and (3) Is point B. At this time, the angle formed by the line segment BC is 2 °.
Next, line segments BD and CD are drawn from points B and C in the opposite directions at similar angles ψ and φ, respectively. Intersection D is on radius OA. By repeating this, zigzag folding lines ACDFGI..., ABFEGH. Since ΔOBC is an isosceles triangle with a vertex angle 2Θ,
∠DBC = δ = π / 2-Θ-φ, α = ∠DCB = π / 2-Θ-ψ
……………………… (33)
Is obtained. The following equation (34) is derived by using the outer angle relationship between ΔOBA and ΔOAC.
∠CBA = γ = π / 2 + Θ− (φ + 2Θ−θ^*),
∠BCA = β = π / 2 + Θ− (ψ + θ^*) ………………… (34)
Expressions (15) and (16) are obtained from Expressions (33) and (34), and the folding conditions at all nodes are satisfied.
FIG. 41 corresponds to this case, and FIG. 39 can also be represented in this form.
FIG. 60 is an explanatory diagram of how to draw the developed view of FIG. 44A.
In FIG. 60, the line segments (1) and (2) are drawn from the points A and G at the same angle φ, and the line segments OB and OH taken symmetrically with respect to the perpendicular drawn from the point O to the base AG of △ OAG. Are assumed to be B and H.
Take φ in the opposite direction from points B and H, and let C and I be the intersections with OA and OG. By such operations, zigzag folding lines ABCDE... And GHLJ. The folding condition at each node is clarified in the description of FIG.
Further, it is easily understood that the developed view of FIG. 51A is a conformal spiral from the description of FIG.
FIG. 61 is an explanatory view of a pseudo-cone having an exploded view in which FIG. 44 is made into an equiangular spiral shape. FIG. 61A is an exploded view, and FIG. 61B is a half-folded conical wall with a fold line having the exploded view of FIG. 61A. FIG.
Exploded views forming an isosceles trapezoid in which the folding lines are arranged along the spiral as shown in FIGS. 61 and 61B can also form a foldable conical wall.
FIG. 62 is a developed view of a folding conical wall with a folding line in which the circumferential spiral of FIG. 51A is raised one step at the right end.
When the developed view of FIG. 62 is a conical wall, the right edge and the left edge are connected so that the right end points A, B, C,... And the left end points D, E, F, D overlap. I do.
As described above, the folding condition at the node is automatically established when the equiangular spiral or the inverted type equiangular spiral is combined, but the circumferential folding condition is the sum of the folding angles at each point in the circumferential direction. Must be set using FIG. 45 or the previous geometrical consideration so that is 2π.
The nodes on these developments are obtained by calculating the p², P³… Can be determined from the intersection of the concentric circle and the radius.
5. Manufactured collapsible conical shell and its characteristics
Observation of the folding state of the conical shell of FIG. 51B manufactured in the developed view shown in FIG. 51A and the conical shell of FIG. 56B manufactured in the developed view shown in FIG. 56A using a polypropylene sheet having a thickness of 0.2 mm. did. As a result, it was found that good folding was possible as predicted by the origami model.
6. Consideration
Assuming mainly the case of N = 6, the creation of a conical structure that can be folded in the axial direction was geometrically studied using an origami model, and it was shown that this was possible. Here, since these conical shells are formed by folding lines, they are formed in a pseudo-conical shape, and it is difficult to expand the fan-shaped development view to a conical shape obtained by joining.
It is thought that these structures can be manufactured by connecting thin metal plates, etc., processed into triangular or trapezoidal elements with joints, etc. Seems to get.
Also, the folding mechanism shown here is considered to be a basic model of a large structure such as a foldable dome roof or a tent structure. There are likely to be many problems to overcome in these realizations, but adding another ingenuity to the proposed folding model would likely lead to new forms of processing and products.
7. Conclusion
In order to create an unfolded conical shell structure that can be folded in the axial direction, several new developments have been proposed and geometric folding conditions have been verified. It was shown that it was represented by a combination of conformal spirals. As a result of examining the folding characteristics using origami and thin polymer plates, it was confirmed that folding was possible as expected with all of the proposed models.
(4) Disc-shaped folding structure with folding line
By forming a fold line using the Archimedes spiral and the Bernoulli spiral (conformal spiral), it is possible to create a disk-shaped folding structure with a folding line that can be folded in the radial direction or the circumferential direction.
1. Basic relationship
FIG. 63 is an explanatory diagram of the simplest folding method for origami.
FIG. 63 shows a case where one contact point (black dot) is composed of four folding lines. Assuming that the mountain fold is (1), (2), (3) and the valley fold is (4), the angle α formed by the extension lines (5) and (2) of (1) and the fold lines (3) and (4) ) Can be folded when their angles are equal.
This folding condition is also interpreted as follows. A line segment bisecting the angle formed by the mountain fold lines (2) and (3) is defined as (A), and a line segment perpendicular to this is defined as (B). The angle between the valley fold line (4) and the extension (5) of (1) is bisected (at an angle β) by (A). At this time, the angle between (1) and (A) also becomes β. Assuming that (B) is a mirror surface, (2) and (3) can be regarded as incident light and (4) can be regarded as reflected light.
In other words, the intersection of two orthogonal straight lines considered as mirror surfaces is defined as a node, and at this point, two zig / zag fold lines are incident and reflected at an equal angle, respectively. Is satisfied. This is named "mirror rule" of the 4-fold line method.
2. Radial / circumferential folding method
FIG. 64 is an explanatory view of a development view of a disc-shaped folding structure with a folding line. FIG. 64A is an enlarged view of a main part for explaining folding conditions, and FIG. 64B is an overall view.
As shown in FIG. 64A, consider a method of folding in the center direction by combining the folding line (1) of zig / zag toward the center direction and (2) in the circumferential direction.
N isosceles triangle elements (△ OAB, △ OBC...) Having a vertex angle of 2₀(2ΘN = 2π, base angle = π / 2Θ). Draw another sub-radiation OF, OG, OH... Rotated from the main radiation OA, OB, OC... Constituting △ OAB, △ OBC. A straight line is drawn from the outer points A, B, C... So as to form an angle φ with the main radiation, the intersections with the sub-radiation are F, G, H.₁And
Concentric circles (radius R₂) Are on the original radiation OA, OB, OC. With such a procedure, a zig / zag folding line is drawn in the radial direction. The fold lines in the circumferential direction, FG, GH, ... and IJ, JK rotate around the center at an angle of 2 ° due to symmetry.
Assuming that the point of intersection of the extension line of the line segment OG and the outer peripheral circle is point E, △ OBE becomes an isosceles triangle with a vertex angle 2θ, and ∠OBE = (π / 2) −θ.
Since {OBC = (π / 2) −}, the following equation (35) is obtained.
∠CBE = Θ-θ ……………………………………… (35)
Using 式 OBG = φ as p≡∠BGE and considering the external angle relationship of △ OBG, the following equation (36) is obtained.
p = φ + 2θ ……………………………………… (36)
∠GBC = (π / 2) −Θ−φ≡α
Is defined, and the following equation (37) is obtained by using the above equation (36).
p = (π / 2) − (α + Θ) + 2θ (37)
Next, the folding condition at the point G will be considered.
Assuming that the angle between the extension line of the line segment GH and the line segment GB is ζ, the folding condition at the point G is
ζ = ∠FGJ
Given by
ζ = π-∠EGH-p = π- (π / 2 + Θ) -p = α-2θ
Therefore, the folding condition at the point G is expressed by the following equation (38) as β≡∠FGJ.
β = α-2θ ………………………………… (38)
If we define ∠JGO≡q,
q + β = (π / 2) −Θ
From the following equation (39) is obtained.
q = (π / 2-Θ)-(α-2θ)
= Π / 2- (α + Θ) + 2θ …………………………… (39)
From Expressions (37) and (39), p = q (this relationship at point G corresponds to the establishment of a mirror law with the radiation OE as a mirror surface).
Next, when ∠BJG≡r is set in △ OJG, r = q + 2θ is obtained. The folding condition at the point J is given by r = s (∠OJP≡s), considering the line segment OB as a mirror surface. Since ∠OJK = π / 2Θ = ΘOJP + ∠PJK, if ∠PJK≡γ, γ is given by the following equation (40).
γ = (π / 2-Θ) -s
= (Π / 2-Θ)-(q + 2θ)
= Π / 2-{-2θ- {π / 2- (α + Θ) + 2θ} = α-4θ (40)
If the “swing angle” of the zig / zag fold line in the radial direction is set to 2θ, the fold line BGJP in the radial direction becomes β = α−2θ, γ = α, where α is the angle at the point B on the outer side. A value obtained by subtracting the angle by 2θ, such as −4θ.
When the two main and sub radiations (OB and OG) are considered as mirror surfaces, the relationship between the incident angle and the reflection angle is as follows.
p = q = π / 2− (α + Θ) + 2θ = φ + 2θ,
r = s = π / 2 (α + Θ) + 4θ = φ + 4θ (41)
And the angle is increased by 2θ.
Disk radius OB = R₀, The length of the line segments OG, OJ, OP is R₁, R₂, R₃When the sine theorem is used for △ OBG, △ OGJ, the following equation (42) is obtained.
R₁/ R₀= Sinφ / sin (φ + 2θ),
R₂/ R₀= Sinφ / sin (φ + 4θ),
R₃/ R₀= Sin φ / sin (φ + 6θ) (42)
After obtaining the primary and secondary radiation groups from the center, give φ to give radius R₁/ R₀, R₂/ R₀If concentric circles are drawn, and these intersections are used as nodes, a developed view that satisfies the folding condition at all nodes is obtained.
FIG. 65 is an enlarged view of a development view of the disc-shaped folding structure with a folding line shown in FIG. 64B.
FIG. 66 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 65 in a half-folded state and a small amount of folding.
FIG. 67 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 65 in a half-folded state and a state in which the amount of folding is large.
FIG. 68 is a perspective view showing a state in which the disk-shaped folding structure with folding lines having the developed view of FIG. 65 is completely folded.
The disk-shaped folding structure S with a folding line shown in FIGS. 65 to 68 has a circular hole Sa formed at the center in the developed view shown in FIG. The inner diameter of the circular hole Sa becomes smaller as it is folded from FIG. 65 to FIG. 66, FIG. 67, and FIG.
In FIG. 65, in the disc-shaped folding structure S with a folding line, a number of mountain fold lines M having a convex upper surface and a number of valley fold lines V having a concave shape are formed in a half-fold state.
At a node, which is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. Then, the number of mountain fold lines M intersecting at each node = 3, the number of valley fold lines V = 1, and the difference is 2 (= 3-1). That is, the folding line pattern of the foldable circular colored sheet is a one-node four-fold line. The fold lines are formed along a plurality of conformal spirals so as to satisfy the folding condition of the circular sheet.
The disk-shaped folding structure S with a folding line shown in FIGS. 65 to 68 has a beautiful shape according to the amount of folding when configured from a colored sheet or the like that can be folded. The colors seen in the image also change. As for the disc-shaped folding structure S with a folding line, a large one can be used as an upholstery and a small one can be used as a body decoration such as a brooch.
FIG. 69 is an explanatory view of a development view of the disc-shaped folding structure with a folding line when the swing angle of the folding line of zig / zag in the radial direction is increased as approaching the center, and FIG. 69A is for explaining the folding conditions. 69B is an overall view of FIG.
When a zig / zag fold line is drawn at the same swing angle, the interval between the fold lines is sharply reduced as the position approaches the center. Therefore, consider increasing the swing angle gradually (FIG. 69A).
When the folding lines BG and GJ are drawn at the initial swing angle 2θ, p = q and r = p + 2θ. Next, when s = r from the point J and the swing angle is, for example, 4θ, the angle t in FIG. 69 becomes s + 4θ. At the point P, a line segment PQ is drawn at an angle t = u based on the mirror rule, and the point Q is determined. When the folding lines are sequentially obtained in accordance with the mirror surface rule, the angular relationship when the swing angles are 2θ, 4θ, and 6θ is given by the following equation (43).
p = q = π / 2− (α + Θ) + 2θ = φ + 2θ,
r = s = φ + 4θ, t = u = φ + 8θ (43)
Given by Line segment OG = R₁, Line segment OJ = R₂... can be formulated by the same procedure as that for obtaining the equation (8).
FIG. 70 is an exploded view of a disc-shaped folding structure with a folding line in the case where the swing angle of the folding line of zig / zag in the radial direction is increased toward the center and the folding line in the circumferential direction is also zig / zag. 70A is an enlarged view of a main part for explaining folding conditions, and FIG. 70B is an overall view.
In FIG. 70A, the radius R₀And R₀ ^*(R₀> R₀ ^*) Are drawn alternately, and the sub-rays OF, OG... Shifted by 2θ from these are drawn. Here, F, G, and H are the intersections of line segments drawn from points A, B, and C at an angle φ with the main radiation and the sub-radiation. In this way, when drawing according to the mirror surface rule, the folding condition is satisfied at all nodes.
64B, N = 36 (2Θ = 100), and FIGS. 69B and 70B are divided into N = 18. The folding line method was used up to the eighth stage from the outer periphery. In the central part, a mountain fold and a valley fold line facing the center were alternately provided to avoid a blank area in the central part. 3. Folding combining Archimedean spiral winding and radial folding
FIG. 71 is an explanatory view of a conventionally known winding method in which the intersection of the spiral folding lines is on the Archimedes spiral.
In FIG. 64A, it is considered that the folding line zig / zag in the radial direction is eliminated.
In FIG. 71, the blank area at the center is indicated by a regular N-gon. A perpendicular is drawn from the vertex B of the regular N-gon to the side AB, and the intersection of the perpendicular and the folding line AF ((1)) is defined as C. A line segment CD is drawn so as to be symmetrical to the folding line (1) (） ACD = 2π / N).
As described above, when N fold lines are drawn from the vertices of the regular N-gon so as to be symmetrical each time the fold line is intersected, a spiral pattern at equal intervals is obtained. It is easy to see that the intersection of the radial fold line and this helical fold line is on the Archimedean spiral centered on the center.
This is a basic form of the folding (winding) method proposed by Guest et al.
FIG. 72 is a view showing a new folding line considered by the present inventor. FIG. 72A is a folding line in which the folding line (1) in the radial direction has one bending point and the spiral is reversed at this bending point in FIG. FIG. 72B is a diagram showing a line, and FIG. 72B is a diagram in which the outside of the bending point of FIG. 72A is replaced by a method of folding in a radial direction.
When a large number of bending points are introduced into the folding line in the radial direction as shown in FIG. 72A, a new folding (winding) structure is created in which the spiral of Archimedes is combined with the developed view of FIG. 64B.
In the case of FIGS. 72A and 72B, when N is set to a large value (N> 20), the interval between the folding lines becomes fine, so that the folding angle becomes extremely small at the time of winding, and this is replaced by elastic deformation in practical use. It becomes possible. For winding a polymer film or fabric having a low elastic modulus, only the main folding line is sufficient, and the introduction of the Archimedes spiral is practically formal.
4. Folding method by conformal spiral style
Folding in a conformal spiral manner refers to a folding method having a straight fold line formed along the conformal spiral.
Here, a method of folding a circular film using a conformal spiral will be described.
4.1 Basic relational expressions
FIG. 73 is an explanatory diagram of fold lines when forming a fold line for folding a circular film or a partial circular film (sector-shaped film) in a radial direction and a circumferential direction along an equiangular spiral.
As shown in FIG. 73, the circular film is divided at equal angles by radial radiation from N centers and is replaced by N isosceles triangular elements (要素 OAM, △ OMN...) Having a vertex angle of 2Θ (2Θ ·). N = 2π). Each point is defined as shown in the figure. From the point A on the outer side, a straight line forming each line of the radiation and each φ is drawn, and an intersection of the radiation (OM) rotated by 2 ° at the central angle is defined as a point B.
With the point A as a starting point, a straight line forming φ with the radiation OA is drawn, and an intersection with the radiation OM rotated by 2 ° is set as B. Next, a straight line forming an angle χ with the radiation OM is drawn, and an intersection C with the radiation ON rotated by 2Θ is determined. Next, points D, E... Are determined by taking angles φ and χ alternately in the same procedure. This zigzag line is defined as (1). Here, the angle between the line segment AB and the base of the isosceles triangle is defined as β. That is, β≡90 ° −Θ−φ. The angle between the line segment BC and the MN (that is, the angle between the line segment BB 'drawn from B in parallel with the MN and the line segment BC) is defined as γ. γ = (90 ° −Θ) −χ. The value of γ is positive when C is on the same side as the center O with respect to the line segment BB ′, and negative when C is on the opposite side to the center O. When γ = 0, the line segments BC and MN are parallel.
The radius of the circular plate is R₀When the sine theorem is used for △ OAM, the length of the radius of the point B (OB) ≡R₁Is given by the following equation (44).
R₁/ R₀= {Sin φ / sin (φ + 2})｝ ≡p (44)
In addition, the radius length (OC) of the point C is represented by R₂When the sine theorem is used for △ OBC, R₂/ R₁Is represented by the following equation (45).
R₂/ R₁= Sinχ / sin (χ + 2Θ) ≡q ……………… (45)
That is, R₂/ R₀The following equation (46) is obtained by using equations (44) and (49).
pq = R₂/ R₀
= Sinφ · sinχ / {sin (φ + 2Θ) / sin (χ + 2Θ)}
............ (46)
That is, the radius of the circular film at points D, E, F...²q, p²q², P³q².. Are given by values obtained by alternately multiplying p and q.
Now, assuming that a line (2) connecting the points A, C, E, G,... Giving the lower limit of the zigzag line (1), the dimensionless radii of these points are 1, pq, (pq), respectively.², (Pq)³,..., Each of these points is given by the intersection of a conformal helix and a ray drawn every 4 °. The line (3) connecting the points B, D, F, H,... Giving the upper limit of the zigzag line is also given by the intersection of the conformal spiral and the radiation.
FIG. 74 is a basic explanatory diagram of a folding line formed along a conformal spiral while folding a circular film or a partial circular film (sector-shaped film) around the central axis while folding the film in the circumferential direction.
Next, as shown in FIG. 74, points P and Q that are advanced clockwise by an angle of an odd multiple of 2 ° (described later) from the start point A of the folding line (1) are determined, and from these points, points (1) and (1) are completely determined. Similarly, zigzag folding lines (4) and (5) are drawn.
At this time, the fold lines (1) and (5) are alternately determined with the mountain fold line, and the fold line (4) is alternately determined with the valley fold line.
Points on the folding line (1) are named I, J, and K, points on the folding line (4) are named R, S, and T, and points on the folding line (5) are named Q, U, and V as shown in the figure. The points Q, R, I and U, S, J on the radiation, which are displaced counterclockwise by 2 °, are connected by straight lines, and they are connected to another folding line group (6), (7), (8). ).
As shown in FIG. 74, when points P, Q,... Are taken every five isosceles triangular elements, the number of zigzags n (one zigzag once, n = 1) is changed to zigzag when n = 2. Since it is repeated twice, it proceeds counterclockwise through five isosceles triangles (for example, if zigzag is repeated twice along the folding line (4) from point P in FIG. 74, it reaches point R, and from point Q Intersects with the folding line (6) that has come out. If the isosceles triangle passing through the folding line (6) is included, it means that it has advanced counterclockwise through five isosceles triangles.)
The dimensionless radius of the points Q, R, I ... is 1, (pq)², (Pq)⁴△ OQR and △ ORI in the figure are similar.
That is, the new folding line groups (6) to (8) also become equiangular spirals toward the center O. Assuming that the angle between the QR of the fold line (6) and the PE of the fold line (9) and radiation is φ, α in the figure is α = (90 ° −Θ) −φ. The angle between the outer side (the base of the isosceles triangular element) is α.
The zigzag folding line (4) reaches the point R in the figure by repeating the zigzag n times (n = 2 in FIG. 74). At this time, the radius of the point R is (p · q)ⁿGiven by
On the other hand, since the angle formed by the spiral (6) emitted from the outer side point Q and the radiation is ψ, the value of the dimensionless radius giving the point R is represented by sinψ / sin (ψ + 2Θ). If this value is equalized with equation (46), the following equation (47) is obtained.
pⁿqⁿ
= [Sinφsinχ / {sin (φ + 2Θ) sin (χ + 2Θ)}]ⁿ
= Sinψ / sin (ψ + 2Θ) …………………………… (47)
The above equation (47) is the angular relationship to be satisfied between the spirals (1), (4), and (5) which turn clockwise and move toward the center, and the spirals (6) to (8) which cross them and rotate counterclockwise. Is given.
4.2 Folding conditions
As described above, it is assumed that the equiangular spiral is bent every 2 °. Assuming that a point S in FIG. 74 composed of the valley fold line 3 and the mountain fold line 1 and a point U composed of the mountain fold line 1 are representative points, conditions for folding at these points are considered.
FIG. 75 is an enlarged view of a main part of FIG.
FIG. 75 is an enlarged view of FIG. 2 around points S and U. At the point S, since {OSJ =}, {SJR = {+ 2}. Since ∠ORS = φ, considering △ JSR, ∠JSR = π− (ψ + 2ψ) −φ. Assuming that an extension of the line segment JS is SS ', the following expression is obtained: {S'SR = π- {JSR = {+ 2} + φ].
If {USQ = {+ 2} is used, {TUS = π−χ− {USQ = π−χ − {− 2}}. When ∠S′SR = ∠TUS is set according to the folding condition, the following equation (48) is obtained as the folding condition at the point R.
2ψ + φ + χ = π-4Θ ……………………… (48)
As is clear from FIG. 75, the angle relationship of the point U is the same as that of the point S, and therefore the expression (48) is a folding condition. That is, when Expression (48) holds, the folding condition holds at all nodes.
FIG. 76 is an explanatory diagram of folding conditions when forming a fold line along a conformal spiral while folding a circular film or a partial circular film (sector-shaped film) around a central axis.
As shown in FIG. 76, when the χ value is larger than π / 2−Θ, that is, when the fold line is directed upward at points B, D, as shown in FIG. Conditions are given.
4.3 Continuity of spiral group in circumferential direction
In the above, the folding condition was obtained, but these spiral groups are equally distributed around the central axis, and a condition for maintaining the continuity of the spiral is derived. It is assumed that the zig / zag spiral (folding line (1)) starts m times from the outer peripheral point every n n isosceles triangle elements.
At this time, these start points rotate (2n + 1) · (2Θ) around the center (n: an integer). That is, the relationship between the number N of isosceles triangle elements and these values is given by (2n + 1) m = N. In the case of a circular film, it is necessary to divide the central angle 2π equally into (2n + 1) m.
That is, the division angle (vertical angle of the isosceles triangle element; 2 °) for satisfying the continuity is given by the following equation (49).
2Θ = 2π / ｛(2n + 1) · m｝ ……………………… (49)
Only by dividing the circular membrane in this way, the condition that the continuity of the m spiral groups is satisfied in the entire area of the membrane is achieved.
By using φ = π−2 {− {− 4} obtained from Expression (48) for Expression (47), the following Expression (50) is obtained.
(Pq)ⁿ
= [Sin (2ψ + χ + 4Θ) ・ sinχ / ｛sin (2ψ + χ-2Θ) sin (χ + 2Θ)｝]ⁿ
= Sinψ / sin (ψ + 2Θ) ……………………………………… (50)
By giving 2Θ and χ value that are divided so as to satisfy Expression (49), ψ that satisfies Expression (50) can be calculated by numerical calculation. Further, the β value is also obtained by the equation (48), and a developed view is drawn by a spiral folding line that satisfies the folding condition at all the nodes.
4.4 When bending the sub-fold line at an arbitrary rotation angle (φ = φ)
In the above, a development view is obtained in which the circular film is equally divided into N isosceles triangular elements having a vertex angle of 2 °, and the folding line is bent every time these elements are passed. In the case of FIG. 76, in the special case where the m spirals are always bent upward at an equal angle (φ = χ), a configuration of another folded development is possible.
FIG. 77 is an explanatory diagram of folding conditions when the main fold line is bent at an equal angle to radiation.
Points A, B, C and A ', B' on the outer circumference of the circle are determined as shown in FIG. A fold line (1) rising rightward is drawn from point A, and a fold line (2) rising leftward is drawn from point B. (1) is the central angle 2θ₁(Angle of the string AA '), (2) is the central angle 2θ₂(The angle formed by the string A'B) and intersect at the point D. The fold line (1) is at an angle 放射線 (the angle α between the outer side AI) and the fold line (2) is the radiation from the center. And the angle φ (the angle β with the outer side BI).
The folding condition at point D is considered below.
∠ADA '= φ + 2θ₁, ∠BDB '= ψ + 2θ₂
It becomes. If the extension point of BD is H,
∠ADH = π-｛(φ + ψ) + (θ₁+ Θ₂)｝
It becomes.
Since ∠FDO = φ and ∠GDO = ψ,
{FDG = φ +}
It becomes.
When the folding lines (2), (1), and (3) are mountain-folded, GD ((4)) is a valley-folding line, and the folding condition at the point D is as follows: ∠ADH and ∠FDG are equalized. 51) is obtained.
φ + ψ = π / 2−2Θ or (α + β) = π / 2 (51)
OD to R₁Then, if the sine theorem is used for △ OAD, the following equation (52) is obtained.
R₁/ R₀= Sinψ / sin (ψ + θ₁₎      ............ (52)
On the other hand, the following equation (53) is obtained for △ OBD.
R₁/ R₀= Sinφ / sin (φ + θ₂) ………………… (53)
Both of these values give the radius of the point D. If these values are equalized and the above φ = π / 2-{-2} is used, the following equation (54) is obtained.
sin (β-θ₁) / Sin (β + θ₁)
= Sin (π / 2−θ₂−β) / sin (π / 2 + θ)₂−β)… (54)
θ₁, Θ₂Is given, φ that satisfies Expression (53) is determined by numerical calculation. Ψ is obtained from Expression (51), and by using these values, a developed view that satisfies the folding condition at all nodes is obtained.
4.5 Application to the manufacture of conical shells
In FIG. 74, it is assumed that the zigzag spiral (folding line (1)) has m lines, and the angle formed by the starting point on the outer side is (2n + 1) · (2 °). In the case of a disc, (2n + 1) · m · (2Θ) = 2π, but if the value of (2n + 1) · m · (2Θ) is smaller than 2π, a cone develops, and in this case also the folding is performed. Is possible.
5. Examples of folding products
FIGS. 78 to 80 show a developed view obtained by the above-described theory and a folded example thereof.
FIG. 78 shows an example of folding around the center with two zigzag spirals (m = 2) as folding lines, where n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 20 °.
FIG. 79 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 78 is an example of a folded development view when γ = 0 °, showing an example in which the angle of the folding line with respect to the radiation is different from FIG. 78.
FIG. 80 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 10, the number of isosceles triangular elements N = (2n + 1) m = 42, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
78 to 80 are 2８０ = 20 °, 20 ° and 180 ° / 21, respectively, and these values and the γ value determined by χ (γ = χ−90 + Θ) are respectively γ = π / 9, 0 and 0 was given, and the ψ value satisfying the equation (50) was obtained by numerical calculation. When this ψ value is substituted into Expression (48), φ is determined.
From α + ψ = 90−Θ and β + φ = 90−Θ, the values of α and β in FIGS. 78 to 80 can be obtained. For example, in FIG. 78, α = 69.763..., Β = 20.474.
In the examples of FIGS. 78 to 80, the circular film whose main fold line is formed of two spirals is folded to a new plane. In the state of the side surface after folding in FIGS. 78 and 79, when the γ value increases, the central portion is folded in a shape protruding upward. This is advantageous during the operation of folding / unfolding the structure. When FIG. 79 and FIG. 80 are compared, the larger the number of divisions, the smaller the folding.
FIG. 81 shows an example of folding around the center using two zigzag spirals (m = 2) as folding lines, where n = 4, the number of isosceles triangular elements N = (2n + 1) m = 18, It is a figure which shows the example of the development view of the disk-shaped folding structure with a folding line in case of (gamma) = 0 degree.
FIG. 82 is a perspective view of the disc-shaped folding structure with a folding line having the developed view of FIG. 81 in a half-folded state with a small amount of folding.
FIG. 83 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 81 in a half-folded state and a state in which the amount of folding is large.
FIG. 84 is a perspective view showing a state in which the disk-shaped folding structure with a folding line having the developed view of FIG. 81 is completely folded.
81 to 84 folds a circular sheet (a disk-shaped fold structure with a fold line) developed as shown in FIG. 81 along the fold lines M and V. 82 in the half-fold state where the folding amount is small, and the state shown in FIG. 83 is obtained when the folding amount is increased. FIG. 84 is almost folded, and when completely folded, it is folded on a plane.
Since the shape of the folding lines M and V of the disc-shaped folding structure S with folding lines in FIGS. 81 to 84 is different from that in FIGS. In this case, a shape change and a color change different from those in FIGS. 65 to 68 can be obtained.
Like the disc-shaped folding structure S with the folding line, the disc-shaped folding structure S with the folding line can be used as an upholstery with a large size, and can be used as a brooch or the like with a small size. It can be used as a decoration.
FIGS. 85 to 87 show development views in the case of three spirals, four spirals, and one spiral.
FIG. 85 shows an example of folding around the center using four zigzag spirals (m = 4) as folding lines, where n = 7, the number of isosceles triangular elements N = (2n + 1) m = 60, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
FIG. 86 shows an example in which three zigzag spirals (m = 3) are used as folding lines and folded around the center, where n = 8, the number of isosceles triangular elements N = (2n + 1) m = 51, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
FIG. 87 shows an example in which one zigzag spiral (m = 1) is used as a fold line and folded around the center, where n = 10, the number of isosceles triangle elements N = (2n + 1) m = 21, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
When four main fold lines in FIG. 85 are spirals, the main fold lines are folded in a rectangular shape, and when three main fold lines are spirals in FIG. 86, the main fold lines are folded in a triangular shape. In the case of one spiral shown in FIG. 87, the spiral is wound around the central axis.
When γ = 0 ° and α and β values are obtained in the same manner as described above, the following is obtained.
In FIG. 85, γ = 0 °, α = 75.432..., Β = 29.132.
86, γ = 0 °, α = 76.233..., Β = 27.533.
In FIG. 87, γ = 0 °, α = 76.714..., Β = 26.572.
FIG. 88 shows an example in which four zigzag spirals (m = 4) are used as folding lines and folded around the center, where n = 4, the number of isosceles triangular elements N = (2n + 1) m = 60, It is a figure which shows the example of the development view of the disk-shaped folding structure with a folding line in case of (gamma) = 0 degree.
FIG. 89 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 88 in a half-folded state and a state in which the amount of folding is small.
FIG. 90 is a perspective view of the disc-shaped folding structure with a folding line having the developed view of FIG. 88 in a half-folded state and a state in which the amount of folding is large.
FIG. 91 is a perspective view showing a state in which the disk-shaped folding structure with a folding line having the developed view of FIG. 88 is completely folded.
The disc-shaped folding structure S with a folding line shown in FIGS. 88 to 91 has a circular hole Sa formed at the center in the developed view shown in FIG. The inner diameter of the circular hole Sa becomes smaller as it is folded from FIG. 88 to FIG. 89, FIG. 90, and FIG.
The disc-shaped folding structure S with a folding line shown in FIGS. 88 to 91 folds a circular sheet (a disc-like folding structure with a folding line) developed as shown in FIG. 88 along the folding lines M and V. In the half-fold state where the amount of folding is small, the state is as shown in FIG. 89. When the amount of folding is increased, the state shown in FIG. 90 is obtained. FIG. 91 shows the fully folded state in the fully folded state.
88 to 91, the shapes of the folding lines M and V are different from those of FIGS. 65 to 68 and FIGS. 81 to 84, so that the foldable colored sheet is provided. In such a case, a change in shape and a change in color different from those in FIGS. 65 to 68 and FIGS. 81 to 84 can be obtained.
FIG. 92 is a developed view in the case where the number of spirals serving as main folding lines is large (m = 12).
In FIG. 92, m = 12 and n = 1, and the disk is divided into 36 equal parts. When γ = 25 ° is given and α and β are obtained in the same manner as described above, the following is obtained.
α = 55.270 °, β = 44.46 °.
If the number of divisions of the central angle is doubled in this folding, the folding efficiency is reduced by half, but the number of folding lines is increased, which is not suitable for engineering. This is rather interesting from a modeling point of view.
FIG. 93 is a developed view composed of two types of conformal spirals based on FIG. 77. Division number N = 12, θ₁= Π / 180, θ₂= 29π / 180, and φ is approximately π / 18. When the developed view of FIG. 93 is folded, it is satisfactorily wound around the center in a vertically symmetric manner. FIG. 93 suggests that these fold lines are replaced by elastic deformation during winding because the sub-fold lines are fine.
Based on the developed view of FIG. 93, a circular stainless thin plate (thickness t = 0.05 mm, radius R = 140 mm) was cut into 12 pieces along a main fold line, and this was joined with a transparent kraft film. Was produced. This can be wound up in the same manner as that of FIG. 93, and it can be seen that it can be stored only by the main folding line without introducing a fine sub-folding line.
FIG. 94 is an exploded view of a disc-shaped folding structure with fold lines provided with alternating mountain fold lines and valley fold lines.
In FIG. 94, a disc-shaped folding structure S with a folding line has a mountain fold line M along an equiangular spiral toward the center from a point at which the outer periphery is equally divided into N (N is a positive integer and N ≧ 4). A valley fold line V is formed along an equiangular spiral from the point at which the equally-divided outer circumference is further divided into two equal parts.
The disk-shaped folding structure S with a folding line having the development view shown in FIG. 94 can be folded and developed by a simple folding line, and can be deployed by elastic deformation, so that it can be self-deployed. Since the fold line group becomes fine at the center, it is necessary to engineeringly combine it with the folding method such as the above-mentioned method, except for a soft and thin cloth or rubber.
FIG. 95 shows the development of a disk-shaped folding structure with fold lines in which mountain fold lines and valley fold lines are provided alternately, and the circumferential lengths of the valley fold line and the left and right mountain fold lines are different on the left and right. FIG.
In FIG. 95, a disc-shaped folding structure S with a folding line has a mountain fold line M along an equiangular spiral toward the center from a point at which the outer periphery is equally divided into N (N is a positive integer and N ≧ 4). The valley fold line V is formed along the equiangular spiral from the point where the formed outer periphery is further divided into two at an appropriate division ratio. The equiangular spiral in FIG. 95 is wound counterclockwise from the center toward the outer periphery, and the angle between the valley fold line V and the right-hand ridge fold line M is β, and the left fold fold line M is If α is an angle, α> β.
In this case, when folding along the folding line of the disc-shaped folding structure S with a folding line, the outer peripheral portion is folded while being shifted downward in the axial direction.
FIG. 96 is a view in which a fan-shaped portion between adjacent mountain fold lines in FIG. 95 is removed.
When the outer edges of both ends in the circumferential direction in FIG. 96 are connected so as to overlap, a conical wall is formed. This conical wall can also be folded along the mountain fold line M and the valley fold line V. This conical wall is also folded while its outer peripheral portion is shifted downward in the axial direction.
(5) Applications of folding structures with folding lines
Based on the results of the above-mentioned folding method for flat plates and cylinders, the results of basic research aimed at their practical application will be described. Here, the following points are mainly described.
(A) Modeling of a folding method for creating a high-rigidity, high-strength core material by bending a flat plate in a zigzag manner to make it three-dimensional, and a processing method thereof.
(B) A cylindrical deployment structure model with a simple mechanism devised based on the folding characteristics of the cylinder in the axial direction.
The former considers not only the creation of high-strength members for aerospace, but also the realization of reuse of waste paper and the like, and the latter considers the use for consumer such as shooters.
1. Folding and non-folding conditions
97 is an explanatory diagram of the folding condition of the sheet-like member, FIG. 97A is a developed view before folding, and FIG. 97B is a diagram showing a state where the sheet-like member is folded along a folding line in FIG. 97A.
Consider the circular thin flat paper shown in FIG. 97A, the center is O, the line segments OA, OC, OD are mountain-folded, and OB is valley-folded. Angles formed by these line segments are set as α to δ as shown in FIG. 97A.
Now, when OB is folded in a valley, coordinate axes are defined as shown in FIG. 97B, and a line segment OA is taken on the X axis, the coordinates of points B, C, and D are (-cosβ, sinβ, O), (x, y, z) and (−cos α, sin α, O).
The angle between the line segments OB and OC is γ, the angle between the line segment OD and OC is δ, α + β + γ + δ = 2π, x²+ Y²+ Z²If = 1 is used, the z coordinate of the point C is given by the following equation (55).
(1-z²) Sin (α-β)
= Cos²γ + cos²δ-2 cos γ cos δ cos (α-β)
............ (55)
Since the coordinates of the point C are determined by the equation (55), the angle between the plane OBC and the bottom surface (xy plane) is obtained. If z = 0 in equation (55), the condition for folding is satisfied.
When z = 0 and δ is deleted from the right side and compared with the left side, the following equation (56) is obtained.
cos²(Α + β + γ) + cos²γ = cos²α + cos²β,
cos (α + β + γ) · cosγ = cosαcosβ
……………………… (56)
The relationship satisfying the two equations (55) and (56) is given by the following equations (57) and (58).
α + γ = π ………………………………………… (57)
β + γ = π ……………………………………… (58)
Since Expression (58) is a condition for folding a circular plane into two, Expression (57) is employed here as a folding condition.
A structure formed in a state where the folding condition is satisfied has low stability, and a structure in which the folding condition is not satisfied generally has a high stability as a structure. Therefore, in this report, the condition (a) is mainly used for non-folding, and the condition (b) is used for folding.
2. Modeling core materials
2.1 Origami model
For the creation of core materials using origami models, the concept has already been proposed by Miura. A typical example is a double corrugated core (DCC) based on a flat plate folding method (miura ori).
FIG. 98 is an explanatory diagram of a DCC (double corrugated core), and is a diagram in which the DCC is developed.
FIG. 99 is a diagram showing the vertical folding line group of FIG. 98 as zig / zag.
In these, the nodes are composed of four fold lines, and the folding condition is satisfied at all the nodes. Therefore, when subjected to surface pressure, these cores are structures that are expanded to the original plane, and are unstable.
In order to avoid this, it is essential that the upper and lower surfaces of the core are firmly joined to the surface material. However, since the joint is not a surface, the bonding technique is considered to govern the success or failure of this structure.
100A is an explanatory view of a newly devised model of a core having a joint, FIG. 100A is a developed view, FIG. 100B is a plan view of the developed view of FIG. 100A in a half-folded state, and FIG. 100C is an expanded view of FIG. 100A. It is an external view of what folded the figure and made it three-dimensional.
FIG. 101 is an explanatory view of another model of a newly devised core having a joint. FIG. 101A is a developed view, FIG. 101B is a plan view of the developed view of FIG. 101A in a half-folded state, and FIG. 101C is FIG. 3 is an external view of a three-dimensional view obtained by folding the development view of FIG.
It can be seen that these have large joints, with the part A being the upper surface and the part B being the lower surface. Here, the node is composed of four or five fold lines.
FIG. 102 is an explanatory view of a model devised by the present inventor that does not satisfy another folding condition of a core having a joint, FIG. 102A is a developed view, and FIG. 102B is an enlarged view of a main part of FIG. 102A.
FIG. 103 is an explanatory view of a core formed by folding the developed view of FIG. 102A, FIG. 103A is a perspective view of the folded core, and FIG. 103B is a perspective view of a sheet bonded to the lower surface of the core of FIG. 103A. .
The folding line shown in FIG. 102A does not satisfy the folding condition, and when the flat plate is made three-dimensional, it is considered that the folding line has a square shape. In FIG. 102B, oblique fold lines DB, EC, A'E ', B'F', etc., are at 45 ° to the vertical fold lines AC, DF, A'C ', D'F'.
When the valley fold line DB is folded, the AE portions come into contact with each other, and △ ABD and △ EDB are joined. All joints similar to the joints S1 and S2 are denoted by S1 and S2.
When the valley fold line A'-E 'is folded, the B'-D' members come into contact with each other, and △ D'A'E 'and △ B'A'E' are joined. All joints similar to the joints S3 and S4 are denoted by S3 and S4.
By bonding the joints S1 and S2 and bonding the joints S3 and S4, a structurally stable core material (FIG. 103A) composed of square fold lines is created. The core shown in FIG. 103B with a sheet adhered to the lower surface of the core can withstand a large compressive force.
FIG. 104 is an explanatory view of a model devised by the present inventor that does not satisfy another folding condition of a core having a joint, FIG. 104A is a developed view, and FIG. 104B is an enlarged view of a main part of FIG. 104A.
The folding line shown in FIG. 104A does not satisfy the folding condition, and is considered so that the folding line has a square shape when the flat plate is made three-dimensional. In FIG. 104B, CD, BE, etc. are at 60 ° with respect to the vertical folding lines AD, CB. When the valley fold line CE is folded, portions AB come into contact, and △ ACE and △ BCE are joined. Bonding the joints creates a structurally stable core material (FIG. 104A) composed of square fold lines.
3.2 Honeycomb core model
The honeycomb core is representative of a lightweight structure.
FIG. 105 is an explanatory diagram of a method of manufacturing a honeycomb core from one plate, FIG. 105A is a developed view, and FIG. 105B is a view of a honeycomb core manufactured from a plate having the developed view of FIG. 105A.
In FIG. 105A, a dotted line is a valley fold line, and a mountain fold line indicated by a dashed line has a cut C (cut portion). When the joining portions AB on both sides of the valley fold line in FIG. 105A are bonded to every other valley fold line and spread on both sides, a mesh-shaped honeycomb core shown in FIG. 105B can be manufactured. When this manufacturing method is used, there is a characteristic that the honeycomb core becomes a cylindrical honeycomb core.
4. Fabrication of core material
4.1 Manufacturing method of core material
The two dies are manufactured by cutting a 0.2-0.3 mm phosphorous copper plate or a steel plate at the folding lines shown in FIGS. 101 to 102 and joining them up and down with a kraft film or joining them with hinges. Then, when a thin paper to be processed or an aluminum alloy plate (up to 0.08 mm) is inserted between them and bent, a product as shown in FIGS. 101B to 102B can be instantaneously manufactured.
By bonding only the bonding regions S1 and S2 of FIG. 102B, not bonding S3 and S4, but bonding a thin film on one side (or bonding the other way) to a cylindrical surface, Thus, it is possible to manufacture a lightweight and highly rigid pipe.
FIG. 106 is a view showing a folding line forming apparatus for manufacturing the core material shown in FIG. 103A.
In FIG. 106, a fold line forming die K is formed by bonding kraft films F to both surfaces of a large number of square parts (metal thin plates) P1 and parallelogram parts P2 separated by fold lines. The folding line forming mold K has a pair of foldable flexible molds K1 and K2 which are configured to be line-symmetric with respect to the central axis L. The above-mentioned flexible molds (folding molds) K1 and K2 are manufactured, and once the fold line is formed as the mountain fold line and the valley fold line, the mountain fold and the valley fold can be easily performed from the next time. Therefore, when the flexible mold K1 is folded along the opening / closing axis L with the paper or resin sheet placed on the surface of the flexible mold K2 on one side of the opening / closing axis L, the paper or the resin sheet becomes a pair of flexible molds. It is sandwiched between the dies K1 and K2. If the flexible molds K1 and K2 are simultaneously folded along the folding line in this state (the state where the flexible molds K1 and K2 overlap), a folding line is formed on a paper or a resin sheet or the like.
4.2 Fabricated core material
A paper core and an aluminum core were manufactured using the above-mentioned folding mold with the model of FIG. 102 which is considered to be the closest to practical use. The paper core is shown in FIG. 103A above.
FIG. 107 is an explanatory view of the manufactured aluminum core. FIG. 107A is a perspective view, and FIG. 107B is a developed view, which has the same shape as the developed view of the paper shown in FIG. 103A.
The compressive strength of these products is about 0.4 to 0.8 MPa (specific gravity; 80 to 120 kg / m) for paper products.³), About 1-1.5MPa (about 100Kg / m³) (Square size: 10 to 11 mm, sample size: 50 × 50 mm).
5. Folding / unfolding model
In the section of “(2) Cylindrical folding structure with folding line” described above, a plurality of examples of the folding method of the cylinder in the axial direction have been described. FIGS. 108 to 109 show development views of these representative ones and examples of new structures using them.
FIG. 108 is an explanatory diagram of an application example of the structure with a cylindrical folding line, and FIG. 108A is a developed view.
When the valley fold line (dotted line) in FIG. 108 is cut and A and B are joined to form a cylinder, a structure composed of hexagonal members is obtained. If the hexagonal member is replaced with a narrow plate, a truss structure that can expand and contract in the axial direction can be manufactured.
FIG. 109 is an explanatory diagram of an application example of a spiral cylindrical structure with a folding line. FIG. 109A is a developed view, and FIG. 109B is a view showing a stretchable inflatable structure formed based on FIG. 109A.
The present invention has been made in view of the above research results, and has an object to be described in the following (1).
(1) A novel folding line of a structure with a folding line, in which a wall-shaped structure is divided into polygonal flat walls by a number of folding lines, and a folding line at a boundary portion of each divided flat wall can be folded. And a novel foldable structure using the novel fold line, a novel fold line method, and a novel mold for forming a fold line and a method of forming a fold line.
Disclosure of the invention
Next, a description will be given of the present invention which has solved the above-mentioned problem. Elements of the present invention include those in parentheses in which reference numerals of the elements of the embodiments are used in order to facilitate correspondence with the elements of the embodiments described later. Add it.
The reason why the present invention is described in correspondence with the reference numerals of the embodiments described below is to facilitate understanding of the present invention, and not to limit the scope of the present invention to the embodiments.
(First invention)
In order to solve the above problems, a structure with a folding line according to a first aspect of the present invention includes the following constituent features (A01) to (A05).
(A01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting portions connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. And a fold line provided with a linear fold line (M, V) foldable along the linear part connection portion, wherein the fold line (M, V) is a fold line. A structure having a fold line having a plurality of mountain fold lines (M) in which the one surface side forms a mountain fold and one or more valley fold lines in which a valley fold is formed when viewed from one surface side of the structure;
(A02) A plurality of nodes, which are intersections of the mountain fold line (M) and the valley fold line, are arranged at predetermined intervals, and the number of the mountain fold lines (M) and the number of the valley fold lines intersecting at one node is determined. The plurality of folding lines (M, V) formed so that the difference is 2,
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and the second mountain fold line (M3) A one-node four-fold line formed by a first valley fold line (V1) disposed between the mountain fold lines (M2) and opposite to the third mountain fold line (M3); A plurality of folding lines (M1 to M3, V1),
(A04) The node is defined as the origin O, the X axis is taken in the direction of the extension of the third mountain fold line (M3), and the first mountain fold line (M1) or the second mountain fold line (M2) is taken out. When one of the mountain fold lines forms an angle with the X axis, α, and the other mountain fold line forms an angle with the first valley fold line (V1), γ is formed such that α = γ. The plurality of folding lines (M1 to M3, V1);
(A05) The structure with a fold line having the quadrangular parts (P; P1, P2; P1 to P5) other than the parallelogram.
(Operation of the first invention)
In the structure with the folding line according to the first aspect of the present invention, the node is set as the origin O, the X-axis is taken in the direction of the extension of the third mountain folding line (M3), and the first mountain folding line (M1) is taken. ) Or the angle formed by one of the second mountain fold lines (M2) with the X axis is α, and the angle formed by the other mountain fold line with the first valley fold line (V1) is γ. In this case, a plurality of polygonal parts (P; P1, P2; P1 to P5) can be folded by the plurality of folding lines (M, V) formed so that α = γ. For this reason, the structure with a folding line can be changed from a folded state having a small outer shape to an extended state having a large outer shape.
In addition, since the structure with folding lines has parts (P; P1, P2; P1 to P5) having a shape (a quadrilateral other than a parallelogram) different from the conventional shape, the folded state is small. In the extended state of the large external shape, it is possible to manufacture a structure with a folding line having a shape different from the conventional one.
(Embodiment 1 of the first invention)
The structure with a folding line according to the first embodiment of the first invention is characterized in that the first invention has the following constituent features (A06).
(A06) The structure with a fold line, wherein the part and the part connection portion provided with the fold line are formed of different members.
(Operation of First Embodiment of First Invention)
In the structure with a fold line according to the first embodiment of the first invention having the above-described configuration, the part and the part connection part provided with the fold line are formed of different members. It can be constituted by a rigid thin plate such as a metal plate, and the part connection portion can be constituted by a hinge member. Therefore, it is possible to provide a robust folding line structure.
(Embodiment 2 of the first invention)
The structure with a fold line according to the second embodiment of the first invention is characterized in that the first invention has the following configuration requirement (A07).
(A07) The structure with a fold line constituted by an integrally molded product with a fold line.
(Operation of Embodiment 2 of First Invention)
Since the structure with the folding line according to the second embodiment of the first invention having the above-described configuration is formed by an integral molded product with the folding line, the structure with the folding line can be easily manufactured by integral molding. it can. The fold line can be formed at the same time as molding, but when the structure with a fold line is a sheet-shaped member, it is also possible to form the fold line on a sheet-like member manufactured integrally. It is.
(Second invention)
A structure with a fold line according to a second aspect of the present invention includes the following components (A01) to (A04) and (A08).
(A01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting portions connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. A fold line structure provided with a linear fold line that is foldable along the linear part connection portion, wherein the fold line is viewed from one surface side of the fold line structure. A structure with a folding line, the structure having a plurality of mountain folding lines (M) having a mountain fold on one surface side and one or more valley fold lines (V) having a valley fold;
(A02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of folding lines (M, V) formed at
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and the second mountain fold line (M3) A one-node four-fold line formed by a first valley fold line (V1) disposed between the mountain fold lines (M2) and opposite to the third mountain fold line (M3); A plurality of folding lines (M1 to M3, V1),
(A04) The node is defined as the origin O, the X axis is taken in the direction of the extension of the third mountain fold line (M3), and the first mountain fold line (M1) or the second mountain fold line (M2) is taken out. When one of the mountain fold lines forms an angle with the X axis, α, and the other mountain fold line forms an angle with the first valley fold line (V1), γ is formed such that α = γ. The plurality of folding lines (M1 to M3, V1);
(A08) The structure with a folding line having the quadrangular and triangular parts (P; P1, P2).
(Operation of the second invention)
Since the structure with the folding line of the second invention having the above-described configuration has quadrangular and triangular parts (P; P1, P2; P1 to P5), it can be used in a folded state with a small outer shape and an extended state with a large outer shape. Thus, it is possible to manufacture a structure with a folding line having a different shape from the conventional one.
(Third invention)
A structure with a folding line according to a third aspect of the invention includes the following constituent features (A01) to (A05) and (A09).
(A01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting portions connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. A fold line structure provided with a linear fold line that is foldable along the linear part connection portion, wherein the fold line is viewed from one surface side of the fold line structure. A structure with a folding line, the structure having a plurality of mountain folding lines (M) having a mountain fold on one surface side and one or more valley fold lines (V) having a valley fold;
(A02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of folding lines (M1 to M3, V1) formed at
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and the second mountain fold line (M3) A one-node four-fold line formed by a first valley fold line (V1) disposed between the mountain fold lines (M2) and opposite to the third mountain fold line (M3); Multiple fold lines,
(A04) The node is defined as the origin O, the X axis is taken in the direction of the extension of the third mountain fold line (M3), and the first mountain fold line (M1) or the second mountain fold line (M2) is taken out. When one of the mountain fold lines forms an angle with the X axis, α, and the other mountain fold line forms an angle with the first valley fold line (V1), γ is formed such that α = γ. The plurality of folding lines (M1 to M3, V1);
(A05) The structure with a fold line having the quadrangular parts (P; P1, P2; P1 to P5) other than the parallelogram.
(A09) When the fold line is extended, the shape becomes a flat plate, and when the fold line is bent along the mountain fold line and the valley fold line, the outer shape is reduced and becomes a flat plate shape having irregularities on the surface. The structure with a fold line, which can be folded and extended in a flat plate shape so that the outer shape becomes a three-dimensional structure with a further reduced size when completely folded along the valley fold line.
(Operation of the third invention)
The structure with a folding line according to the third aspect of the present invention having the above configuration has quadrilateral parts (P; P1, P2; P1 to P5) other than the parallelogram. In this state, a flat plate-shaped folded line structure having a different shape from the conventional flat plate-shaped folded line structure can be manufactured.
(4th invention)
A structure with a fold line according to a fourth aspect of the present invention is provided with the following constituent requirements (A01) to (A04), (A010), and (A011).
(A01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting parts connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. A fold line structure provided with a linear fold line that is foldable along the linear part connection portion, wherein the fold line is viewed from one surface side of the fold line structure. A structure with a folding line, the structure having a plurality of mountain folding lines (M) having a mountain fold on one surface side and one or more valley fold lines (V) having a valley fold;
(A02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of folding lines (M1 to M3, V1) formed at
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and the second mountain fold line (M3) A one-node four-fold line formed by a first valley fold line (V1) disposed between the mountain fold lines (M2) and opposite to the third mountain fold line (M3); A plurality of folding lines (M1 to M3, V1),
(A04) The node is defined as the origin O, the X axis is taken in the direction of the extension of the third mountain fold line (M3), and the first mountain fold line (M1) or the second mountain fold line (M2) is taken out. When one of the mountain fold lines forms an angle with the X axis, α, and the other mountain fold line forms an angle with the first valley fold line (V1), γ is formed such that α = γ. The plurality of folding lines (M1 to M3, V1);
(A010) A cylindrical wall or a conical wall having a cylindrical wall or a conical wall when the fold line is extended, and having an uneven outer shape when the fold line is bent along the mountain fold line and the valley fold line. Forming a cylindrical wall or a cone wall having a thickness having irregularities whose outer shape is further reduced in a completely folded state along the mountain fold line and the valley fold line,
(A011) The structure with a fold line having a plurality of fold lines (M1 to M3, V1) continuous in a plane perpendicular to the axis of the cylindrical wall or the conical wall.
(Operation of the fourth invention)
The structure with a folding line according to the fourth invention having the above configuration has a plurality of folding lines (M1 to M3, V1) that are continuous in a plane perpendicular to the axis of the cylindrical wall or the conical wall, and thus has a small external shape. In the folded state and the extended state with a large external shape, a cylindrical or conical fold line structure having a different shape from the conventional fold line structure can be manufactured.
(Fifth invention)
A structure with a folding line according to a fifth aspect of the present invention is provided with the following constituent requirements (A01) to (A04), (A012), and (A013).
(A01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting portions connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. A fold line structure provided with a linear fold line that is foldable along the linear part connection portion, wherein the fold line is viewed from one surface side of the fold line structure. A structure with a folding line, the structure having a plurality of mountain folding lines (M) having a mountain fold on one surface side and one or more valley fold lines (V) having a valley fold;
(A02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of folding lines (M1 to M3, V1) formed at
(A03) A first mountain fold line (M1), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (M1) and the second mountain fold line (M3) A one-node four-fold line formed by a first valley fold line (V1) disposed between the mountain fold lines (M2) and opposite to the third mountain fold line (M3); A plurality of folding lines (M1 to M3, V1),
(A04) The node is defined as the origin O, the X axis is taken in the direction of the extension of the third mountain fold line (M3), and the first mountain fold line (M1) or the second mountain fold line (M2) is taken out. When one of the mountain fold lines forms an angle with the X axis, α, and the other mountain fold line forms an angle with the first valley fold line (V1), γ is formed such that α = γ. The plurality of folding lines (M1 to M3, V1);
(A012) A tubular wall or cone having irregularities whose outer shape is reduced when the folding line is extended and forms a simple wall or a conical wall, and when the folding line is folded along the mountain fold line and the valley fold line. A wall-forming structure, wherein in the state of being completely folded along the mountain fold line and the valley fold line, the structure with the fold line forming a thick cylindrical wall or a cone wall having irregularities whose outer shape is further reduced,
(A013) The folding line structure in which the parts (P; P1, P2; P1 to P5) have a polygonal shape of a quadrangle or more.
(Operation of the fifth invention)
Since the structure with a folding line according to the fifth aspect of the present invention having the above-described structure has polygonal parts (P; P1, P2; P1 to P5) of four or more squares, the folded state is small and the extended state is large. In the above, a cylindrical or conical fold line structure having a shape different from that of the conventional fold line structure can be manufactured.
(Sixth invention)
A structure with a folding line according to a sixth aspect of the present invention includes the following constituent features (B01) to (B04).
(B01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting portions connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. A fold line structure provided with a linear fold line that is foldable along the linear part connection portion, wherein the fold line is viewed from one surface side of the fold line structure. A structure with a folding line, the structure having a plurality of mountain folding lines (M) having a mountain fold on one surface side and one or more valley fold lines (V) having a valley fold;
(B02) A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of folding lines (M1 to M4, V1, V2) formed in
(B03) a first mountain fold line (M1), a second mountain fold line (M2), a third mountain fold line (M3), and a fourth mountain fold line (M4) extending radially from one node; A first valley formed between the mountain fold line (M1) and the second mountain fold line (M2) and opposite to the third mountain fold line (M3) and the fourth mountain fold line (M4). A fold line (V1) and a third fold line (M3) disposed between the third fold line (M3) and the fourth fold line (M4) and the first fold line (M1) and the second fold line (M2). Has a second valley fold line (M1) and a fourth valley fold line (M4) adjacent to each other and a second valley fold line (M2) and a third valley fold line (M2). A plurality of fold lines (M1 to M4, V1, V2) each having one node and six fold lines in which mountain fold lines (M3) are arranged adjacent to each other;
(B04) The node is defined as the origin O, the X axis is taken in the direction of the extension of the first valley fold line (V1), and the first mountain fold line (M1) and the second mountain fold line (M2) are the second fold line (M2). The angles formed by the first valley fold line (V1) are α and β, respectively, and the angles formed by the third fold line (M3) and the fourth fold line (M4) with the second valley fold line are γ and δ, respectively. And the plurality of fold lines (M1 to M4, V1, V2) formed so that β-α = δ−γ + θ, where θ is the angle between the X axis and the second valley fold line.
(Operation of the sixth invention)
In the structure with a folding line according to the sixth aspect of the invention having the above configuration, the node is set as the origin O, the X-axis is taken in the direction of the extension of the first valley folding line (V1), and the first mountain folding line (M1 ) And the angle formed by the second mountain fold line (M2) with the first valley fold line (V1) are α and β, respectively, and the third mountain fold line (M3) and the fourth mountain fold line (M4) are When the angles formed by the second valley fold line are γ and δ, respectively, and when the angle formed by the X axis and the second valley fold line is θ, the plurality formed so that β−α = δ−γ + θ. , The parts (P; P1, P2; P1 to P5) having different shapes from the conventional ones can be used, and the parts (P; P1, P2; P1 to P1) can be used. P5) can be folded. For this reason, the structure with a folding line can be changed from a folded state having a small outer shape to an extended state having a large outer shape.
Further, in the folded state and the extended state, a structure with a folding line having a shape different from that of the related art can be provided.
(Embodiment 1 of the sixth invention)
The structure with a folding line according to the first embodiment of the sixth invention is characterized in that, in the sixth invention, the following configuration requirement (B05) is provided.
(B05) When the fold line is extended, the shape becomes a flat plate, and when the fold line is bent along the ridge fold line (M) and the valley fold line, the outer shape is reduced and the flat shape is formed with unevenness on the surface. The structure with folding lines that can be folded and extended in a flat plate shape so that the outer shape becomes a three-dimensional structure that is further reduced when completely folded along the fold lines (M) and the valley fold lines.
(Operation of Embodiment 1 of the Sixth Invention)
In the structure with a folding line according to the first embodiment of the sixth invention having the above-described configuration, a flat plate-like structure with a folding line having a shape different from that of the related art is provided in a folded state having a small outer shape and an extended state having a large outer shape. be able to.
(Embodiment 2 of the sixth invention)
A structure with a fold line according to a second embodiment of the sixth invention is characterized in that, in the sixth invention, the following configuration requirement (B06) is provided.
(B06) A cylindrical wall having a cylindrical wall or a conical wall when the fold line is extended, and a concave and convex shape whose outer shape is reduced when the fold line is bent along the mountain fold line (M) and the valley fold line. Or, when forming a conical wall and folding it completely along the mountain fold line (M) and the valley fold line, the outer shape is further reduced to form a thick cylindrical wall or conical wall having unevenness with a further reduced unevenness. The extensible folding lined structure.
(Operation of the Second Embodiment of the Sixth Invention)
In the structure with a folding line according to the second embodiment of the sixth invention having the above-described configuration, a cylindrical or conical structure with a folding line having a shape different from the conventional shape in a folded state with a small outer shape and an extended state with a large outer shape. Can be provided.
(Seventh invention)
A structure with a folding line according to a seventh aspect of the present invention includes the following constituent features (C01) to (C04).
(C01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting portions connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. A fold line structure provided with a linear fold line that is foldable along the linear part connection portion, wherein the fold line is viewed from one surface side of the fold line structure. A structure with a folding line, the structure having a plurality of mountain folding lines (M) having a mountain fold on one surface side and one or more valley fold lines (V) having a valley fold;
(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of folding lines (M1 to M4, V1, V2) formed in
(C03) When the folding line is extended, a cylindrical wall is formed, and when the folding line is bent in accordance with the mountain fold line and the valley fold line, a cylindrical wall having a reduced outer shape is formed. The structure with a fold line, which forms a thick cylindrical wall having irregularities whose outer shape is further reduced in a completely folded state along the fold line and the valley fold line,
(C04) The structure with a folding line having a folding line that is continuous along a plane perpendicular to the axis of the cylindrical wall and forms a closed polygon.
(Operation of the seventh invention)
The structure with the folding line of the seventh invention having the above-described configuration has a plurality of folding lines (M1 to M4, V1, and V2) that are continuous in a plane perpendicular to the axis of the cylindrical wall, so that the outer shape is small. In the state and the extended state in which the outer shape is large, it is possible to manufacture a cylindrical fold line structure having a different shape from the conventional fold line structure.
(Eighth invention)
The structure with a folding line according to the eighth invention is characterized by having the following constituent requirements (C01) to (C03), (C05).
(C01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting portions connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. A fold line structure provided with a linear fold line that is foldable along the linear part connection portion, wherein the fold line is viewed from one surface side of the fold line structure. A structure with a folding line, the structure having a plurality of mountain folding lines (M) having a mountain fold on one surface side and one or more valley fold lines (V) having a valley fold;
(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of folding lines (M, V) formed at
(C03) When the folding line is extended, a cylindrical wall is formed, and when the folding line is bent in accordance with the mountain fold line and the valley fold line, a cylindrical wall having a reduced outer shape is formed. The structure with a fold line, which forms a thick cylindrical wall having irregularities whose outer shape is further reduced in a completely folded state along the fold line and the valley fold line,
(C05) The structure with folding lines, wherein the parts (P; P1, P2; P1 to P5) have a polygonal shape of a quadrangle or more.
(Operation of the eighth invention)
In the structure with a folding line according to the eighth aspect of the present invention, since the parts (P; P1, P2; P1 to P5) have a polygonal shape of a quadrangle or more, the outer shape is small in the folded state and the outer shape. In a large extended state, it is possible to manufacture a cylindrical fold line structure having a different shape from a cylindrical fold line structure having conventional triangular parts (P; P1, P2; P1 to P5). .
(Ninth invention)
A fold lined structure according to a ninth aspect is provided with the following constituent requirements (C01) to (C03), (C06), and (C07).
(C01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting portions connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. A fold line structure provided with a linear fold line that is foldable along the linear part connection portion, wherein the fold line is viewed from one surface side of the fold line structure. A structure with a folding line, the structure having a plurality of mountain folding lines (M) having a mountain fold on one surface side and one or more valley fold lines (V) having a valley fold;
(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of folding lines (M, V) formed at
(C03) When the folding line is extended, a cylindrical wall is formed, and when the folding line is bent in accordance with the mountain fold line and the valley fold line, a cylindrical wall having a reduced outer shape is formed. The structure with a fold line, which forms a thick cylindrical wall having irregularities whose outer shape is further reduced in a completely folded state along the fold line and the valley fold line,
(C06) The folds are all formed along a spiral, and the parts (P; P1, P2; P1 to P5) are only obtuse triangles formed by dividing a parallelogram into two parts by diagonal lines. Structure with wire,
(C07) A structure with a folding line having the above-described configuration having the obtuse angled triangular parts (P; P1, P2; P1 to P5) each having a base angle of 35 ° or more.
(Operation of the ninth invention)
In the structure with fold lines according to the ninth aspect of the present invention, the fold lines are all formed along a spiral, and the parts (P; P1, P2; P1 to P5) divide a parallelogram into two parts by a diagonal line. The conventional oblique triangular structure having only obtuse angled triangles formed by using the obtuse angled triangular parts (P; P1, P2; P1 to P5) having one base angle of 35 ° or more. A cylindrical fold line structure having a different shape from a conventional cylindrical fold line structure having obtuse triangular parts (P; P1, P2; P1 to P5) having a base angle of about 30 ° is manufactured. can do.
(Tenth invention)
A structure with a folding line according to a tenth aspect of the present invention includes the following constituent features (D01) to (D03).
(D01) a plurality of polygonal parts (P; P1, P2; P1 to P5); and linear part connecting parts connecting outer sides of the respective parts (P; P1, P2; P1 to P5) to each other. A fold line structure provided with a linear fold line that is foldable along the linear part connection portion, wherein the fold line is viewed from one surface side of the fold line structure. A structure with a folding line, the structure having a plurality of mountain folding lines (M) having a mountain fold on one surface side and one or more valley fold lines (V) having a valley fold;
(D02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of folding lines (M, V) formed at
(D03) When the fold line is extended, a conical wall is formed, and when the fold line is bent in accordance with a mountain fold line and a valley fold line, a conical wall having an uneven outer shape is formed. The above-mentioned structure with a folding line, which forms a thick conical wall having irregularities with a further reduced outer shape when completely folded along the folding line and the valley folding line.
(Operation of the tenth invention)
The structure with a folding line according to the tenth aspect of the present invention having the above-described structure, forms a conical wall when the folding line is extended, and has an outer shape when folded according to a mountain fold line and a valley fold line of the folding line. A conical wall having reduced concavities and convexities is formed, and in a state where the conical wall is completely folded along the mountain fold line and the valley fold line, a thick conical wall having concavities and convexities whose outer shape is further reduced is formed.
That is, the tenth aspect of the present invention can provide a foldable conical fold line structure which is not conventionally known.
(Embodiment 1 of the 10th invention)
The structure with a fold line according to the first embodiment of the tenth invention is characterized in that, in the tenth invention, the following constituent features (D04) and (D05) are provided.
(D04) The first mountain fold line (M1), the second mountain fold line (M2) and the third mountain fold line (M3), and the first mountain fold line (M1) and the second mountain fold line (M2) The plurality of fold lines (M1 to M1) each having one node and four fold lines formed by a first valley fold line (V1) disposed therebetween and a first valley fold line (V1) disposed on a side opposite to the third mountain fold line (M3). M3, V1),
(D05) The node is defined as the origin O, the X axis is taken in the direction of the extension of the third mountain fold line (M3), and the first mountain fold line (M1) or the second mountain fold line (M2) is taken out. When one of the mountain fold lines forms an angle with the X axis, α, and the other mountain fold line forms an angle with the first valley fold line (V1), γ is formed such that α = γ. The plurality of folding lines (M1 to M3, V1).
(Operation of Embodiment 10 of the Tenth Invention)
In the structure with a folding line according to the first embodiment of the tenth invention having the above-described configuration, a conical folding line with a conventionally unknown shape is provided in a folded state having a small outer shape and an extended state having a large outer shape. be able to.
(Embodiment 2 of the tenth invention)
The structure with a fold line according to the second embodiment of the tenth invention is characterized in that, in the tenth invention, the following constituent features (D06) and (D07) are provided.
(D06) a first mountain fold line (M1), a second mountain fold line (M2), a third mountain fold line (M3) and a fourth mountain fold line (M4), and the first mountain fold line (M1) and A first valley fold line (V1) formed between the second fold line (M2) and opposite to the third fold line (M3) and the fourth fold line (M4); It is arranged between the third mountain fold line (M3) and the fourth mountain fold line (M4) and opposite to the first mountain fold line (M1) and the second mountain fold line (M2). A second valley fold line (V2), the first fold fold line (M1) and the fourth fold fold line (M4) are adjacent to each other, and the second fold fold line (M2) and a third fold fold line ( M3) the plurality of fold lines (M1 to M4, V1, V2) having one node 6 fold lines arranged adjacent to each other;
(D07) The node is defined as the origin O, the X axis is taken in the direction of extension of the first valley fold line (V1), and the first mountain fold line (M1) and the second mountain fold line (M2) are the second fold line (M2). The angles formed by the first valley fold line (V1) are α and β, respectively, and the angles formed by the third fold fold line (M3) and the fourth fold fold line (M4) with the second valley fold line (V2) are respectively γ and δ, and when the angle between the X axis and the second valley fold line (V2) is θ, the plurality of fold lines (M1 to M1) formed so that β−α = δ−γ + θ M4, V1, V2).
(Operation of Embodiment 10 of the Tenth Invention)
In the structure with a folding line according to the second embodiment of the tenth aspect of the present invention having the above-described configuration, a conventionally known conical folding line with a folding line is provided in a folded state having a small outer shape and an extended state having a large outer shape. be able to.
(Third Embodiment of the Tenth Invention)
A structure with a folding line according to a third embodiment of the tenth invention is characterized in that, in the tenth invention, the following structural requirements (D08) and (D09) are provided.
(D08) First mountain fold line (M1), second mountain fold line (M2), third mountain fold line (M3) and fourth mountain fold line (M4), and the first mountain fold line (M1) and The first valley fold line (V1) formed between the second fold lines (M2) and the second valley fold line (M2) and the second valley fold line (M3) arranged between the second fold fold line (M3). A valley fold line (V2), the fourth fold line (M4) being between the first fold line (M1) and the third fold line (M3), and The plurality of fold lines (M1 to M4, V1, V2) having one node 6 fold lines arranged on the opposite side to (M2);
(D09) The node is defined as the origin O, the X axis is taken in the direction of extension of the fourth mountain fold line (M4), and the first mountain fold line (M1) and the second mountain fold line (M2) are the The angles formed by the first valley fold line (V1) are θ1 and θ2, respectively, and the angles formed by the second fold fold line (M2) and the third fold fold line (M3) with the second valley fold line (V2) are respectively defined. θ3 and θ4, and the angle between the X axis and the first mountain fold line (M1) is α^*And the angle between the X axis and the third mountain fold line (M3) is β^*And α^*= Θ2 + θ4, β^*= A plurality of folding lines (M1 to M4, V1, V2) formed so as to satisfy θ1 + θ3.
(Operation of Embodiment 10 of the Tenth Invention)
The structure with a folding line according to the third embodiment of the tenth invention can provide a conventionally known conical folding line structure in a folded state with a small outer shape and an extended state with a large outer shape.
(Eleventh invention)
The eleventh aspect of the present invention provides a structure with a folding line, which has the following constituent requirements (E01) to (E04).
(E01) A plurality of polygonal parts (P; P1, P2; P1 to P5), and linear part connecting parts connecting outer sides of the parts to each other, the linear part connecting parts A fold line structure provided with a linear fold line (M, V) that can be folded along the fold line, wherein the fold line (M, V) is seen from one surface side of the fold line structure. The folding line-attached structure (A; B; C ;;) having a plurality of mountain fold lines (M) whose sides are mountain folds and one or more valley fold lines (V) that are valley folds.
(E02) A plurality of nodes, which are intersections of the mountain fold line (M) and the valley fold line, are arranged at predetermined intervals, and the number of the mountain fold lines (M) and the number of the valley fold lines intersecting at one node is determined. The plurality of folding lines (M, V) formed so that the difference is 2,
(E03) The structure with a fold line constituted by a sheet-like member having a fold line formed along a spiral
(E04) The sheet has a circular sheet shape when the fold line is extended, and has a disk shape having irregularities with a reduced outer shape when bent along the mountain fold line (M) and the valley fold line of the fold line. The folded line structure having a shape having a thickness with irregularities whose outer shape is further reduced in a state of being completely folded along the mountain fold line (M) and the valley fold line.
(Operation of the eleventh invention)
According to the eleventh aspect of the present invention, there is provided a structure with a folding line, in which a plurality of nodes, which are intersections of the mountain fold line (M) and the valley fold line, are arranged at predetermined intervals, and intersect at one node. Since there are the plurality of fold lines (M, V) formed so that the difference between the number of (M) and the number of valley fold lines is 2, in a folded state with a small outer shape and an extended state with a large outer shape, It is possible to provide a foldable circular sheet-like structure with a folding line, which is not known in the related art.
(Twelfth invention)
A fold line forming die according to a twelfth invention is characterized by having the following constituent features (F01) and (F02).
(F01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and is foldable along the linear part connection part is provided. A pair of fold line forming members provided, wherein the fold line is a plurality of mountain fold lines (M) where the one surface side forms a mountain fold and one or more valleys which form a valley fold when viewed from one surface side of the fold linear molding. A plurality of nodes, which are intersections of the mountain fold line (M) and the valley fold line, are arranged at predetermined intervals and intersect at one node, and a valley fold line A pair of fold line forming members having the plurality of fold lines (M, V) formed so that the difference from
(F02) A folded linear molded connecting member that movably supports or connects the pair of folding line forming members between an overlapped state and an open state.
(Operation of the twelfth invention)
In the fold line forming die of the twelfth invention having the above-described configuration, the sheet-like member is folded between the pair of fold line forming members at the same time, and the sheet-like member is folded. A mountain fold line (M) and a valley fold line required for the member can be formed.
(Thirteenth invention)
A fold line forming method according to a thirteenth aspect of the present invention includes the following constituent features (G01) and (G02).
(G01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of each part to each other and that can be folded along the linear part connection part is provided. A fold line structure provided, wherein the fold line is a plurality of mountain fold lines (M) in which the one surface side forms a mountain fold and one or more valley folds when viewed from one surface side of the fold line structure. A plurality of nodes, which are intersections of the mountain fold line (M) and the valley fold line, are arranged at a predetermined interval, and the number of the mountain fold lines (M) intersecting at one node and the valley fold A sheet-like structure in which a foldable sheet member having an integral structure is sandwiched between a pair of fold line forming members having the plurality of fold lines (M, V) formed so that the difference from the number of lines is two. Member clamping process,
(G02) a fold line forming step of simultaneously folding the pair of fold line forming members sandwiching the sheet member along the mountain fold line (M) and the valley fold line to form a fold line in the sheet member.
(Operation of the thirteenth invention)
In the folding line forming method according to the thirteenth aspect having the above configuration, in the sheet-like member holding step, a sheet having an integral structure that can be folded between the pair of folding line forming members having the plurality of folding lines (M, V). Sandwich the member.
Next, in the folding line forming step, the pair of folding line forming members sandwiching the sheet member is simultaneously folded along the mountain fold line (M) and the valley fold line to form a fold line in the sheet member. I do.
BEST MODE FOR CARRYING OUT THE INVENTION
Next, specific examples (examples) of the embodiments of the present invention will be described with reference to the drawings, but the present invention is not limited to the following examples.
(Example 1)
FIG. 110 is a plan view of the folding line forming die according to the first embodiment of the present invention.
In FIG. 110, the folding line forming die 1 has a pair of flexible molds 2 and 2 as a pair of foldable folding line forming members arranged axially symmetrically with respect to the opening / closing axis L. The flexible mold 2 has a plurality of rhombic parts P and a kraft film 3 bonded to both surfaces of each part P in a state where outer sides of the plurality of parts P are adjacent to each other. Adjacent outer sides of the parts P are connected by the kraft film 3, and a foldable linear fold line is formed by the kraft film 3 at the connection part (part connection part).
Nodes, which are intersections of the plurality of fold lines, are arranged at predetermined intervals, and a single node has a total of four fold lines. The fold line has a mountain fold line in which the one surface side forms a mountain fold and a valley fold line in which a valley fold is formed when viewed from one surface side of the flexible mold (fold line forming member) 2, and a ridge that intersects at one node It is formed so that the difference between the number of fold lines and the number of valley fold lines is two. In the first embodiment, the number of fold lines intersecting at one node is 4, and at each node, three mountain fold lines and one valley fold line intersect, or three mountain fold lines intersect. And one valley fold line intersect.
The mountain fold lines and the valley fold lines of the flexible molds 2 and 2 that are folded and stacked along the opening / closing axis L are formed to overlap.
A flexible mold formed by bonding a kraft film to both sides of each part (each part, that is, each thin metal plate) P can be easily formed from the next time if a folding habit is given to the mountain fold line and the valley fold line once. Mountain folds and valley folds are possible. Therefore, when a folding mold is folded along the opening / closing axis L with a paper or resin sheet placed on the surface of a flexible mold on one side of the opening / closing axis L, the paper or resin sheet or the like becomes a pair of flexible molds. Sandwiched between. In this state, when the flexible mold is folded along the folding line, a folding line is formed on the sheet-shaped member S such as paper or a resin sheet.
FIG. 111 is a perspective view of a paper or resin sheet on which a folding line is formed.
As can be seen from FIG. 111, by using the folding line forming mold 1 shown in FIG. 110, the folding line can be easily formed on the sheet member S such as paper or resin sheet.
(Example 2)
FIG. 112 is an explanatory view of a folding line forming die according to the second embodiment of the present invention, and is a perspective view of one of a pair of flexible dies for sandwiching both sides of a sheet-like member forming a folding line. FIG.
In FIG. 112, the flexible mold 2 forming the folding line forming mold 1 according to the second embodiment of the present invention is formed by a plurality of rhombic parts P, and each part P is formed on a side edge of each part. Are connected rotatably by the hinge Pa.
The hinge Pa of each part P is arranged on the same surface side of each part, and the sheet-like member is sandwiched by the surface opposite to the surface on which the hinge Pa is provided.
Other configurations are the same as those of the first embodiment.
(Example 3)
FIG. 113 is a plan view of a folding line forming die according to Embodiment 3 of the present invention.
FIG. 114 is an explanatory view of a use state of the folding line forming die of FIG. 113, FIG. 114A is a diagram showing a state where the folding line forming die is folded in two, and FIG. 114B is a folding diagram of FIG. 114A. It is a figure which shows the state which folded the folding line forming die.
In FIG. 113, the folding line forming mold 1 has a pair of flexible molds 2 and 2 as a pair of foldable folding line forming members arranged axially symmetrically with respect to the opening / closing axis L. The flexible mold 2 includes a plurality of square parts P1 and a parallelogram part P2, and a kraft film bonded to both surfaces of each of the parts P1 and P2 in a state where outer sides of the plurality of parts P1 and P2 are adjacent to each other. And 3.
The smaller of the interior angles of the parallelogram is 60 °.
When a sheet-shaped member such as paper or a resin sheet is placed on the surface of the flexible mold 2 on one side of the opening / closing axis L, the folding line forming mold 1 is folded along the opening / closing axis L to obtain the paper or resin sheet or the like. Is sandwiched between a pair of flexible molds 2 and 2. In this state, the paired flexible molds 2 and 2 are folded along the folding line into the state shown in FIG. 114A and further folded into the state shown in FIG. 114B, so that the sheet-shaped member S such as paper or a resin sheet is easily folded. Can be formed.
FIG. 115 is an explanatory view of a sheet-like member in which a folding line is formed by using the folding line forming mold shown in FIGS. 113 and 114. FIG. 115A is a plan view of the sheet-like member in a half-folded state, and FIG. It is a top view of the state where it was completely folded.
116 is an explanatory view of the folded sheet member shown in FIG. 115B, FIG. 116A is a perspective view, and FIG. 116B is a flat sheet member on one surface (lower surface) of the folded sheet member shown in FIG. 116A. It is a perspective view of what adhered.
The castles S1 and S2, and S3 and S4 of the sheet member S in the half-folded state shown in FIG. 115A are joined in the fully folded state shown in FIG. 115B or FIG. Therefore, a strong core member can be formed by applying an adhesive to one of the joints S1 and S2 and one of S3 and S4 when folding. By bonding the sheet S ′ (see FIG. 116) to one side (lower surface) or both sides of the folded sheet member S shown in FIG. 116A with an adhesive, a plate member having a large compressive stress resistance can be manufactured.
Note that the folding line forming mold described in the first and third embodiments uses a pair of folding line forming members (flexible molds) for sandwiching the sheet member. It is possible to form a fold line on the sheet-like member by using the fold line forming member (flexible mold). In this case, a small suction port is formed in each part of the fold line forming member, the one side of the fold line forming member is set to a negative pressure, and the sheet member is sucked to the other side, and the fold line forming member ( It is possible to form a folding line on the sheet member by folding the flexible mold.
In addition, a configuration in which the pair of fold line forming members are supported by separate support members, and the other fold line forming member is mechanically moved to the close contact position with respect to one of the fold line forming members or is separated therefrom. It is possible to adopt.
(Example 4)
FIG. 117 is a side view of a plastic bottle as a structure with a folding line according to Embodiment 4 of the present invention.
FIG. 118 is a side sectional view of the plastic bottle of the fourth embodiment.
FIG. 119 is an explanatory view of a state in which the plastic bottle of FIG. 117 is compressed in the axial direction (semi-folded state), FIG. 119A is a view showing a half-folded state, and FIG. 119B is a cover almost completely folded in an opening portion. FIG.
117 and 118, the PET bottle A has a bottom wall A0, a cylindrical wall A1, a conical wall A2, and an opening A3. As shown in FIGS. 117 and 118, the cylindrical wall A1 has a large number of mountain fold lines M (see the solid line in FIG. 117) and a large number of concave valley fold lines V (see FIG. 117-1). (See dotted line).
In FIGS. 117 and 118, in the plastic bottle A of the fourth embodiment, the part P, which is a portion formed (enclosed) by the folding lines M and V, is formed in a trapezoid (square). At a node, which is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. Then, the number of the mountain fold lines M intersecting at the nodes = 3, the number of the valley fold lines V = 1, and the difference is 2 (= 3-1).
When the cylindrical wall A1 of the plastic bottle A according to the fourth embodiment is compressed in the axial direction, it is folded along the folding lines M and V, and then into the state shown in FIG. 119A through the state shown in FIG. 119A. The folded PET bottle tries to return to its original shape (extended shape) by elasticity, but when folded in the state shown in FIG. 119B, a lid (cap) C is placed on the opening A3, and the inside of the PET bottle A is inserted. When air is prevented from flowing, the PET bottle A is held in a folded state (the state shown in FIG. 122B). In this folded state, the space required to accommodate the cylindrical wall A1 can be reduced to 1/3 or less of the state shown in FIGS. 117 and 118.
Therefore, it is possible to reduce the space required for storage of the used plastic bottle A until the cylindrical wall A1 is recycled.
FIG. 120 is an explanatory diagram of the method of manufacturing the PET bottle A, and is a diagram illustrating a state in which a mold (a mold having a folding line forming surface) is opened.
FIG. 121 is an explanatory diagram of the method for manufacturing the PET bottle A, showing a state in which the mold is closed and a tubular or bag-shaped raw tube (parison) is stretched in the mold.
FIG. 122 is a diagram showing a state where compressed air is blown into the inside of the raw tube of FIG. 121 to expand the tube.
In FIG. 120, a mold K includes a circular bottom mold K1, an intermediate mold K2a, K2a obtained by dividing a cylinder into two, and an upper first mold for clamping an upper end of the intermediate mold K2a, K2a. K3a and an upper second mold K3b supported on the upper surface thereof. As shown in FIG. 120, the raw tube C is arranged so as to cover the tip of the air supply tube B, and the die tube C is clamped and extended in the mold as shown in FIG. 121. Next, as shown in FIG. 122, when air is blown out from the air supply pipe B, the plastic bottle A is manufactured. By cooling the PET bottle A in FIG. 122, the shape of the mold cavity is transferred to the outer wall of the PET bottle A. Therefore, by forming a concave portion or a convex portion on the inner surface of the mold, the mountain fold line M or the valley fold line V can be formed on the outer wall of the plastic bottle A.
(Example 5)
FIG. 123 is an explanatory diagram of a PET bottle as a fifth embodiment of the folded line structure according to the present invention, and is a diagram illustrating a folded line structure (pet bottle) formed along a spiral.
In the description of the fifth embodiment, the same reference numerals are given to the components corresponding to the components of the fourth embodiment, and the detailed description is omitted.
The fifth embodiment differs from the fourth embodiment in the following points, but has the same configuration as the fourth embodiment in other points.
In FIG. 123, the plastic bottle A of the fifth embodiment is different from the fourth embodiment in the shape of a part P which is a portion formed (enclosed) by the folding lines M and V. That is, the shape of the part P in the fifth embodiment is a trapezoid as in the fourth embodiment, but the height of the trapezoid is smaller than that in the fourth embodiment. The fold lines M and V of the fifth embodiment have fold lines formed along the spiral.
As in the fifth embodiment, a cylindrical wall (a structure with a cylindrical folding line) A1 having a fold line along a spiral is folded when compressed in the axial direction while being twisted, the outer shape is reduced, and the shape is reduced. When it is pulled in the axial direction, it expands and the outer shape expands.
(Example 6)
FIG. 124 is an explanatory diagram of a plastic bottle as a sixth embodiment of the folded line structure of the present invention, and is a diagram illustrating a folded line structure (pet bottle) having a cylindrical wall formed along a spiral.
In the description of the sixth embodiment, components corresponding to the components of the fifth embodiment are denoted by the same reference numerals, and detailed description thereof will be omitted.
The sixth embodiment differs from the fifth embodiment in the following points, but is otherwise the same as the fifth embodiment.
In FIG. 124, the plastic bottle A of the sixth embodiment differs from the fourth embodiment in the shape of a part P which is a portion formed (enclosed) by the folding lines M and V. That is, the shape of the part P in the sixth embodiment is a trapezoid as in the fifth embodiment, but the height of the trapezoid is formed higher than that in the fourth embodiment. The fold lines M and V in the sixth embodiment have fold lines formed along the spiral as in the fifth embodiment, but the inclination of the spiral is larger than that in the embodiment. , The inclination angle is about 45 °.
The cylindrical wall (structure having a cylindrical folding line) A1 having a folding line along a spiral with a large inclination angle as in the sixth embodiment is folded and reduced in outer shape when it is compressed in the axial direction while being twisted. Is the same as that of the fifth embodiment, but requires a slightly larger force than the fifth embodiment when folded. Then, once folded, the cylindrical wall A1 of the plastic bottle is plastically deformed, so that the cylindrical wall A1 does not automatically return to its original shape due to elasticity. For this reason, when the PET bottle is used and compressed in the axial direction while being twisted and folded, the folded state can be maintained without covering the opening A3.
(Example 7)
FIG. 125 is a side view of a coffee can as a structure with a folding line according to Embodiment 7 of the present invention.
FIG. 126 is a side sectional view of the coffee can of the seventh embodiment.
FIG. 127 is an explanatory view of a state in which the coffee can of FIG. 126 is compressed in the axial direction (semi-folded state). FIG. 127A is a side view of the half-folded state, and FIG. 127B is a side view of a state of being almost completely folded. .
125 and 126, the coffee can A has a bottom wall A0, a cylindrical wall A1, and an upper wall A2 made of aluminum or steel. It has a similar shape. As shown in FIGS. 125 and 126, the cylindrical wall A1 has a large number of mountain fold lines M (see solid lines in FIG. 125) and a large number of valley fold lines V (1 in FIG. 125). (See dotted line).
In the coffee can A according to the seventh embodiment, the part P, which is a portion formed (enclosed) by the folding lines M and V, is formed in a trapezoid (square). At a node, which is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. Then, the number of the mountain fold lines M intersecting at the nodes = 3, the number of the valley fold lines V = 1, and the difference is 2 (= 3-1).
When the cylindrical wall A1 of the coffee can A according to the seventh embodiment is compressed in the axial direction, the cylindrical wall A1 is folded along the folding lines M and V, and plastically deforms through the state of FIG. 127A to the folded state of FIG. 127B.
In the case of a thin can such as a coffee can, if a pattern as shown in FIG. 33 is provided only in one step on the outer periphery of the central portion in the axial direction, if the coffee can is twisted at the time of disposal, the folding line extends from the pattern as a starting point. Will be folded.
Therefore, it is possible to reduce the space required for storage of the used coffee can A until the cylindrical wall A1 is recycled.
FIG. 128 is an explanatory view of a method for manufacturing the coffee can A, and is an explanatory view of an inner mold (a mold having a folding line forming surface) disposed on the inner surface of the cylindrical member. FIG. FIG. 128B is a cross-sectional view in which a pair of inner second dies are inserted between the pair of inner first dies of FIG. 128A; FIG. 128C is a cross-sectional plan view showing a state where a cam rod is inserted into the center of the inner first and second molds of FIG. 128B, and FIG. 128D is a diagram showing a state where the cam rod of FIG. It is a figure showing the state where the inside 1st and 2nd metallic molds were pushed out by pushing out.
FIG. 129 is an explanatory view of the method for manufacturing the coffee can A. FIG. 129A shows a state in which an inner mold (a mold having a folding line forming surface) is set on the inner surface of a cylindrical member, and the outer mold K2 is clamped. FIG. 129B is a diagram showing a state before, and FIG. 129B is a diagram showing a state where the mold is clamped from the state of FIG. 129A.
The inner mold K1 shown in FIGS. 128 and 129 includes a pair of inner first molds K1a, K1a arranged to face each other, and a pair of inner second molds K1b, K1b arranged therebetween. And a cam rod K1c inserted between the inner first and second molds K1a, K1a, K1b, K1b. On the outer surface of the inner first and second molds K1a, K1a, K1b, K1b, an uneven surface (FIG. 125, FIG. 126) forming the mountain fold line M and the valley fold line V of the coffee can A shown in FIG. (Not shown). The outer mold K2 has four outer divided molds K2a formed by dividing the cylindrical mold into four equal parts, and the inner surface of each outer divided mold K2a has the structure shown in FIGS. An uneven surface (not shown) forming a mountain fold line M and a valley fold line V of the coffee can A shown is formed.
As shown in FIG. 128C, when the inner mold K1 is set inside the aluminum cylindrical member that is a material for manufacturing the coffee can A, and the cam rod K1c is rotated by 90 ° in this state, the inner first and second molds are rotated. K1a, K1a, K1b, and K1b are pushed outward to the state shown in FIG. 128D.
In this state, by clamping the outer mold K2 of FIG. 129A to the state of FIG. 129B, the coffee can A having the folding lines M and V shown in FIGS. 125 and 126 can be manufactured.
The inner first and second dies K1a, K1a, K1b, K1b of the inner die K1 are provided with air vent holes (not shown) for discharging air in recesses formed on the outer surfaces thereof. By forming it between the concave portion on the outer surface and the inner surface, the coffee can A can be easily formed.
(Example 8)
FIG. 130 is an explanatory view of a coffee can as the eighth embodiment of the folded line structure of the present invention, and is a diagram showing a folded line structure (coffee can) having a cylindrical wall formed along a spiral.
In the description of the eighth embodiment, the same reference numerals are given to the components corresponding to the components of the seventh embodiment, and the detailed description thereof will be omitted.
The eighth embodiment differs from the seventh embodiment in the following points, but has the same configuration as the seventh embodiment in other points.
In FIG. 130, in the coffee can A of the eighth embodiment, a part P, which is a portion formed (enclosed) by the folding lines M and V, is formed along a spiral having an inclination angle of 45 °.
As in the eighth embodiment, a cylindrical wall (a structure with a cylindrical folding line) A1 having a folding line along a spiral having an inclination angle of 20 ° to 30 ° or more is folded when it is compressed in the axial direction while being twisted. Since the cylindrical wall A1 of the coffee can A is plastically deformed once it is folded, the cylindrical wall A1 does not automatically return to its original shape. For this reason, when the coffee can A is used, it is compressed and folded in the axial direction while being twisted when being used, so that the coffee can A is kept in a small folded state.
FIG. 131 is an explanatory diagram of another embodiment of the method for manufacturing the coffee can A.
In FIG. 131, the inner mold K1 set inside the cylindrical wall A1 having the bottom wall A0 is fixed to the upper end of the liquid container V, and the cylindrical wall A1 is accommodated in the liquid container V in the liquid container V. Fill with liquid. A tube T is connected to the upper end of the liquid container V, and the inside of the tube T is also filled with liquid.
In this state, when impact pressure is applied to the liquid in the tube T by the piston P, a fold line is formed on the cylindrical wall A1 according to the unevenness of the surface of the inner mold K1.
(Example 9)
132 is an explanatory diagram of a small container as a structure with a folding line according to Embodiment 9 of the present invention. FIG. 132A is a perspective view of a lid of the small container, and FIG. 132B is a perspective view of the small container in an extended state.
133 is an explanatory view of the small container of Example 9; FIG. 133A is a perspective view of the folded small container; FIG. 133B is a sectional view taken along the line 109B-109B of FIG. 133A; It is sectional drawing of the state which covered the container.
In FIGS. 132 and 133, the small container B (see FIG. 132B) has a circular bottom plate 6, an upper end plate 7, and a foldable pseudo-cylindrical wall 8. The outer shape of the upper end plate 7 is circular, and a hexagonal opening 7a is formed in the center.
As shown in FIG. 132B, the pseudo-cylindrical wall 8 is formed with a number of mountain fold lines M having a convex outer surface and a number of valley fold lines V having a concave outer surface.
132B and 133, the pseudo-cylindrical wall 8 of the small container B of the ninth embodiment has a plurality of parts P1 and P2 which are portions (enclosed) formed by the folding lines M and V. The part P1 is triangular and one side thereof is foldably connected to the bottom plate 6, and the part P2 is triangular and one side thereof is foldably connected to the upper end plate 7. A mountain fold line M, M,... Is formed at a connection portion between the bottom plate 6 and one side of each of the six parts P1 so that the mountain fold lines M, M,. Connected endlessly.
A mountain fold line M, M,... Is formed at a connection portion between the upper end plate 7 and one side of each of the six parts P2, and the mountain fold lines M, M,. Connected endlessly.
Each of the endlessly connected mountain fold lines M, M,... Forms a continuous and closed polygon along a plane perpendicular to the axis of the pseudo cylindrical wall 8.
When the pseudo-cylindrical wall 8 of the small container B of the ninth embodiment is compressed in the axial direction while being twisted, the pseudo-cylindrical wall 8 is folded along the folding lines M and V to be in a state shown in FIGS. 133A and 133B.
A lid 9 (see FIGS. 132A and 133C) for opening and closing the hexagonal opening 7a at the upper end of the small container B includes a circular upper plate 9a, a short cylindrical wall 9b provided on the outer periphery of the upper plate 9a, and a cylinder. A pair of protruding portions 9c, 9c extending downward from the lower end of the wall 9b, a lower end locking portion 9d provided at the lower end of the protruding portions 9c, 9c, and a cylindrical wall 9b above the protruding portions 9c, 9c. And an upper locking portion 9e which protrudes slightly on the inner side surface of the upper surface.
When the small container B is not used, as shown in FIG. 133B, when the cylindrical wall 9b of the lid 9 is fitted to the upper end plate 7 of the small container B in a state where the small container B is folded, the locking portions 9d, 9d locks the lower surface of the bottom plate 6, and the locking portions 9e, 9e lock the lower surface of the upper end plate 7. In this state, since the capacities of the small container B and the lid 9 are small, the storage space is small.
When the small container B is used, when the cylindrical wall 9b of the lid 9 is fitted to the upper end plate 7 of the small container B in a state where the small container B is extended (see FIG. 132B), the locking portions 9e, 9e , Is locked to the lower surface of the upper end plate 7. In this state, the lid 9 is held at the upper end of the small container B while closing the opening 7a of the elongated small container B. Therefore, the object contained in the small container B can be shielded from the outside air to protect the contained object.
FIG. 134 is an explanatory diagram of the method of manufacturing the small container B, and shows a state in which a mold (a mold having a folding line forming surface) is closed.
In FIG. 134, the mold 11 is divided into upper molds 11a and 11b and a lower mold 11c. The upper molds 11a and 11b are molds divided along division lines L1 and L2 formed along the mountain fold lines M and M arranged at positions facing each other in FIG. 132B.
After the resin is injected into the cavity 12 formed in the mold 11 and cured to form the small container B, the upper molds 11a and 11b are opened. Thereafter, when the small container B formed on the lower mold 11c is pulled upward while twisting, the formed small container B can be easily taken out from the lower mold 11C.
(Example 10)
FIG. 135 is an explanatory diagram of a paper pack as a structure with a folding line according to the tenth embodiment of the present invention, and is a perspective view of a used state in which the paper pack is extended.
FIG. 136 is a view showing a state in which the paper pack of FIG. 135 is being folded.
FIG. 137 is a view showing a state where the paper pack of FIG. 136 is further folded.
FIG. 138 is a developed view of the paper pack shown in FIGS.
FIG. 138 is a development view of a paper pack that is folded in two steps by a folding line that satisfies the folding condition, and a one-dot chain line in the vertical direction is a mountain fold line in the state of FIG. 135. The left and right side edges of FIG. 138 are glued to form a cylinder, and then folded along the horizontal and vertical mountain fold lines M and valley fold lines V to form the paper pack of FIG. ) Can be configured.
135 can be folded from the state of FIG. 136 to the state of FIG. 137 by folding the paper pack of FIG. 135 along the oblique mountain fold line M and the valley fold line V.
(Example 11)
FIG. 139 is an explanatory diagram of a paper pack as a structure with a folding line according to Embodiment 11 of the present invention, and is a perspective view of a used state where the paper pack is extended.
FIG. 140 is a view showing a state in which the paper pack of FIG. 139 is being folded.
FIG. 141 is a diagram showing a state where the paper pack of FIG. 140 is further folded.
FIG. 142 is a developed view of the paper pack shown in FIGS. 139 to 141.
FIG. 142 is a developed view of the paper pack folded in four steps by a folding line satisfying the folding condition, which is different from the developed view of FIG. 138 in which the paper pack is folded in two steps. 142 is a mountain fold line in the state of FIG. 139. The paper pack shown in FIG. 139 (the paper pack in use) is formed by bonding the left and right side edges of FIG. 142 into a tubular shape and then folding it along the horizontal and vertical mountain fold lines M and valley fold lines V. ) Can be configured. Other configurations and operations are the same as those of the tenth embodiment.
(Example 12)
FIG. 143 is an explanatory view of a paper pack as a structure with a folding line according to a twelfth embodiment of the present invention, and is a perspective view of a used state in which the paper pack is extended.
FIG. 144 is a view showing a state in which the paper pack of FIG. 143 is being folded.
FIG. 145 is a view showing a state where the paper pack of FIG. 144 is further folded.
FIG. 146 is a developed view of the paper pack shown in FIGS. 143 to 145.
FIG. 146 is an exploded view of a paper pack that is folded in four steps along a folding line that satisfies the folding condition, in which vertical mountain fold lines M are formed alternately inclined. The paper pack (paper pack in use) of FIG. 143 is formed by bonding the left and right side edges of FIG. 146 into a tubular shape, and then folding along the mountain fold line M and the valley fold line V. be able to. Other configurations and operations are the same as those of the eleventh embodiment.
(Example 13)
FIG. 147 is an explanatory diagram of a paper pack as a structure with a folding line according to Embodiment 13 of the present invention, and is a perspective view of a used state in which the paper pack is extended.
FIG. 148 is a view showing a state in which the paper pack of FIG. 147 is being folded.
FIG. 149 is a view showing a state where the paper pack of FIG. 148 is further folded.
FIG. 150 is a developed view of the paper pack shown in FIGS. 147 to 149.
FIG. 150 is an exploded view of a paper pack that is folded in four steps along a folding line that satisfies the folding condition, and a vertical mountain fold line M is formed to be inclined in the same direction. The paper pack (paper pack in use) of FIG. 147 is formed by bonding the left and right side edges of FIG. 150 into a tubular shape, and then folding along the mountain fold line M and the valley fold line V. be able to. As can be seen from FIG. 147, since the paper pack is twisted in a fixed direction from the upper end to the lower end, the paper pack can be easily extended or folded into a use state by changing the twisting direction. Other configurations and operations are the same as those of the twelfth embodiment.
(Example 14)
FIG. 151 is an explanatory diagram of a pump as a structure with a folding line according to Embodiment 14 of the present invention.
In FIG. 151, the pump chamber A is configured similarly to the plastic bottle A of the fifth embodiment, and the opening at the upper end is opened and closed by the cap C. The upper end of the fluid tube T is connected to the lower end of the pump chamber A. The fluid tube T has a suction tube T1 and a discharge tube T2. The suction tube T1 is provided with a suction valve V1, and the discharge tube T2 is provided with a discharge valve V2. When the pump chamber A is contracted with the cap C closed, V1 is closed and V2 is opened, and the fluid in the pump chamber A is discharged from the discharge tube T2. When the pump chamber A is expanded, V1 is opened and V2 is closed, and the fluid flows into the pump chamber A from the suction tube T1.
The pump according to the fourth embodiment can be used for supplying kerosene, inflating a bicycle, and the like.
(Example 15)
FIG. 152 is an explanatory diagram of a trash can as a structure with a folding line according to Embodiment 15 of the present invention. FIG. 152A is a side view, and FIG. 152B is a side sectional view.
In FIG. 152, the trash can A is formed of a cylindrical body with a folding line made of the paper or resin, and has a bottom wall A0, a cylindrical wall A1, and an upper wall A2. An opening A2a for introducing dust is formed in the upper wall portion A2. The cylindrical wall A1 of the trash can A is formed by a plurality of trapezoidal parts P obliquely formed by a mountain fold line M and a valley fold line V. Since the part P is formed along a spiral that is inclined at about 45 °, the extended trash can A can maintain that state (shape).
(Example 16)
FIG. 153 is an explanatory diagram of a pencil stand as a structure with a folding line according to Example 16 of the present invention. FIG. 153A is a side view, and FIG. 153B is a side sectional view.
In FIG. 153, a brush stand A is formed of a cylindrical body with a folding line made of the paper or resin, and has a bottom wall A0, a cylindrical wall A1, and an upper wall A2. An opening A2a for inserting a writing instrument such as a pencil is formed in the upper wall portion A2. The cylindrical wall A1 of the brush stand A is formed of a plurality of obliquely trapezoidal parts P formed by a mountain fold line M and a valley fold line V. Since the part P is formed along a spiral that is inclined at about 45 °, the brush stand A in an extended state can maintain its shape.
(Example 17)
FIG. 154 is an explanatory diagram of a gusset (partition member inside a box) as a structure with a folding line according to a seventeenth embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 155 is a perspective view of the gusset of FIG.
FIG. 156 is a developed view of the gusset of FIG. 155.
In FIG. 154, the guesses G are accommodated in the paper box C. The guess G is manufactured by folding along the mountain fold line M and the valley fold line V in the developed view shown in FIG. In the gusset G of the seventeenth embodiment, two rows of rising walls G1 are formed, and the rising walls G1 are formed as partition walls. The stored item support surface G2 formed between the rising walls G1 is a surface for supporting stored items such as buns and cookies, and is inclined in the seventeenth embodiment.
Since the guess G is made of one sheet of paper, the time required for the setting operation can be reduced as compared with the case where a guess formed of a plurality of papers is set in the paper box C. .
(Example 18)
FIG. 157 is an explanatory view of a gusset (partition member inside a box) as a structure with a folding line according to Embodiment 18 of the present invention, and is a perspective view of the gusset taken out of the paper box.
FIG. 158 is a development view of the gusset of FIG. 157.
157 and 158, the rising wall G1 is formed on both sides of the gusset G of the seventeenth embodiment. When the rising walls G1 on both sides of the gusset G are accommodated in the paper box C (not shown), they are supported by the side walls of the paper box C, so that the position of the guess G in the paper box C is stabilized, and The rigidity of the stored object support surface G2 is reinforced.
(Example 19)
FIG. 159 is an explanatory diagram of a gusset (partition member inside a box) as a structure with a folding line according to a nineteenth embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 160 is a perspective view of the gusset shown in FIG.
FIG. 161 is a developed view of the gusset of FIG. 159.
In FIG. 159, the guesses G are accommodated in the paper box C. The storage object support surface G2 formed between the rising walls G1 of the guesses G is a surface that supports storage items such as buns and cookies, and the embodiment 19 is horizontally (parallel to the bottom surface of the paper box C). Is formed. In the nineteenth embodiment, a rising wall G3 extending in a direction perpendicular to the rising wall G1 is provided. Further, the storage object support surface G2 is formed so as to be surrounded by the rising walls G1 and G2.
Since the guess G of the nineteenth embodiment is made of one sheet of paper, the time required for the setting operation is shorter than when a guess formed of a plurality of sheets is set in the paper box C. Can be shortened.
(Example 20)
FIG. 162 is an explanatory view of a gusset (partitioning member inside a box) as a structure with a folding line according to a twentieth embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 163 is a perspective view of the gusset of FIG.
FIG. 164 is a developed view of the gusset of FIG. 163.
In FIG. 163, a paper box C accommodates a guess G. The rising walls G1 and G3 of the gusset G are formed so as to extend in directions perpendicular to each other, and a stored article support surface G2 is formed between the rising walls G1 and G3. The storage item support surface G2 is a surface that supports storage items such as buns and cookies, and the embodiment 20 is formed horizontally (parallel to the bottom surface of the paper box C).
Since the guesses G of the twentieth embodiment are also made of one sheet of paper, the time required for the setting operation is shorter than when a guess made of a plurality of sheets is set in the paper box C. Can be shortened.
(Example 21)
FIG. 165 is an explanatory diagram of a gusset (partition member inside a box) as a structure with a folding line according to a twenty-first embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 166 is a perspective view of the gusset of FIG.
FIG. 167 is a developed view of the gusset of FIG. 166.
In FIG. 165, a paper box C contains a guess G. The rising walls G1 and G3 of the gusset G are formed so as to extend in directions perpendicular to each other, and a stored article support surface G2 is formed between the rising walls G1 and G3. The storage item support surface G2 is a surface that supports storage items such as buns and cookies, and the twenty-first embodiment is formed horizontally (parallel to the bottom surface of the paper box C).
The guess G of Example 21 is formed by bending a single sheet of square paper along a mountain fold line M and a valley fold line V formed in a diagonal direction. Since the embodiment 21 is also made of one sheet of paper, the time required for the setting operation can be reduced as compared with the case where a guess made of a plurality of sheets is set in the paper box C. it can.
(Example 22)
168 is an explanatory view of the foldable passage cover, FIG. 168A is a perspective view of a half-folded state, and FIG. 168B is a perspective view of a completely folded state.
FIG. 169 is a developed view of a foldable passage cover as a structure with a folding line according to Embodiment 22 of the present invention.
The foldable passage cover 16 shown in FIG. 168 is a member arranged and used so as to cover the upper side and both sides of the passage through which a person passes, and in particular, a passage portion of a connecting portion between railway vehicles, It is suitable for use in places where people pass through, such as a passage between the terminal bridge tip of an airport and an aircraft entrance, where the structures at both ends of the passage are not fixed.
The foldable passage cover 16 is a member obtained by attaching a fold line to an elastic and flexible sheet-like member, and is foldable at the fold line portion. The folded passage cover 16 has a shape shown in FIG. 168 in a half-folded state, and is arranged so as to cover the upper side and the left and right of the passage along the passage, and both ends in the passage direction are fixed to the structure.
In the developed view of the foldable passage cover 16 shown in FIG. 169, the foldable passage cover 16 has a number of mountain fold lines M having a convex outer surface and a number of valley folds having a concave shape when used in a half-folded state. A line V is formed.
At a node, which is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. Then, the number of mountain fold lines M intersecting at each node = 3, the number of valley fold lines V = 1, and the difference is 2 (= 3-1). That is, the fold line pattern of the foldable passage cover 16 of the twenty-second embodiment is a one-node four-fold line.
In FIG. 169, the foldable passage cover 16 according to the twenty-second embodiment has a plurality of parts P1, P2, and P3 that are portions (enclosed) formed by the folding lines M and V. Part P1 is triangular, part P2 is equilateral trapezoid, and part P3 is trapezoidal.
The foldable passage cover 16 is folded in a state where the outer shape is reduced as shown in FIG. 168 during storage or transportation.
(Example 23)
170 is an explanatory view of the foldable passage cover having the developed view of FIG. 171. FIG. 170A is a perspective view of a half-folded state, and FIG. 170B is a perspective view of a completely folded state.
FIG. 171 is a development view of a foldable passage cover as a structure with a folding line according to Embodiment 23 of the present invention.
In the description of the twenty-third embodiment, the same reference numerals are given to the components corresponding to the components of the twenty-second embodiment, and the detailed description thereof will be omitted.
The embodiment 23 is different from the embodiment 22 in the following points, but is configured similarly to the embodiment 22 in other points.
As in the case of the twenty-second embodiment, the foldable passage cover 16 shown in FIG. 170 is a passage portion where a person passes, such as a passage portion of a connecting portion between vehicles of a railroad vehicle or a passage between a terminal bridge end of an airport and an aircraft entrance. Therefore, it is suitably used in a place where the distance between the structures at both ends of the passage is not fixed.
The foldable passage cover 16 shown in FIG. 171 has an outer shape excluding a fan-shaped central portion in a developed view. The foldable passage cover 16 is formed with a number of mountain fold lines M and a number of valley fold lines V having convex outer surfaces when used in a half-folded state. is there. Further, each node satisfies the folding condition.
In FIG. 171, the foldable passage cover 16 of the twenty-third embodiment has a plurality of parts P1, P2, P3, and P4 that are portions (enclosed) formed by the folding lines M and V. The part P1 is a triangle, and the parts P2 to P4 are all quadrilaterals.
The foldable passage cover 16 according to the twenty-third embodiment is folded into a reduced outer shape as shown in FIG. 170B at the time of storage or transportation as in the twenty-second embodiment.
(Example 24)
FIG. 172 is an explanatory view of a lamp shade as a structure with a fold line according to Embodiment 24 of the present invention. FIG. 172A is a development view of a sheet-like member which is a material for manufacturing the lamp shade, and FIG. 172B is a sheet of FIG. FIG. 5 is a perspective view of a lampshade formed by manufacturing a pseudo cone by joining left and right sides of a shaped member into a half-folded state.
The lamp shade 17 shown in the half-folded state shown in FIG. 172B is a member used as a lamp umbrella in an extended state, and is made of a sheet-like resin.
In the developed view of the lamp shade 17 shown in FIG. 172A, the transparent resin sheet for manufacturing the lamp shade 17 of FIG. 172B has a shape excluding the central portion of the fan shape. An adhesive margin 17a is provided on one of both sides of the resin sheet to be joined to each other. After forming the fold line on the resin sheet in the expanded state by using the same member as the fold line forming die shown in the first or third embodiment, the glue margin 17a has elasticity at the time of curing. An adhesive is applied to adhere to the other of the two sides. At this time, a foldable pseudo-conical wall can be manufactured using the transparent resin sheet.
The foldable pseudo-cylindrical wall of the transparent resin sheet is formed with a large number of mountain fold lines M having a convex outer surface and a number of concave valley lines V having a concave shape in a half-fold state.
At the node, which is the intersection of the mountain fold line M and the valley fold line V, a total of six fold lines of four mountain fold lines M and two valley fold lines V intersect. Then, the number of mountain fold lines M intersecting at each node = 4, the number of valley fold lines V = 2, and the difference is 2 (= 4-2). That is, the folding line pattern of the foldable pseudo-conical wall of the twenty-fourth embodiment is a one-node six-fold line.
In FIG. 172, the foldable pseudo-cone wall of the twenty-fourth embodiment has a plurality of parts P1a, P1b, P2a, P2b,... Which are parts (enclosed) formed by the folding lines M and V. . The shapes of the parts P1a, P2a, ... are similar triangles having different sizes, and the shapes of the parts P2a, P2b, ... are similar triangles having different sizes.
A lamp shade 17 is formed by adhering a transparent cellophane paper having a desired color such as red, blue, yellow or the like or a normal color paper to each of the parts P1a, P1b, P2a,. The lamp shade 17 is folded into a small outer shape when stored or transported, and is extended into a pseudo cone having a larger outer shape when used.
(Example 25)
FIG. 173 is an explanatory diagram of a Christmas card as a structure with a fold line according to Embodiment 25 of the present invention. FIG. 173A is a plan view of a folded Christmas card, and FIG. 173B is a plan view of FIG. 173A opened. FIG. 173C is a diagram viewed from obliquely above the arrow 173C in FIG. 173B.
In FIG. 173, the Christmas card C has a tree bonding part C1 to which the Christmas tree T is bonded, and a tree pressing part C2 for pressing the Christmas tree. The Christmas tree T is formed by a conical wall with a folding line made of a colored sheet that satisfies folding conditions. As shown in FIG. 173A, when the Christmas card C is folded, the Christmas tree T is held in a folded state.
When the Christmas card C is opened as shown in FIG. 173, the Christmas tree T expands due to elasticity, and has a three-dimensional shape as shown in FIG. 173C when viewed from obliquely above. Therefore, the person who has received the Christmas card C can feel unusual, enjoyable, and the like.
(Example 26)
174A is an explanatory view of a hat as a structure with a fold line according to Embodiment 26 of the present invention. FIG. 174A is a perspective view of the hat, FIG. 174B is a sectional view taken along the line 174B-174B of FIG. 174A, and FIG. It is the figure seen from arrow 174C of 174B.
FIG. 175 is an explanatory view of the hat of Example 26. FIG. 175A is a plan view of the folded state of the hat, and FIG. 175B is a view seen from the arrow 175B of FIG. 175A.
174 and 175, the hat C (see FIG. 174) has a donut-shaped collar 13 and a foldable crown 14 provided on the upper surface of the central portion of the collar 13. The crown 14 has a hexagonal upper surface portion 14a and a side surface portion (pseudo-conical wall) 14b formed by twisting a hexagonal pyramid.
As shown in FIG. 174B, a large number of mountain fold lines M having a convex outer surface and a large number of valley fold lines V having a concave surface are formed on the side surface (pseudo-cone wall) 14b.
At a node, which is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. Then, the number of mountain fold lines M intersecting at each node = 3, the number of valley fold lines V = 1, and the difference is 2 (= 3-1). That is, the folding line pattern of the side surface portion (pseudo-conical wall) 14b of the ninth embodiment is a one-node four-fold line.
174 and 175, the side portion 14b of the hat C of the twenty-sixth embodiment has a plurality of parts P1 and P2 which are portions formed (enclosed) by the folding lines M and V. The part P1 is triangular and one side thereof is foldably connected to the collar 13. The part P2 is triangular and one side thereof is foldably connected to the upper surface 14a. A mountain fold line M, M,... Is formed at a connection portion between the collar 13 and one side of each of the six parts P1 so that the mountain fold lines M, M,. Connected endlessly.
A mountain fold line M, M,... Is formed at a connection portion between the upper surface member 14a and one side of each of the six parts P2, and the mountain fold lines M, M,. Connected endlessly.
The endlessly connected mountain fold lines M, M,... Are perpendicular to the axis of the side surface portion (pseudoconical wall) 14b when the side surface portion (pseudoconical wall) 14b is extended and folded. It forms a closed polygon in a simple plane.
When the side head 14b of the hat C of the twenty-sixth embodiment is compressed in the axial direction while being twisted, it is folded along the folding lines M and V to be in the state shown in FIGS. 175A and 175B.
The angle between the mountain fold line M and the valley fold line V formed at the connecting portion between the collar 13 and one side of the part P1 is set to an angle larger than 45 °. For this reason, even if the rigidity of the side portion 14b is small, it is easy to maintain the extended state due to the rigidity when it is extended once.
When the hat C is not used, when the hat C is folded as shown in FIG. 175B, the space required for housing the hat C can be reduced.
(Example 27)
FIG. 176 is an explanatory view of a hat as a structure with a folding line according to a twenty-seventh embodiment of the present invention. FIG. 176A is a perspective view of the hat, FIG. 176B is a sectional view taken along the line 113B-113B of FIG. 176A, and FIG. It is the figure seen from arrow 113C of 176B.
FIG. 177 is an explanatory view of the hat of Example 27, FIG. 177A is a plan view of the folded state of the hat, and FIG. 177B is a view from the arrow 114B of FIG. 177A.
In the description of the twenty-seventh embodiment, the same reference numerals are given to components corresponding to the components of the twenty-sixth embodiment, and a detailed description thereof will be omitted.
The embodiment 27 is different from the embodiment 26 in the following points, but is configured similarly to the embodiment 26 in other points.
In FIG. 176A, on the temporal part (pseudo-conical wall) 14b, a plurality of parts P1 to P5 of a trapezoidal shape are formed by a large number of one-node four-fold lines. Each fold line is formed by joining and stitching the ends of the fabric. The mountain fold and the valley fold of the fold line are determined by the joining state of the ends of the fabric. When the end protrudes outward, a mountain fold line M is formed. When the end protrudes inward, the valley fold line is formed. V is formed. The parts P1 to P5 of the isosceles trapezoid are sequentially reduced in size from the part P1 arranged at the bottom to the part P5 arranged at the top.
Each of the isosceles trapezoidal parts P1 has one bottom side foldably connected to the collar 13, and one bottom side of the part P5 is foldably connected to the upper surface 14a. At the connection portion between the collar 13 and one side of each of the six parts P1, a mountain fold line M and a valley fold line V are formed so as to be connected alternately, and the three mountains connected alternately are formed. The fold line M and the three valley fold lines V are connected endlessly so as to form a hexagon.
Three mountain fold lines M and three valley fold lines V are alternately connected to a connection portion between the upper surface member 14a and one side of each of the six parts P5, and a total of six fold lines are formed. They are connected endlessly to form a hexagon.
Similarly to the isosceles trapezoidal parts P1 and P2, six parts P2 to P4 are also arranged in the circumferential direction, and the bases of the isosceles trapezoids alternately form mountain fold lines and valley fold lines. It is connected endlessly in the circumferential direction.
That is, the three mountain fold lines M and the three valley fold lines V connected alternately and endlessly are in the state where the temporal portion (pseudoconical wall) 14b is extended and folded. A closed polygon is formed in a plane perpendicular to the axis of the temporal part (pseudoconical wall) 14b.
When the side head 14b of the hat C of this embodiment 27 is compressed in the axial direction, it is folded along the folding lines M and V to be in the state shown in FIGS. 177A and 177B.
When the hat C is not used, as shown in FIG. 177, when the hat C is folded, the space required for housing the hat C can be reduced.
(Example 28)
FIG. 178 is a perspective view of a rewindable hat as a structure with a folding line according to Embodiment 28 of the present invention.
FIG. 179 is a perspective view of the retractable hat of FIG. 178 in a state of being folded.
FIG. 180 is a perspective view of the retractable hat in a state further folded from the state of FIG. 179.
In FIG. 178, the wind-up hat H is constituted by a flange portion A, a temporal portion B, and a top portion C. As shown in FIGS. 179 and 180, a hatch line M and a valley line V are formed. It can be wound up while being folded along.
FIG. 181 is an explanatory view of the method of manufacturing the wind-up hat shown in FIGS. 178 to 180. FIG. 181A is a developed view of the flange portion A of FIG. 178, FIG. 181B is a developed view of the temporal portion B, and FIG. It is a development view of the crown part C.
As shown in FIG. 181A, an inner radius RAi (“i” means “in”) is drawn in a fan shape (outer radius RAo: “o” means “out”) having a central angle Θ1, and the outer circumference is divided into N (even numbers). A1, A2, A3,... Are drawn, and N equiangular spirals (angle φ = 5 to 10 ° with the radial direction) are drawn from these points in the counterclockwise direction toward the center. If the intersections are B1, B2, B3,..., The line segments B1B2, B2B3, B3B4,. The fan shape is cut by these line segments, and this is defined as a flange portion A. When winding and storing, this spiral is alternately formed into a mountain fold and a valley fold line. In FIG. 181A, Θ1 = 300 ° and N = 12. When both ends of this curved strip-shaped element are joined, a frustoconical shape is formed, and since Θ1 <360 °, the flange A is tapered.
Similarly, the temporal part B is made of a curved strip-shaped element cut out from a fan shape. However, as shown in FIG. 181B, an extremely small apex angle Θ2 is used as compared with the central angle Θ1 of the flange. The outer periphery of the curved strip-shaped element is represented by points C1, C2, C3, C4,. Here, these points are on concentric circles, and the radius is RBo. From these points, draw N spiral or inclined straight lines at an angle φ = 5 to 10 ° in the same manner as above, and define the points D1, D2, D3, D4, ... on the concentric circles of RBi, Determine the inner circumference of the element. When both ends of a curved strip-shaped element are joined, a 台 2 value is small, so that a frustoconical shell close to a cylinder is obtained. The arc length B1B2 = B2B3 = B3B4,... Of the inner periphery of the flange element and the arc length C1C2 = C2C3 = C3C4,. The part B is joined or stitched.
Next, the top portion C is similarly made of a sector shape with a vertical angle Θ3 close to 360 ° or a circular film with Θ3 = 360 °. FIG. 181C shows a case where Θ3 = 360 °. The central angle Θ3 is equally divided into N (= 12) to determine points E1, E2, E3, E4,. The arc length E1E2 = E2E3 = E3E4,... Of the outer periphery of the crown C is taken to be equal to that of the inner periphery of the temporal region B (D1D2 = D2D3 = D3D4 = D4D5,. Join with the inner circumference. That is, when these three elements are joined, the hat shown in FIG. 178 is obtained. When the twelve fold lines are wound alternately around the central axis as mountain folds and valley folds, the result is as shown in FIG.
FIG. 182 is an explanatory diagram of another method of manufacturing the wind-up hat shown in FIGS. 178 to 181.
In FIG. 182, twelve small elements obtained by dividing the three elements into an even number (the modified sectoral elements shown in FIG. 182 in which a, b, and c of FIGS. 181A, 181B, and 181C are stacked) are manufactured. The sides A1B1C1D1E1 and the sides A1B1C1DIE1 are joined or sewn such that the points A1 and A1, B1 and B1, C1 and C1, D1 and D1, and E1 and E1 coincide with each other, and the joining is performed for 12 sector elements. In this way, the retractable hat shown in FIGS. 178 to 180 can be manufactured.
(Example 29)
FIG. 183 is a perspective view of a take-up tent as a structure with a folding line according to Embodiment 29 of the present invention.
FIG. 184 is a perspective view of the retractable tent of FIG. 183 in a state of being folded.
FIG. 185 is a perspective view of the tent in a state further folded from the state of FIG. 183.
In FIG. 183, the winding tent H has a mountain fold line M and a valley fold line V formed along an equiangular spiral (a Bernoulli spiral), and a fan-shaped tent formed by the fold lines M and V. The part can be wound up while being folded along the folding lines M and V. The tent H has a dome shape in an extended state, and ring-shaped flexible tubes H1 and H2 extending in the circumferential direction are fixed to an outer peripheral portion and a radially central portion of an outer surface thereof, respectively. The tent H is maintained in the extended state in FIG. 183 by supplying air to the flexible tubes H1 and H2 and inflating the tent H.
FIG. 186 is an explanatory view of the method of manufacturing the roll-up tent shown in FIGS. 183 to 185. FIG. 186A is a diagram illustrating a dome-shaped roll-up tent in a stretched state, which is divided in a circumferential direction. FIG. 186B is a view in which one of the parts formed at this time is developed, and FIG. 186B is a view showing a conical wall formed when the end AB and the CD of the part shown in FIG. 186A are connected.
FIG. 187 is an explanatory view of the method of manufacturing the roll-up tent shown in FIGS. 183 to 185. FIG. 187 shows a roll-up tent having a dome shape with a radius r1 in an extended state, and coordinates of the center position of the dome shape. When r = 0, j = 1, 2,..., And 10 are divided by a circle having a radius of coordinates rj (rj = r1 × (11−j) / 10) at positions equally divided in the radial direction. FIG. 9 is a view showing a shape of a part (conical wall) (j) formed in FIG.
FIG. 188 is a diagram showing the part number (j) of FIG. 187, the shape and length Lj of the bus, and the inclination θj.
FIG. 189 shows divided parts (J: J = 1, 2,...) Obtained by dividing the developed view of the parts (1), (2),. FIG. 189A is a diagram showing that each part (j) is composed of 16 divided parts (J), and FIG. 189B is a diagram for connecting the divided parts (J) in the radial direction. FIG.
Consider a curved strip ABCD having a curvature of width L at the outer periphery on a sector (outer radius R *) having a central angle Θ as shown in FIG. 186A. When the left and right ends AB and CD of the strip are joined, a truncated cone as shown in FIG. 186B is obtained. Assuming that the radius of the bottom of the truncated cone is R 'and the apex angle of the conical shell obtained by extending the truncated cone is 2θ, the outer circumference of the bottom of the truncated cone is equal to the outer circumference of the strip,
2πR '= R * Θ ……………………………… (59)
Get. From FIG. 186B, since sin θ = R ′ / R *, Θ is given by the following equation (60).
Θ = 2πsin θ ……………………………………… (60)
As shown in FIG. 187, a curve passing through a gentle origin such as a parabola is represented by Z = f (r) on the ZX plane, and a thin film-like rotating shell obtained by rotating this around the Z axis is considered. . The radius of the upper end of the container-shaped rotary shell obtained by this rotation is r1. This rotating shell is divided into n parts on a plane perpendicular to the Z axis, and the rotating shell is approximated by n frusto-conical elements using the relationship in FIG. The intersection of the dividing plane and the shell forms a circle. The radii of the circles are r2, r3,... The n frustoconical elements are named sequentially (1), (2), (3),..., And the angles corresponding to the 切 り values in FIG. Θ3 ...
Since the inner diameter of the element (1) is equal to the outer diameter of the element (2), and the inner diameter of the element (2) is equal to the outer diameter of the element (3), the following equation (61) holds for the i-th and j + 1-th elements.
2πrjΘj = 2πrj + 1Θj + 1 ... (61)
Now, assuming that the previous rotary shell is a paraboloid, Z = C (r / r0)²Let n = 10, and consider a simple case where the cutting radius is given by r2 = 0.9r1, r3 = 0.8r1, r4 = 0.7r1,. FIG. 188 shows a cross-sectional shape after division when C = 0.8, cut on the ZX plane, and each element is approximated by a truncated cone as described above. The length Lj (corresponding to L in FIG. 186) of each of the n truncated cone elements (1), (2), (3),... when they are cut open and expanded is easily calculated. Further, since the angle θj (θ in FIG. 186B) formed by these elements with the Z axis is also obtained, the Θj value of each element can be calculated by using the equation (60). The width of the element (1) is W1 and its outer peripheral length is 2πr1. The ratio between the width and the length is set as κ1 as the aspect ratio (κ1 = W1 / 2πr1). When this strip element is drawn on a circle having a radius Ro, the width W1 = κ1Θ1 ・ Ro = (W1 / 2πr1) Θ1 ・ Ro = W1 ｛Θ1 / (2πr1)｝ Ro, where the apex angle Θ1. That is, the dimensionless width W1 / R0 when represented on the radius Ro is given by W1Θ1 / (2πr0). The other elements are generally given by the following equation (62), with αj≡Wj / (2πrj).
Lj / Ro = αjΘj ………………………………… (62)
If the outer radius of the sector j is Rjo and the inner radius is Rji,
Lj = (Rj) o- (Rj) i ........................ (63)
And (Rj) iΘj = (Rj + 1) oΘj + 1. That is, in FIG. 189A, (R1) iΘ1 = (R2) oΘ2. Using this relationship and equations (59) to (63), Θj, Lj, Wj, and (Rj) i, (Rj) o values can be calculated in the order of elements (1), (2),. FIG. 189A shows a developed view of each element (j) obtained by using these values.
The numerical values in FIG. 188 are as follows.

Next, the developed view of each element in FIG. 189A is equally divided into 2N (N: integer). At this time, a dividing line is drawn on the developed view at an angle forming an angle φ with the radial direction as shown in the figure so as to form a spiral folding line. FIG. 189A is obtained by dividing each developed view into 16 equal parts. The divided small elements are stacked in the radial direction to create a new sector element. The stacked sector is shown in FIG. 189B, which represents a curved shaped sector. When 16 curved sector-shaped elements are joined and the joining line is alternately formed as a crest or valley fold line, a parabolic shell having a spiral fold line (see FIG. 183) is obtained. 183 and 185 are wound around the central axis passing through the apex of the parabolic shell of FIG. 183.
(Example 30)
FIG. 190 is a perspective view of a retractable tent as a structure with a folding line according to Example 30 of the present invention.
FIG. 191 is a perspective view of the retractable tent of FIG. 190 in a state of being folded.
FIG. 192 is a perspective view of the tent further folded from the state of FIG. 190.
In FIG. 190, a winding tent H has a mountain fold line M and a valley fold line V formed along an equiangular spiral (a Bernoulli spiral), and a fan-shaped tent formed by the fold lines M and V. The part can be wound up while being folded along the folding lines M and V. The tent H has a dome shape in an extended state, and ring-shaped flexible tubes H1 and H2 extending in the circumferential direction are fixed to an outer peripheral portion and a radially central portion of an outer surface thereof, respectively. The tent H is maintained in the extended state in FIG. 190 by supplying air to the flexible tubes H1 and H2 and inflating the tent H.
In this embodiment 30, when the film thickness constituting the shell is large, the winding may be cramped at the central portion. Therefore, in order to avoid this, when dividing the FIG. Is divided unequally.
That is, after dividing into eight equal parts, this is further divided into two parts at a central angle ratio of 0.475: 0.525, and eight sets (16 elements) of curved fan-shaped elements are alternately joined. The curved surface is shown in FIG. Here, when the left side of the element having a small central angle is folded into a valley and the right side is folded into a mountain, the element is wound while being shifted downward around the central axis. This is shown in FIGS. 191 and 192. This winding method has an advantage of alleviating the above-mentioned degree of cramp.
These models can be used to form parabolic surfaces of parabolic antennas, as well as large windable / unfoldable tents.
Industrial applicability
As mentioned above, although the Example of this invention was described in full detail, this invention is not limited to the said Example, Various changes are made within the range of the gist of this invention described in the claim. It is possible. Modified embodiments of the present invention are exemplified below.
(1) In Example 1 and FIG. 2, the folding line forming mold has a pair of foldable folding line forming members (flexible molds), and the sheet-like member is sandwiched between the pair of folding line forming members. Although a pair of folding line forming members are simultaneously folded in a folded state to form a folding line on the sheet-like member, the number of folding line forming members (flexible molds) that can be folded is not a pair but only one. May be. When one fold line forming member is used, the fold line forming member may be folded in a state where the sheet-like member is attracted to one surface thereof. As a method of adsorbing the sheet-shaped member, for example, it is possible to adsorb the sheet-shaped member on one surface side by opening a ventilation hole in a part of the folding line forming member and reducing the pressure on the other surface side. Become.
In addition, it is possible to form a fold line by folding the fold line forming member with a sheet-like member sandwiched between a fold line forming member using magnetized material parts and a flexible magnetic rubber sheet. It becomes.
(2) As can be seen from the results of the study by the present inventor and the description of each embodiment, the present invention makes it possible to use fold lines and parts of various shapes with a novel foldable fold line. It is possible to obtain a foldable structure with a fold line. Therefore, according to the present invention, it is possible to configure an expandable and contractible space structure having various shapes.
[Brief description of the drawings]
FIG. 1 is a fold line explanatory diagram showing a representative example of a fold line, which is a straight line to be folded of an origami or a folded structure, and a node, which is an intersection of a plurality of fold lines.
FIG. 2 is an explanatory view of a so-called “Miura ori” folding structure devised by Miura for deployment of a space structure.
FIG. 3 is a view in which the horizontal fold line shown in FIG. 2 is zigzag at an equal angle.
FIG. 4 is a view showing an example of a foldable line of a part (sector-shaped portion) of a disk formed by six sector-shaped elements having a vertex angle of 2 °.
FIG. 5 is a diagram in which the horizontal fold lines shown in FIG. 2 are taken at an arbitrary inclination. The fold lines (7) to (9) are equal at all the nodes with respect to the fold lines (1) to (6). It is the figure drawn in angle and symmetry.
FIG. 6 is a diagram showing an example of a folding line in which the periodicity of the folding method of FIG. 5 is taken into consideration.
FIG. 7 is a view showing plane folding by the one-node four-fold line method and the one-node six-fold line method, showing an example of the folding method considered by the present inventors.
FIG. 8 is a view showing a folding condition of one node where six folding lines of the nodes shown in FIG. 7 intersect and six folding lines (one node and six folding lines) around the node.
FIG. 9 is a view for explaining the condition in which both ends of the band plate are joined to form a cylinder when the band plate is folded along the folding line, and FIG. 9A shows the band plate, the folding line, and the angle of the folding line. FIG. 9B is a diagram showing a change in the direction of the reference axis when folded along the folding line shown in FIG. 9A.
FIG. 10 is an explanatory view of an example in which the above formula (5) is satisfied and the folding direction is folded in a regular quadrangle by a fold line in the same direction (either mountain fold or valley fold). FIG. FIG. 10B is a diagram showing folding lines (1), (2), (3), and (4) of the band plate, FIG. 10B is a diagram showing a state of being folded, and FIG. 10C is a diagram showing a folded state.
FIG. 11 is an explanatory view of an example in which the expression (5) is satisfied and the folding direction is a regular hexagonal folding line along a folding line in the same direction (either mountain fold or valley fold). FIG. FIG. 11B is a diagram showing the folding lines (1), (2), (3), (4), (5), and (6) of the band plate, FIG. 11B is a diagram showing a state in the middle of folding, and FIG. FIG.
FIG. 12 is an explanatory view of an example in which the above-mentioned expression (5) is satisfied and the folding direction is folded in a regular octagonal shape by a folding line in the same direction. FIG. 12A shows folding lines (1) and (2) of the strip in a developed state. ),..., (8), FIG. 12B is a view showing a state in which the sheet is being folded, and FIG. 12C is a view showing a state in which the sheet is folded.
FIG. 13 is an explanatory diagram of an example of folding into a regular hexagon by a fold line that satisfies the expression (5) and the folding direction is alternately reversed (reversed in the mountain fold direction and the valley fold direction), and FIG. 13A is expanded. FIGS. 13B to 13F are views showing a state in the middle of folding, and FIG. 13G is a view showing a folded state.
FIG. 14 is a typical development view in the case where the belt-like plate shown in FIG. 9A is bent in the same direction at equal intervals by π · (N−2) / N to form a regular N-gon and N = 6. FIG.
FIG. 15 shows a trapezoidal element having unequal sides obtained by decomposing twice (π / 3) the angle between the mountain fold line and the horizontal fold line in FIG. 14 into α = 2π / 9 and β = π / 9. FIG.
FIG. 16 shows a case where six sets of fold lines obtained by decomposing the mountain fold line in the Y-axis direction of FIG. 14 into a mountain fold line I of α = π / 3 and a valley fold line II of β = π / 6 are introduced. 16A is an exploded view of a manufactured cylinder, FIG. 16A is a developed view, FIG. 16B is a view showing a half-folded state of a folded cylinder manufactured when both ends of the developed view of FIG. 16A are joined, and FIG. FIG. 4 is a perspective view of the same thing as seen from a different direction.
FIG. 17 is a diagram in which the points A and B in FIG. 14 are matched and the mountain fold is removed from the horizontal fold line. The diamond pattern ((1) to (1) to (6)) is a horizontal isosceles triangle having a base angle π / 6. It is a development view of (3)).
FIG. 18 is a developed view of a deformed diamond pattern composed of scalene triangular elements.
19 is an explanatory view of a pseudo-cylindrical body having a development view symmetrical and foldable one by one with respect to a horizontal folding line, FIG. 19A is a development view, and FIG. 19B is both ends of the development view of FIG. 19C is a view showing a half-folded state of a folding cylinder manufactured when the above is joined, and FIG. 19C is a view of the same thing as FIG. 19B seen from a different direction.
FIG. 20 is a diagram showing an example of a developed development of a fold constituted by only fold lines similar to the point B in FIG.
FIG. 21 is a development view of a foldable cylindrical wall having a plurality of polygonal parts (flat walls) formed by folding lines.
FIG. 22 shows a cylindrical structure in which a connecting portion of a divided flat plate made of a triangular divided flat plate examined by Guest et al. Has a spiral shape, and the spiral (1) rises one step every time it goes around. Is a development view of the present inventor.
FIG. 23 corresponds to FIG. 17 in which the whole of FIG. 17 is inclined by ψ = π / 6, and three diamond patterns in oblique directions are formed.
24 is an explanatory view of a pseudo cylindrical body having a development view equivalent to that of FIG. 23. FIG. 24A is a development view, and FIG. 24B is a fold manufactured when both ends of the development views of FIGS. 23 and 24A are joined. It is a figure showing the half-fold state of a cylinder.
FIG. 25 is an explanatory view of a pseudo cylindrical body k having a development view obtained by inclining FIG. 14 by π / 6. FIG. 25A is a development view, and FIG. 25B is manufactured when both ends of the development view of FIG. 25A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 26 is an explanatory view of a pseudo-cylindrical body having a development view in which FIG. 15 is inclined by π / 6. FIG. 26A is a development view, and FIG. 26B is manufactured when both ends of the development view of FIG. 26A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 27 is a developed view obtained by tilting FIG. 16 by π / 6.
FIG. 28 is a spiral type shown in FIG. 19, which is obtained by cutting along a straight line connecting points A and D in the figure. The angle (up to 0.193π) shown in FIG. 28 indicates the angle between the cutting line and the horizontal line. In this case, the angle of the valley fold line is limited because the shape of the triangular element is given. Become.
FIG. 29 is an explanatory view of a spiral-shaped folding cylinder having a folding line generalized from FIG. 24, FIG. 29A is a developed view, and FIG. 29B is manufactured when both ends of the developed view of FIG. 29A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 30 is a development view in the case where the value of β is changed for each one of the six development steps of FIG. 29 by three steps.
FIG. 31 is a development view of a repetitive spiral type obtained by inverting the spiral mountain fold line and the valley fold line of FIG. 29 for each stage. This development can also be obtained by matching points A and B in FIG.
FIG. 32 is a view showing a portion cut by two parallel straight lines AB 'and C'D of the developed view of the cylindrical body shown in FIG. 21 so that A and B' and D and C 'overlap. FIG. 33 is a developed view of a foldable cylinder formed by connecting left and right edges of FIG.
FIG. 33 is an exploded view of a collapsible cylinder having an arbitrary-shaped quadrilateral element (part).
FIG. 34 is an explanatory diagram of a method for maintaining continuity when both ends of a developed view are joined.
FIG. 35 is a diagram showing an angle relationship between folding lines satisfying folding conditions when a valley fold line is symmetrically inserted in the case of one node 6 fold lines. FIG.
FIG. 36 is a diagram showing an angular relationship between folding lines satisfying the folding condition when the valley folding lines (4) and (6) are inserted alternately between the mountain folding lines (2), (3) and (5). FIG. 58 is an explanatory diagram of folding conditions in the case of FIGS. 56B and 57 described later.
FIG. 37 shows the case of one node 4-fold line. The folding conditional expression is obtained by the same procedure as above.
FIG. 38 is an enlarged view of a main part of a development view in a case where a development view of a cone whose main fold line is parallel to the outer side of the development view is composed of N isosceles triangles having a vertex angle of 2 °.
FIG. 39 is an explanatory view of a pseudo-cone wall having a development view of a pseudo-cone wall with a folding line obtained by using the value obtained by Expression (14). FIG. 39A is a development view, and FIG. 39B is a development view of FIG. 39A. It is a perspective view of the half-fold state of the conical wall with a folding line which has a.
FIG. 40 is an enlarged view of a main part of a development view of a conical wall with a fold line when divided into inequilateral triangular elements by a fold line.
FIG. 41 is a development view of a conical wall with a fold line when divided into inequilateral triangular elements by a fold line, where N = 3, 2Θ = π / 9, α = π / 9, and δ = π / 6. Of development (θ^*= About 0.0688π).
FIG. 42 is a development view of a conical wall with a fold line when it is divided into a trapezoidal triangular element by a fold line having an angle α at the upper right and an angle δ at the upper left at the point F in FIG. , Δ values are the same as those in FIG. 41.
FIG. 43 is an enlarged view of a main part of a development view of a conical wall with a fold line in the case of dividing by a trapezoidal element instead of dividing by the isosceles triangular element of FIG.
FIG. 44 is a view of a conical wall with a fold line, which is divided into an equilateral trapezoidal shape by a fold line and folded into a regular N pyramid, where N = 6, φ in FIG.^*= Π / 36, 2Θ = π / 12 is an explanatory view of a pseudo-conical wall having a development view, FIG. 44A is a development view, and FIG. 44B is a half-fold of a conical wall with a folding line having the development view of FIG. 44A. FIG.
FIG. 45 is a view showing a development view of a conical wall with a folding line composed of N isosceles triangular elements (vertical angle 2 °), in which only one step is written out as a curved strip portion.
FIG. 46 is an exploded view of a conical wall with a fold line having a simple, spiral exploded view consisting of three isosceles triangular elements.
FIG. 47 is a top view when the development view of FIG. 46 is folded.
48 is an explanatory diagram of a practical model obtained by modifying the model described in FIGS. 45 and 46. FIG. 48A is an explanatory diagram of a modification method, and FIG. 48B is an enlarged view of a main part of FIG. 48A.
FIG. 49 is a view showing a state in which the figure ABGHFE formed by the folding line in FIG. 48A is sequentially folded along folding lines AF and BF, and FIG. 49A is a state of rectangles ABFE and BGHF after AF is trough-folded. 49B is a view showing a state after the mountain fold is further performed at B′F (original line segment BF) in the state of FIG. 49A.
FIG. 50 is a view showing a portion corresponding to the first-stage band plate and a portion corresponding to the second-stage band shown in FIG. 48A.
FIG. 51 shows N = 6, γ + ψ in the fold line-shaped conical wall having the fold lines shown in FIGS.^*= Π / 3, ψ^*51A is an explanatory view of a pseudo-cone wall having a development view (2Θ = π / 18) when γ / 6 and γ = π / 6, FIG. 51A is a development view, and FIG. 51B is a development view of FIG. It is a perspective view of the state where the conical wall with a fold line was folded in half.
FIG. 52 shows N = 6, γ + ψ in the conical wall with a fold line having the fold lines shown in FIGS.^*= Π / 3, ψ^*= Π / 4, γ = π / 12 (2１２ = π / 6).
FIG. 53 shows an example in which the number of stages in the development view of FIG.^*FIG. 6 is a development view when the value of “” is increased.
FIG. 54 is a developed view showing the same conical wall as the folded conical wall having the developed view of FIG. 53.
FIG. 55 is a view when the second valley fold line in FIG. 50 is taken in an opposite direction to that of the first tier at an angle γ.
FIG. 56 is an explanatory view of a pseudo-cone having a development view in which the FIG. 51 is made into a repetitive spiral type. FIG. 56A is a development view, and FIG. 56B is a half-fold of a conical wall with a folding line having the development view of FIG. It is a perspective view of the state which carried out.
FIG. 57 shows 2Θ = π / 6, ψ^*= [Pi] / 6, [gamma] = [pi] / 6;
58 is an explanatory view of a development view of a foldable conical wall with a folding line having a folding line along an equiangular spiral, FIG. 58A is an overall explanatory view, and FIG. 58B is an enlarged view of a main part of FIG. 58A.
FIG. 59 is an explanatory view of a development view of the conical wall with a folding line when the spiral of FIG. 58 is reversed.
FIG. 60 is an explanatory diagram of how to draw the development view of FIG.
FIG. 61 is an explanatory view of a pseudo-cone having an exploded view in which FIG. 44 is made into an equiangular spiral shape. FIG. 61A is an exploded view, and FIG. 61B is a half-folded conical wall with a fold line having the exploded view of FIG. 61A. FIG.
FIG. 62 is a developed view of a folding conical wall with a folding line in which the circumferential spiral of FIG. 51A is raised one step at the right end.
FIG. 63 is an explanatory diagram of the simplest folding method for origami.
FIG. 64 is an explanatory view of a development view of a disc-shaped folding structure with a folding line. FIG. 64A is an enlarged view of a main part for explaining folding conditions, and FIG. 64B is an overall view.
FIG. 65 is an enlarged view of a development view of the disc-shaped folding structure with a folding line shown in FIG. 64B.
FIG. 66 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 65 in a half-folded state and a small amount of folding.
FIG. 67 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 65 in a half-folded state and a state in which the amount of folding is large.
FIG. 68 is a perspective view showing a state in which the disk-shaped folding structure with folding lines having the developed view of FIG. 65 is completely folded.
FIG. 69 is an explanatory view of a development view of a disc-shaped folding structure with a folding line when the swing angle of the folding line of Zig / Zag in the radial direction is increased as approaching the center, and FIG. 69A is for explaining the folding conditions. 69B is an overall view of FIG.
FIG. 70 is an exploded view of a disc-shaped folding structure with a folding line when the swing angle of the folding line of Zig / Zag in the radial direction is increased as approaching the center and the folding line in the circumferential direction is also Zig / Zag. 70A is an enlarged view of a main part for explaining folding conditions, and FIG. 70B is an overall view.
FIG. 71 is an explanatory view of a conventionally known winding method in which the intersection of the spiral folding lines is on the Archimedes spiral.
FIG. 72 is a view showing a new folding line considered by the present inventor. FIG. 72A is a folding line in which the folding line (1) in the radial direction has one bending point and the spiral is reversed at this bending point in FIG. FIG. 72B is a diagram showing a line, and FIG. 72B is a diagram in which the outside of the bending point of FIG. 72A is replaced by a method of folding in a radial direction.
FIG. 73 is an explanatory diagram of fold lines when forming a fold line for folding a circular film or a partial circular film (sector-shaped film) in a radial direction and a circumferential direction along an equiangular spiral.
FIG. 74 is an explanatory diagram of fold lines when folding a circular film or a partial circular film (sector-shaped film) in the radial direction and the circumferential direction along an equiangular spiral.
FIG. 75 is an enlarged view of a main part of FIG.
FIG. 76 is an explanatory view of folding conditions when forming a folding line for folding a circular film or a partial circular film (sector-shaped film) in a radial direction and a circumferential direction along an equiangular spiral.
FIG. 77 is an explanatory diagram of folding conditions when the main fold line is bent at an equal angle to radiation.
FIG. 78 shows an example of folding around the center with two zigzag spirals (m = 2) as folding lines, where n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 20 °.
FIG. 79 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 78 is an example of a folded development view when γ = 0 °, showing an example in which the angle of the folding line with respect to the radiation is different from FIG. 78.
FIG. 80 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 10, the number of isosceles triangular elements N = (2n + 1) m = 42, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
FIG. 81 shows an example of folding around the center using two zigzag spirals (m = 2) as folding lines, where n = 4, the number of isosceles triangular elements N = (2n + 1) m = 18, It is a figure which shows the example of the development view of the disk-shaped folding structure with a folding line in case of (gamma) = 0 degree.
FIG. 82 is a perspective view of the disc-shaped folding structure with a folding line having the developed view of FIG. 81 in a half-folded state with a small amount of folding.
FIG. 83 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 81 in a half-folded state and a state in which the amount of folding is large.
FIG. 84 is a perspective view showing a state in which the disk-shaped folding structure with a folding line having the developed view of FIG. 81 is completely folded.
FIG. 85 shows an example of folding around the center using four zigzag spirals (m = 4) as folding lines, where n = 7, the number of isosceles triangular elements N = (2n + 1) m = 60, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
FIG. 86 shows an example in which three zigzag spirals (m = 3) are used as folding lines and folded around the center, where n = 8, the number of isosceles triangular elements N = (2n + 1) m = 51, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
FIG. 87 shows an example in which one zigzag spiral (m = 1) is used as a fold line and folded around the center, where n = 10, the number of isosceles triangle elements N = (2n + 1) m = 21, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
FIG. 88 shows an example of folding around the center using four zigzag spirals (m = 4) as folding lines, where n = 7, the number of isosceles triangular elements N = (2n + 1) m = 60, It is a figure which shows the example of the development view of the disk-shaped folding structure with a folding line in case of (gamma) = 0 degree.
FIG. 89 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 88 in a half-folded state and a state in which the amount of folding is small.
FIG. 90 is a perspective view of the disc-shaped folding structure with a folding line having the developed view of FIG. 88 in a half-folded state and a state in which the amount of folding is large.
FIG. 91 is a perspective view showing a state in which the disk-shaped folding structure with a folding line having the developed view of FIG. 88 is completely folded.
FIG. 92 is a developed view in the case where the number of spirals serving as main folding lines is large (m = 12).
FIG. 93 is a developed view composed of two types of conformal spirals based on FIG. 77. Division number N = 12, θ₁= Π / 180, θ₂= 29π / 180, and φ is approximately π / 18. When the developed view of FIG. 93 is folded, it is satisfactorily wound around the center in a vertically symmetric manner. FIG. 93 suggests that these fold lines are replaced by elastic deformation during winding because the sub-fold lines are fine.
FIG. 94 is a developed view of a circular thin plate in which mountain fold lines and valley fold lines are provided alternately.
FIG. 95 shows the development of a disk-shaped folding structure with fold lines in which mountain fold lines and valley fold lines are provided alternately, and the circumferential lengths of the valley fold line and the left and right mountain fold lines are different on the left and right. FIG.
FIG. 96 is a view in which a fan-shaped portion between adjacent mountain fold lines in FIG. 95 is removed.
97 is an explanatory diagram of the folding condition of the sheet-like member, FIG. 97A is a developed view before folding, and FIG. 97B is a diagram showing a state where the sheet-like member is folded along a folding line in FIG. 97A.
FIG. 98 is an explanatory view of a DCC (double corrugated core), FIG. 98A is a developed view of the DCC, and FIG. 98B is an external view of the half folded state.
FIG. 99 is an explanatory view of zig / zag of the vertical fold line group of FIG. 98, FIG. 99A is an expanded view thereof, and FIG. 99B is an external view of the half-folded state.
100A is an explanatory view of a newly devised model of a core having a joint, FIG. 100A is a developed view, FIG. 100B is a plan view of the developed view of FIG. 100A in a half-folded state, and FIG. 100C is an expanded view of FIG. 100A. It is an external view of what folded the figure and made it three-dimensional.
FIG. 101 is an explanatory view of another model of a newly devised core having a joint. FIG. 101A is a developed view, FIG. 101B is a plan view of the developed view of FIG. 101A in a half-folded state, and FIG. 101C is FIG. 3 is an external view of a three-dimensional view obtained by folding the development view of FIG.
FIG. 102 is an explanatory view of a model devised by the present inventor that does not satisfy another folding condition of a core having a joint, FIG. 102A is a developed view, and FIG. 102B is an enlarged view of a main part of FIG. 102A.
FIG. 103 is an explanatory view of a core formed by folding the developed view of FIG. 102A, FIG. 103A is a perspective view of the folded core, and FIG. 103B is a perspective view of a sheet bonded to the lower surface of the core of FIG. 103A. .
FIG. 104 is an explanatory view of a model devised by the present inventor that does not satisfy another folding condition of a core having a joint, FIG. 104A is a developed view, and FIG. 104B is an enlarged view of a main part of FIG. 104A.
FIG. 105 is an explanatory diagram of a method of manufacturing a honeycomb core from one plate, FIG. 105A is a developed view, and FIG. 105B is a view of a honeycomb core manufactured from a plate having the developed view of FIG. 105A.
FIG. 106 is a view showing a folding mold for manufacturing the core material shown in FIG. 103A.
FIG. 107 is an explanatory view of the manufactured aluminum core. FIG. 107A is a perspective view, and FIG. 107B is a developed view, which has the same shape as the developed view of the paper shown in FIG. 103A.
FIG. 108 is an explanatory diagram of an application example of the structure with a cylindrical folding line, and FIG. 108A is a developed view.
FIG. 109 is an explanatory diagram of an application example of a spiral cylindrical structure with a folding line. FIG. 109A is a developed view, and FIG. 109B is a view showing a stretchable inflatable structure formed based on FIG. 109A.
FIG. 110 is a plan view of the folding line forming die according to the first embodiment of the present invention.
FIG. 111 is a perspective view of a sheet-like member on which a folding line is formed using the folding line forming mold of FIG.
FIG. 112 is an explanatory view of a folding line forming die according to the second embodiment of the present invention, and is a perspective view of one of a pair of flexible dies for sandwiching both sides of a sheet-like member forming a folding line. FIG.
FIG. 113 is a plan view of a folding line forming die according to Embodiment 3 of the present invention.
FIG. 114 is an explanatory view of a use state of the folding line forming die of FIG. 113, FIG. 114A is a diagram showing a state where the folding line forming die is folded in two, and FIG. 114B is a folding diagram of FIG. 114A. It is a figure which shows the state which folded the folding line forming die.
FIG. 115 is an explanatory view of a sheet-like member in which a folding line is formed by using the folding line forming mold shown in FIGS. 113 and 114. FIG. 115A is a plan view of the sheet-like member in a half-folded state, and FIG. It is a top view of the state where it was completely folded.
116 is an explanatory view of the folded sheet member shown in FIG. 115B, FIG. 116A is a perspective view, and FIG. 116B is a flat sheet member on one surface (lower surface) of the folded sheet member shown in FIG. 116A. It is a perspective view of what adhered.
FIG. 117 is a side view of a plastic bottle as a structure with a folding line according to Embodiment 4 of the present invention.
FIG. 118 is a side sectional view of the plastic bottle of the fourth embodiment.
FIG. 119 is an explanatory view of a state in which the plastic bottle of FIG. 117 is compressed in the axial direction (semi-folded state), FIG. 119A is a view showing a half-folded state, and FIG. 119B is a cover almost completely folded in an opening portion. FIG.
FIG. 120 is an explanatory diagram of the method of manufacturing the PET bottle A, and is a diagram illustrating a state in which a mold (a mold having a folding line forming surface) is opened.
FIG. 121 is an explanatory diagram of the method for manufacturing the PET bottle A, showing a state in which the mold is closed and a tubular or bag-shaped raw tube (parison) is stretched in the mold.
FIG. 122 is a diagram showing a state where compressed air is blown into the inside of the raw tube of FIG. 121 to expand the tube.
FIG. 123 is an explanatory diagram of a PET bottle as a fifth embodiment of the folded line structure according to the present invention, and is a diagram illustrating a folded line structure (pet bottle) formed along a spiral.
FIG. 124 is an explanatory diagram of a plastic bottle as a sixth embodiment of the folded line structure of the present invention, and is a diagram illustrating a folded line structure (pet bottle) having a cylindrical wall formed along a spiral.
FIG. 125 is a side view of a coffee can as a structure with a folding line according to Embodiment 7 of the present invention.
FIG. 126 is a side sectional view of the coffee can of the seventh embodiment.
FIG. 127 is an explanatory view of a state in which the coffee can of FIG. 126 is compressed in the axial direction (semi-folded state). FIG. 127A is a side view of the half-folded state, and FIG. 127B is a side view of a state of being almost completely folded. .
FIG. 128 is an explanatory view of a method for manufacturing the coffee can A, and is an explanatory view of an inner mold (a mold having a folding line forming surface) disposed on the inner surface of the cylindrical member. FIG. FIG. 128B is a cross-sectional view in which a pair of inner second dies are inserted between the pair of inner first dies of FIG. 128A; FIG. 128C is a cross-sectional plan view showing a state where a cam rod is inserted into the center of the inner first and second molds of FIG. 128B, and FIG. 128D is a diagram showing a state where the cam rod of FIG. It is a figure showing the state where the inside 1st and 2nd metallic molds were pushed out by pushing out.
FIG. 129 is an explanatory view of the method for manufacturing the coffee can A. FIG. 129A shows a state in which an inner mold (a mold having a folding line forming surface) is set on the inner surface of a cylindrical member, and the outer mold K2 is clamped. FIG. 129B is a diagram showing a state before, and FIG. 129B is a diagram showing a state where the mold is clamped from the state of FIG. 129A.
FIG. 130 is an explanatory view of a coffee can as the eighth embodiment of the folded line structure of the present invention, and is a diagram showing a folded line structure (coffee can) having a cylindrical wall formed along a spiral.
FIG. 131 is an explanatory diagram of another embodiment of the method for manufacturing the coffee can A.
132 is an explanatory diagram of a small container as a structure with a folding line according to Embodiment 9 of the present invention. FIG. 132A is a perspective view of a lid of the small container, and FIG. 132B is a perspective view of the small container in an extended state.
133 is an explanatory view of the small container of Example 9; FIG. 133A is a perspective view of the folded small container; FIG. 133B is a sectional view taken along the line 109B-109B of FIG. 133A; It is sectional drawing of the state which covered the container.
FIG. 134 is an explanatory diagram of the method of manufacturing the small container B, and shows a state in which a mold (a mold having a folding line forming surface) is closed.
FIG. 135 is an explanatory diagram of a paper pack as a structure with a folding line according to the tenth embodiment of the present invention, and is a perspective view of a used state in which the paper pack is extended.
FIG. 136 is a view showing a state in which the paper pack of FIG. 135 is being folded.
FIG. 137 is a view showing a state where the paper pack of FIG. 136 is further folded.
FIG. 138 is a developed view of the paper pack shown in FIGS.
FIG. 139 is an explanatory diagram of a paper pack as a structure with a folding line according to Embodiment 11 of the present invention, and is a perspective view of a used state where the paper pack is extended.
FIG. 140 is a view showing a state in which the paper pack of FIG. 139 is being folded.
FIG. 141 is a diagram showing a state where the paper pack of FIG. 140 is further folded.
FIG. 142 is a developed view of the paper pack shown in FIGS. 139 to 141.
FIG. 143 is an explanatory view of a paper pack as a structure with a folding line according to a twelfth embodiment of the present invention, and is a perspective view of a used state in which the paper pack is extended.
FIG. 144 is a view showing a state in which the paper pack of FIG. 143 is being folded.
FIG. 145 is a view showing a state where the paper pack of FIG. 144 is further folded.
FIG. 146 is a developed view of the paper pack shown in FIGS. 143 to 145.
FIG. 147 is an explanatory diagram of a paper pack as a structure with a folding line according to Embodiment 13 of the present invention, and is a perspective view of a used state in which the paper pack is extended.
FIG. 148 is a view showing a state in which the paper pack of FIG. 147 is being folded.
FIG. 149 is a view showing a state where the paper pack of FIG. 148 is further folded.
FIG. 150 is a developed view of the paper pack shown in FIGS. 147 to 149.
FIG. 151 is an explanatory diagram of a pump as a structure with a folding line according to Embodiment 14 of the present invention.
FIG. 152 is an explanatory diagram of a trash can as a structure with a folding line according to Embodiment 15 of the present invention. FIG. 152A is a side view, and FIG. 152B is a side sectional view.
FIG. 153 is an explanatory diagram of a pencil stand as a structure with a folding line according to Example 16 of the present invention. FIG. 153A is a side view, and FIG. 153B is a side sectional view.
FIG. 154 is an explanatory diagram of a gusset (partition member inside a box) as a structure with a folding line according to a seventeenth embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 155 is a perspective view of the gusset of FIG.
FIG. 156 is a developed view of the gusset of FIG. 155.
FIG. 157 is an explanatory view of a gusset (partition member inside a box) as a structure with a folding line according to Embodiment 18 of the present invention, and is a perspective view of the gusset taken out of the paper box.
FIG. 158 is a development view of the gusset of FIG. 157.
FIG. 159 is an explanatory diagram of a gusset (partition member inside a box) as a structure with a folding line according to a nineteenth embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 160 is a perspective view of the gusset shown in FIG.
FIG. 161 is a developed view of the gusset of FIG. 159.
FIG. 162 is an explanatory view of a gusset (partitioning member inside a box) as a structure with a folding line according to a twentieth embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 163 is a perspective view of the gusset of FIG.
FIG. 164 is a developed view of the gusset of FIG. 163.
FIG. 165 is an explanatory diagram of a gusset (partition member inside a box) as a structure with a folding line according to a twenty-first embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 166 is a perspective view of the gusset of FIG.
FIG. 167 is a developed view of the gusset of FIG. 166.
168 is an explanatory view of the foldable passage cover, FIG. 168A is a perspective view of a half-folded state, and FIG. 168B is a perspective view of a completely folded state.
FIG. 169 is a developed view of a foldable passage cover as a structure with a folding line according to Embodiment 22 of the present invention.
170 is an explanatory view of the foldable passage cover having the developed view of FIG. 171. FIG. 170A is a perspective view of a half-folded state, and FIG. 170B is a perspective view of a completely folded state.
FIG. 171 is a development view of a foldable passage cover as a structure with a folding line according to Embodiment 23 of the present invention.
FIG. 172 is an explanatory view of a lamp shade as a structure with a fold line according to Embodiment 24 of the present invention. FIG. 172 is a development view of a sheet-like member that is a material for manufacturing the lamp shade. FIG. 172B is a sheet of FIG. FIG. 4 is a perspective view of a lamp shade formed by manufacturing a pseudo cone by joining left and right sides of a shape member to a half-folded state.
FIG. 173 is an explanatory diagram of a Christmas card as a structure with a fold line according to Embodiment 25 of the present invention. FIG. 173A is a plan view of a folded Christmas card, and FIG. 173B is a plan view of FIG. 173A opened. FIG. 173C is a diagram viewed from obliquely above the arrow 173C in FIG. 173B.
FIG. 174 is an explanatory view of a hat as a structure with a folding line according to Embodiment 26 of the present invention. FIG. 174A is a perspective view of the hat, FIG. 174B is a sectional view taken along the line 111B-111B of FIG. 174A, and FIG. It is the figure seen from arrow 111C of 174B.
FIG. 175 is an explanatory view of the cap of Example 26, FIG. 175A is a plan view of the folded state of the hat, and FIG. 175B is a view from the arrow 112B of FIG. 175A.
FIG. 176 is an explanatory view of a hat as a structure with a folding line according to a twenty-seventh embodiment of the present invention. FIG. 176A is a perspective view of the hat, FIG. 176B is a sectional view taken along the line 113B-113B of FIG. 176A, and FIG. It is the figure seen from arrow 113C of 176B.
FIG. 177 is an explanatory view of the hat of Example 27, FIG. 177A is a plan view of the folded state of the hat, and FIG. 177B is a view from the arrow 114B of FIG. 177A.
FIG. 178 is a perspective view of a rewindable hat as a structure with a folding line according to Embodiment 28 of the present invention.
FIG. 179 is a perspective view of the retractable hat of FIG. 178 in a state of being folded.
FIG. 180 is a perspective view of the retractable hat in a state further folded from the state of FIG. 179.
FIG. 181 is an explanatory view of the method of manufacturing the wind-up hat shown in FIGS. 178 to 180. FIG. 181A is a developed view of the flange portion A of FIG. 178, FIG. 181B is a developed view of the temporal portion B, and FIG. It is a development view of the crown part C.
FIG. 182 is an explanatory diagram of another method of manufacturing the wind-up hat shown in FIGS. 178 to 181.
FIG. 183 is a perspective view of a take-up tent as a structure with a folding line according to Embodiment 29 of the present invention.
FIG. 184 is a perspective view of the retractable tent of FIG. 183 in a state of being folded.
FIG. 185 is a perspective view of the tent in a state further folded from the state of FIG. 183.
FIG. 186 is an explanatory view of the method of manufacturing the roll-up tent shown in FIGS. 183 to 185. FIG. 186A is a diagram illustrating a dome-shaped roll-up tent in a stretched state, which is divided in a circumferential direction. FIG. 186B is a view in which one of the parts formed at this time is developed, and FIG. 186B is a view showing a conical wall formed when the end AB and the CD of the part shown in FIG. 186A are connected.
FIG. 187 is an explanatory view of the method of manufacturing the roll-up tent shown in FIGS. 183 to 185. FIG. 187 shows a roll-up tent having a dome shape with a radius r1 in an extended state, and coordinates of the center position of the dome shape. When r = 0, j = 1, 2,..., And 10 are divided by a circle having a radius of coordinates rj (rj = r1 × (11−j) / 10) at positions equally divided in the radial direction. FIG. 9 is a view showing a shape of a part (conical wall) (j) formed in FIG.
FIG. 188 is a diagram showing the part number (j) of FIG. 187, the shape and length Lj of the bus, and the inclination θj.
FIG. 189 shows divided parts (J: J = 1, 2,...) Obtained by dividing the developed view of the parts (1), (2),..., (10) shown in FIG. FIG. 189A is a diagram showing that each part (j) is composed of 16 divided parts (J), and FIG. 189B is a diagram connecting the divided parts (J) in the radial direction. FIG.
FIG. 190 is a perspective view of a retractable tent as a structure with a folding line according to Example 30 of the present invention.
FIG. 191 is a perspective view of the retractable tent of FIG. 190 in a state of being folded.
FIG. 192 is a perspective view of the tent further folded from the state of FIG. 190.

[0005]
. It is well known that the following equation holds between NM and NV at a node.
| NM−NV | = 2 ………………………………… (1)
When the total number of folding lines is set to NT, NT = NM + NV. If Equation (1) is, for example, NM-NV = 2, NT = 2 (1 + NV), and it can be seen that the number of fold lines forming the node is "even". The total number of folding lines NT is NT ≧ 4, and NT = 4 is the minimum number of folding lines for forming a node.
As shown in FIG. 1, when the X axis is aligned with the mountain fold line (M3) and the mountain folds (M1) and (M2) are performed, a valley fold (V1) occurs. If the angles between the mountain folds (M1) and (M2) and the X axis are α and β, respectively, the angle γ between the fold lines (V1) and (M2) is
γ = α …………………………………………… (2)
Given by Expression (2) is a relational expression of the angle when completely folded along the folding lines (M1), (M2), (M3), and (V1) in the Y-axis direction.
By this operation, the band-shaped paper is folded in half, and the axial direction to the right of the node is folded by 2α (when α <β) or 2β (when α> β).
When α = β, the axial direction is not bent in the Y-axis direction. At this time, it is easily presumed that the band-shaped paper bends in a zigzag manner when the mountain fold and the valley fold are alternately performed, and that when the mountain fold (or the valley fold) is continuously performed, the paper becomes cylindrical.
In the present specification, the term “planar fold” refers to folding plane paper in a zigzag manner and folding it into a new plane in this manner, and the term “cylindrical” refers to a method of folding a sheet in the same direction to produce a cylindrical structure that can be folded in the Y-axis direction. Ori ".
2 Flat folding 2.1 Miura ori (prior art)
In order to consider the possibility of the structure of the structure, consider the simplest case of "one-node four-fold line".
FIG. 2 is an explanatory view of a so-called “Miura ori” folding structure devised by Miura for deployment of a space structure.
In FIG. 2, the fold lines of the folded structure are three horizontal fold lines ((1) to (3)) and three zigzag fold lines (peak, valley, peak fold, respectively). To (6)). The folding lines (1) to (3) are alternately mountain-folded and valley-folded so that the expression (1) is satisfied.

[0006]
Each of the fold lines (4) to (6) is "symmetric" with respect to all of the fold lines (1) to (3). Therefore, at each node (black dot), the folding condition of Expression (2) is automatically satisfied at an arbitrary angle α in the drawing, and the node can be completely folded in the Y-axis direction in the drawing.
At this time, it also contracts in the X-axis direction depending on the angle α, and the contraction amount increases as the folding angle α increases. Also, as can be seen from FIG. 2, the horizontal fold line alternates from a mountain fold to a valley fold and from a valley fold to a mountain fold at the left and right of the node. The characteristic of the 4-fold line method enables the flat paper to be periodically folded from Y = + ∞ to −∞.
FIG. 3 is a view in which the horizontal fold line shown in FIG. 2 is zigzag at an equal angle.
In FIG. 2, at each node, the folding lines (4) to (6) are symmetrical with respect to the horizontal folding lines (1) to (3), but the horizontal folding is zigzag at an equal angle as shown in FIG. 3, the folding condition in the Y-axis direction in Expression (2) is satisfied, and the plane paper in FIG. 3 is completely folded in a new shape. It can be seen that when the fold is in a half-folded state, the flat paper can be made three-dimensional, that is, in a state having an “apparent” thickness, and a flat plate with high rigidity and light weight can be manufactured.
2.2 Generalization of Planar Folding If the horizontal folding lines provided in zigzag in FIG. 3 are continued in the same direction, the fan or disk can be folded in the radial direction.
FIG. 4 is a view showing an example of a foldable line of a part (sector-shaped portion) of a disk formed by six sector-shaped elements having a vertex angle of 2 °.
In FIG. 4, the circumferential folding lines (1) to (5) are bent by 2 °. The radial fold lines (7), (8), (9)... Are provided in a zigzag manner within the angle 、, and the outer sides A, B, C.
At this time, since the angle β in FIG. 4 is α0 + か ら due to the periodicity of these fold lines, the angle α1 between the circumferential fold line (1) and the radial fold line is taken as α0−Θ. The folding conditional expression, Expression (2), is satisfied. That is, if the angles of the radial fold line and the circumferential fold line are selected from time to time as shown in the figure, α0−Θ, α0−2Θ... An exploded view can be created in which the board can be folded radially.
In addition, like the fan-shaped plate, a circular plate can be folded in the radial direction.

[0010]
The angle Θ4 formed by the axis X4 and the axis X0 is Θ4 = 2 (θ1−θ2 + θ3−θ4) = 2 (135 ° −45 ° + 135 ° −45 °) = 2π. Therefore, n in equation (5) is n = (Θ4 / 2π) = 1, and the axis X4 overlaps the axis X0. In this case, both ends of the strip are joined without any gap.
FIG. 11 is an explanatory view of an example in which the expression (5) is satisfied and the folding direction is a regular hexagonal folding line along a folding line in the same direction (either mountain fold or valley fold). FIG. FIG. 11B is a diagram showing the folding lines (1), (2), (3), (4), (5), and (6) of the band plate, FIG. 11B is a diagram showing a state in the middle of folding, and FIG. FIG.
In FIG. 11A, the folding lines (1) to (6) of the strip extending in the X-axis direction, which is the reference axis, form angles θ1 to θ6 with respect to the X-axis, respectively, and θ1 = θ3 = θ5. = 150 ° and θ2 = θ4 = θ6 = 30 °. That is, the fold lines (1) to (6) are formed zigzag at 30 ° (= π / 6) with respect to the X axis.
In FIG. 11, the angle Θ6 formed by the axis X6 and the axis X0 is Θ6 = 2 (θ1−θ2 + θ3−θ4 + θ5−θ6) = 2 (150 ° −30 ° + 150 ° −30 ° + 150 ° −30 °) = 2 × 2π. . Therefore, n in equation (5) is n = (Θ6 / 2π) = 2, and the axis X6 overlaps the axis X0. In this case, both ends of the strip are joined without any gap.
FIG. 12 is an explanatory view of an example in which the above-mentioned expression (5) is satisfied and the folding direction is folded in a regular octagonal shape by a folding line in the same direction. FIG. 12A shows folding lines (1) and (2) of the strip in a developed state. ,... (8), FIG. 12B is a diagram showing a state of being folded, and FIG. 12C is a diagram showing a state of being folded.
In FIG. 12A, the folding lines (1) to (8) of the strip extending in the X-axis direction, which is the reference axis, form angles θ1 to θ8 with respect to the X-axis, respectively, and θ1 = θ3 = θ5. = Θ7 = 157.5 °, θ2 = θ4 = θ6 = θ8 = 22.5 °. That is, the fold lines (1) to (8) are formed zigzag at 22.5 ° (= π / 8) with respect to the X axis.
In FIG. 12, the angle Θ8 formed by the axis X8 with the axis X0 is Θ8 = 2 (θ1−θ2 + θ3−θ4 + θ5−θ6 + θ7−θ8) = 2 (157.5 ° -22.5 ° + ... + 157.5 ° -22.5 °) ) = 3 × 2π. Therefore, n in the equation (5) is n = (Θ8 / 2π) = 3, and the axis X8 overlaps the axis X0. In this case, both ends of the strip are joined without any gap.

[0014]
It is a figure which shows the half-fold state of the folding cylinder made.
In the example shown in FIGS. 23 to 24B, when the left end L and the right end R of the developed view are joined to form a cylinder, the pattern formed by the folding lines is continuous.
FIG. 25 is an explanatory view of a pseudo-cylindrical body having a development view in which FIG. 14 is inclined by π / 6. FIG. 25A is a development view, and FIG. 25B is manufactured when both ends of the development view of FIG. 25A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 25A corresponds to a view obtained by cutting FIG. 14 along a horizontal line GH inclined by π / 6 with respect to a horizontal line, and setting the cut line as a horizontal lower end.
FIG. 26 is an explanatory view of a pseudo-cylindrical body having a development view in which FIG. 15 is inclined by π / 6. FIG. 26A is a development view, and FIG. 26B is manufactured when both ends of the development view of FIG. 26A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 27 is a developed view obtained by tilting FIG. 16 by π / 6.
In the examples shown in FIGS. 25 to 27, when the left end L and the right end R of the developed view are joined to form a cylinder, the pattern formed by the folding lines is generally not continuous. Details of the continuity of the development view will be described later.
FIG. 28 shows the spiral type shown in FIG. 19, which is obtained by cutting along a straight line connecting points A and D in FIG. The angle (up to 0.193π) shown in FIG. 28 indicates the angle between the cutting line and the horizontal line. In this case, the angle of the valley fold line is limited because the shape of the triangular element is given. Become.
FIG. 29 is an explanatory view of a spiral-shaped folding cylinder having a folding line generalized from FIG. 24, FIG. 29A is a developed view, and FIG. 29B is manufactured when both ends of the developed view of FIG. 29A are joined. It is a figure which shows the half-fold state of a folding cylinder.
The folding condition does not depend on the value of β in FIG. 29A (described later).
FIG. 30 is a developed view when the developed view of the six steps in FIG. 29A is changed to three steps, α is set to 30 °, and the value of β is changed for each step.
As shown in FIG. 30, the folding condition can be satisfied even if the value of β is set independently for each stage.
FIG. 31 is a developed view of a repetitive spiral type obtained by inverting the spiral mountain fold line and the valley fold line of FIG. 29A step by step. This development also shows that points A and B in FIG.

[0015]
Can also be obtained by
FIG. 32 is a view showing a portion cut by two parallel straight lines AB 'and C'D of the developed view of the cylindrical body shown in FIG. 21 so that A and B' and D and C 'overlap. FIG. 33 is a developed view of a foldable cylinder formed by connecting left and right edges of FIG.
The cylindrical wall having the development shown in FIG. 32 can create a collapsible cylinder having a plurality of polygonal parts.
FIG. 33 is an exploded view of a collapsible cylinder having an arbitrary-shaped quadrilateral element (part).
In FIG. 33, when a straight line obtained by extending AF is AE, the folding condition is ∠BAE = ∠DAC = α. The value of α can be arbitrarily determined as α = 180 ° / N (N is a positive integer). For example, when N = 8, α = 180 ° / 8 = 22.5 °. Therefore, by setting ∠BAE = ∠DAC = α = 22.5 ° and setting the length of the AE to an appropriate arbitrary value, a foldable cylinder having an arbitrary-shaped part can be created.
4. Continuity of Fold Lines in Spiral Development As described above, when the left and right ends of the spiral development are joined, the continuity of the folding lines is not always satisfied at both ends of the development. When a developed view is given by a trapezoidal element as in the case of FIGS. 25 to 27, continuity can be maintained by appropriately selecting the upper base length Lu of the trapezoid in FIG.
FIG. 34 is an explanatory diagram of a method for maintaining continuity when both ends of a developed view are joined.
In FIG. 34, a point A is determined by drawing N trapezoidal elements in the direction of the main fold line (angle ψ) from the origin O as a base point. Assuming that the height of the trapezoid is h, the length OA = N {(h / tan θ) + Lu} for a regular N-gon. Draw m (even number) elements below the N-th trapezoidal element, and determine point B as shown in the figure. In order that the developed view is continuous for an arbitrary ψ, the point B needs to be on the X axis. Since AB = mh, the following equation (6) is obtained from tanψ = AB / OA.
Lu = {2N-m-tan} / tanθ {h / tan} (6)
That is, when Lu is properly determined by the equation (6), the left and right ends of the developed views in these cases are obtained.

[0016]
Is obtained.
5. Verification of folding condition of cylinder with fold line When a cylinder having the fold line described above is folded, it is verified with a representative example whether or not the condition for closing in the circumferential direction (see Equation (5)) is satisfied.
In the cylinder given in FIG. 25, consider the folding line of the strip portion (small width D) at the lowermost end of this developed view. Here, there are 18 fold lines, and fold lines having the same inclination repeatedly appear every 6 lines from the left side. Therefore, they are formed of three sets of 6 fold lines. Using equation (4), the rotation angle of the axis by these fold lines is expressed by ψ (= π / 6) as the inclination angle.
ΘN = 2 ｛(α + ψ) -ψ + ψ-ψ + (α + ψ) -ψ｝ × 3 = 12 (7)
It becomes. Since α = π / 6, ΘN = 2π in equation (4), which satisfies equation (5). Thus, it can be seen that the condition for closing after folding is satisfied.
In the case of FIG. 29A, the following equation is obtained by considering the rotation angles of the lowermost six parallelogram portions by the folding lines.
{T = 2} (α + β) −β} × 6 = 12α (8)
If α = π / 6 is used, ΔT = 2π, and the closing condition (see equation (5)) is satisfied. As can be seen from equation (8), it can be seen that ΔT does not depend on the β value.
That is, in the models of FIGS. 29 to 31, the condition for folding into a regular N-gon shape is α = π / N, and the angle β in the figures can be freely selected.
In the spiral model shown in FIGS. 23 to 31 described above, except for FIG. 28 (considering hexagonal folding), the inclination angle の of the valley fold line is all π / N. However, as seen in the example of FIG. 25, the inclination angle の of the main folding line is not limited to π / N as long as the continuity of the developed view can be satisfied.
6. Fabrication of Foldable Pseudo-Cylinder According to the development described above, the present inventor examined the axial folding characteristics of a pseudo-cylinder made of a polypropylene sheet having a thickness of 0.2 mm, and confirmed that it was possible. . When the spiral type folding model shown in FIGS. 25 and 27 is pressed by the material testing machine, the upper part of the cylinder is folded while the lower part stops while rotating.

[0019]
β ^* = θ ₁ + θ ₃
Therefore, the folding condition in this case is expressed by the following equation (10).
α ^* = θ ₂ + θ ₄ , β ^* = θ ₁ + θ ₃ (10)
FIG. 37 shows the case of one node 4-fold line. The folding conditional expression is obtained by the same procedure as above.
_{Q 2/2 = q 1 -q} 2 + q 3 = π / 2 + α-γ
Because
Q ₂ = Q ₁ = π
And put
α = γ.
That is, when the mountain fold lines (M1) to (M3) are given, a valley fold (V1) occurs at a position having a γ value equal to the angle α formed between the X axis, which is an extension of (M3), and (M1).
2. A conical wall with a fold line whose main fold line is parallel to the outer side of the developed view is shown in FIG. 38. FIG. 4 is an enlarged view of a main part of a development view in the case of
The valley fold line (dashed line) in FIG. 38 is called a main fold line. The vertex is 0, the points on the outer side are A, B, C, and D. From these points, straight lines forming an angle α with the outer side are plotted, and the intersections are E, F, and G.
Lines forming angles α with the line segments EF, FG are drawn from the points E, F, G in the same manner as above, and their intersections are designated as H, I. By this drawing, the developed view is divided by two kinds of isosceles triangle elements. O, H, B and O, I, C form a straight line from the symmetry, and a diamond pattern symmetrical to the left and right of the straight line OF is obtained. The straight line OF forms a right angle with the outer side BC. The folding line forming the node F corresponds to that of FIG.
∠CFG = ∠BFE = β, and in consideration of the symmetry at the node F, δ in FIG. Since the angle between the valley fold line EF and the FG is 2 °, when θ = 2 °, the equation (10) becomes β−α = Θ...... …… (11)
It becomes. Since ΔOFE and ΔOFG are isosceles triangles with a vertex angle of 2 ° (base angle π / 2 °), if ΔHFI = γ） t * ￥ t, the following equation (12) is obtained.

[0021]
By substituting θ ^* in Expression (16) into Expression (15) and considering that the angle between the valley fold lines EF and FG is 2 °, the following folding condition expression (17 ′) is satisfied.
β-α = δ-γ + 2Θ ........................ (17 ')
If ∠HFI = γ ^* is set similarly to the above, the angle formed by the valley fold lines EF and FG when folded at the node F is γ ^* − (α + δ). Considering the folding of a regular N-gon, this value and (N−2) / N · π are equalized, and γ ^* + (α + δ) = π−2 obtained from a geometric relationship is used. The folding condition expression (17) is obtained.
(Α + δ) = π / N−Θ ………………………… (17)
When α and δ satisfying the expression (17) are selected, a foldable development view composed of scalene triangular elements is obtained.
FIG. 41 is a development view of a conical wall with a fold line when divided into inequilateral triangular elements by a fold line, where N = 3, 2Ｎ = π / 9, α = π / 9, δ = π / 6. (Θ ^* = about 0.0688π).
FIG. 42 is a development view of a conical wall with a fold line when it is divided into a trapezoidal triangular element by a fold line having an angle α at the upper right and an angle δ at the upper left at the point F in FIG. , Δ values are the same as those in FIG. 41.
Even if the angle α is set to the upper right and the angle δ is set to the upper left at the point F in FIG. 40, a developed view that can be folded is obtained. The obtained rectangle is a dashed parallelogram, and the points F, 1,... Rotate around the center at an angle θ ^* . The folding condition at the node is established in the same manner as in FIG.
FIG. 43 is an enlarged view of a main part of a development view of a conical wall with a fold line in the case of dividing by a trapezoidal element instead of dividing by the isosceles triangular element of FIG.
In FIG. 43, two straight lines (AC, BD) that form an angle α with AB from points A and B on the outer side are drawn symmetrically with respect to a straight line OI, and points C and D are determined so as to have an apex angle φ ^* .
When ∠DCE = Γ ^* and ∠DCE = ∠DCO + ∠OCE, and ∠DCO = π / 2−φ ^* / 2 and ∠OCE = (π / 2−Θ) −α, Γ ^* becomes the following equation ( 18).
Γ ^* = π- (φ ^* / 2 + Θ + α) …………………… (18)
Since the line segment CF is a valley fold line, it is folded by folding at the node C.

[0022]
The angle between the later mountain fold DC and the valley fold CF is given by Γ ^* −α, and this value can be expressed by the following equation (19) using the above equation (18).
Γ ^* −α = π− (φ ^* / 2 + Θ + 2α)... (19)
Considering the case of folding at a regular N-gon, the following equation (20-1) is obtained by equalizing (Γ ^* −α) and {(N−2) / N} · π.
α = π / N− (φ ^* / 2 + Θ) / 2 (20-1)
Since ∠HCF = Θ + φ ^* / 2 and AB and CD are parallel, ∠ACH = α, and β = ∠ACF is expressed by the following equation (20-2).
β = α + φ ^* / 2 + Θ
= Π / N + (φ ^* / 2 + Θ) / 2 (20-2)
At the point C, ∠ACH = ∠ECF = α, so that the conditional expression (17) for folding is satisfied.
FIG. 44 shows the development of a conical wall with a fold line, which is divided into an equilateral trapezoidal shape by a fold line and folded into a regular N pyramid, in the case of N = 6, φ ^* = π / 36, 2Θ = π / 12 in FIG. FIG. 44A is an exploded view of a pseudo-cone wall having a drawing, FIG. 44A is a developed view, and FIG. 44B is a perspective view of a state in which the conical wall with a folding line having the developed view of FIG.
3. 1. a conical wall with a fold line in which the main fold line is a spiral In the section, a development view in which a valley fold line is parallel to a bottom surface when a cone is formed has been described. Here, the folding in the case where the valley fold line serving as the main fold line has a spiral shape will be considered.
FIG. 45 is a view showing a development view of a conical wall with a folding line composed of N isosceles triangular elements (vertical angle 2 °), in which only one step is written out as a curved strip portion.
Here, it is assumed that the mountain fold and the valley fold are periodically introduced, and the angles formed by the folding lines with the outer sides AB,... Are ζ, η (0 ≦ (ζ, η) ≦ π / 2).
When this strip is bent along these folding lines, it is bent in the circumferential direction by φ = 2 (ζ−η) N. Originally, this band plate was bent at an angle ψ = 2N 、. Therefore, in order to join both ends of this band plate without gaps after folding, it is necessary that φ + ψ = 2π. This corresponds to the circumferential folding condition, which is expressed by the following equation (21).

[0023]
φ + ψ = 2 (ζ−η + Θ) N = 2π (21)
FIG. 46 is an exploded view of a conical wall with a fold line having a simple, spiral exploded view consisting of three isosceles triangular elements. FIG. 47 is a top view when the development view of FIG. 46 is folded.
In FIG. 46, three radiations ((1) to (3)) and a group of lines ((4), (5)...) Parallel to the outer side are mountain fold lines. The valley fold line forms an angle α with the outer side. Considering that the angles β to δ in FIG. 46 are isosceles triangular elements (vertical angle 2 °), the following expression holds.
β = π / 2 + Θ-α
γ = π / 2 + Θ + α
δ = π / 2-Θ-α
The valley fold line forming the spiral is bent by 2 ° every time it passes through one triangular element. When θ = 2Θ is set in the folding condition expression (17) and α to δ are substituted, it can be seen that expression (17) holds for an arbitrary α.
The α value is obtained under the condition of closing in the circumferential direction after folding, and in the case of folding in a regular N-gonal shape, using ζ = α, η = π / 2-Θ in the equation (21), the following equation (22) Is obtained.
α = {(N−2) / 2N} · π ………………………… (22)
In FIG. 47, three spirals (1) to (3) coming out of points A, F, and G are formed by the radial mountain fold lines of FIG.
Although this model gives a typical spiral pattern, it is folded down to the center in FIG. 46 without any gap, and thus it is difficult to practically use it as a method for folding a thin plate or film having a thickness.
48 is an explanatory diagram of a practical model obtained by modifying the model described in FIGS. 45 and 46. FIG. 48A is an explanatory diagram of a modification method, and FIG. 48B is an enlarged view of a main part of FIG. 48A.
In FIG. 48A, the points C and D are rotated around the center O by the angle 2θ ^* on the circumference and moved to the points E and F, respectively. Then, ∠CAE = ∠DBF =... = Ψ ^* is set.
By this operation, the congruent rectangles ABFE, BGHF... Are periodically arranged on the same circumference.

[0024]
be painted.
In FIG. 48B, the valley fold line is set to AF, and angles α to δ and p and q are given as shown in the figure.
∠OAB = ∠OBA = π / 2ΘΘ
Is obtained, the following equation is obtained.
p = π / 2−Θ + ψ ^* , β = π / 2 + Θ−γ−ψ ^* ,
δ = π / 2−Θ− (γ + ψ ^* ) ………………………… (23)
Since ∠ACE = π / 2 + θ ^* , ∠AEC = π / 2−θ ^* −ψ ^* is obtained by focusing on △ AEC. Considering that ＯOCE and △ OEF are isosceles triangles, and using ∠AEF = q = 2π- (∠OEC + ∠OEF + ∠AEC) obtained from the angular relationship around point E, the following equation (24) is obtained. .
q = π / 2 + 2θ ^* + ψ ^* + Θ, α = γ-2θ ^*
……………………… (24)
FIG. 49 is a view showing a state in which the figure ABGHFE formed by the folding line in FIG. 48A is sequentially folded along folding lines AF and BF. FIG. FIG. 49B is a view showing a state after the mountain fold is further performed at B′F (original line segment BF) in the state of FIG. 49A.
When each point is determined as shown in Fig. 49B, ∠AFB '= β, ブ ロ ッ ク FB'H "= δ.The two blocks are divided into the straight line AF in FIG. And B′H ″. Assuming that this angle is ψ as shown in the figure, ψ = π− (β + δ). Using β + δ = π−2 (γ + ψ ^* ) obtained from the equation (23), the following equation (25) is obtained.
ψ = 2 (γ + ψ ^* ) ……………………………… (25)
Considering the folding in a regular N-gonal shape, one of the inner angles is (N−2) π / N.
(Γ + ψ ^* ) = (N−2) π / 2N (26)
Get.
FIG. 50 corresponds to the portion corresponding to the first-stage band plate shown in FIG. 48A and the second-stage band plate.

[0025]
It is a figure showing a part.
In FIG. 50, the second-stage drawing can be newly performed based on points E, F, and H in the same procedure as that performed in FIG. The rectangle groups in the second row are similar to those in the first row.
Next, the folding condition is examined by taking the point F in FIG. 50 as an example. From Expressions (23) and (24), β−α = π / 2 + Θ−ψ ^* + 2θ ^* −2γ and δ−γ = π / 2−Θ−ψ ^* -2γ are obtained. That is, the following equation (27) is obtained.
β−α = δ−γ + 2 (Θ + θ ^* ) ...... (27)
The angle between the fold lines (1) and (2) in FIG. 50 is 2 ° due to the periodicity, and similarly, the angle between the fold lines (2) and (3) is 2θ ^* . That is, considering that (1) and (3) form an angle of 2 (Θ + θ ^* ), Expression (27) shows that the conditional expression for folding at the node F is satisfied.
FIG. 51 is a developed view in the case where N = 6, γ + ψ ^* = π / 3, ψ ^* = π / 6, and γ = π / 6 in the conical wall with a folding line having the folding lines shown in FIGS. 51A is an explanatory view of a pseudo-conical wall having (2Θ = π / 18), FIG. 51A is a developed view, and FIG. 51B is a perspective view of a folded-conical wall having the developed view of FIG. .
FIG. 52 is a development view in the case where N = 6, γ + ψ ^* = π / 3, ψ ^* = π / 4, and γ = π / 12 in the conical wall with fold lines having the fold lines shown in FIGS. (2Θ = π / 6).
FIG. 53 is a developed view in the case where the number of steps in the developed view of FIG. 51A is reduced and the value of ψ ^* is increased for each step.
In FIG. 53, for a conical wall, ψ ^* + γ = 60 °. divides the ψ ^{* +} γ = 60 ° Under [psi ^* and gamma. Each stage can be arbitrarily divided into 段^* and γ values. In the case of the equiangular spiral, the pattern becomes smaller toward the center. To avoid this, ψ ^* is reduced.
FIG. 54 is a developed view showing the same conical wall as the folded conical wall having the developed view of FIG. 53.
FIG. 54 is a developed view of a conical wall having the same shape as that of FIG. In FIG. 54, the joining of both side edges is easier than in FIG.
FIG. 55 shows the valley fold line of the second step in FIG.

[0026]
FIG.
Assuming that the intersection of this valley fold line and OA (O; center) is K, ∠KEO becomes ψ ^* , and the newly obtained rectangle EFIK is similar to that of the first stage. The state of the folding line at point F corresponds to FIG. When the mountain fold line (M4) in FIG. 36 is made to correspond to the mountain fold line FH, θ ₁ to θ _{4 in} FIG. 36 are θ ₁ = δ, θ ₂ = γ, θ ₃ = α, θ ₄ = β.
Since the line segments FH and FE in FIG. 55 form an angle of 2 °, α ^* and β ^* in FIG.
α ^* = δ + γ + 2Θ, β ^* = α + β-2Θ (28-1)
It becomes.
Using equations (23) and (24), α ^* and β ^{* in the} above equation are
α ^* = π / 2-ψ ^* + Θ = β + γ
β ^* = π / 2-ψ ^* -Θ-2θ ^* = α + δ
.................. (28-2)
It becomes. If θ ₁ = δ, θ ₂ = γ, θ ₃ = α, θ ₄ = β are used in these equations, equation (10) is obtained, and the folding condition is satisfied.
Drawing a valley fold line in the opposite direction for each stage in this way creates a repetitive, spiral-shaped folding structure.
FIG. 56 is an explanatory view of a pseudo-cone having a development view in which the FIG. 51 is formed into a repetitive spiral type. FIG. 56A is a development view, and FIG. It is a perspective view of the state which carried out.
FIG. 57 is a developed view (N = 6) of the repetitive spiral type obtained as 2Θ = π / 6, ψ ^* = π / 6, γ = π / 6.
4. Analytical Study Using Conformal Spiral The two types of patterns formed by the folding lines in the above-described development are similar and become smaller toward the center.
FIG. 58 is an explanatory view of a development view of a foldable conical wall having a folding line along a conformal spiral, FIG. 58A is an overall explanatory view, and FIG. 58B is an enlarged view of a main part of FIG. 58A.
The developed views shown in FIG. 39A and FIG.

[0027]
Assuming that the angle formed by the pattern with respect to the center O is 2 °, the pattern is generally represented as shown in FIG. 58A. This FIG. 58A is drawn as follows. First, line segments (1) and (2) are drawn in the upper right direction from the points A and I so as to form an angle と with the radiation OA and OI from the center O.
Next, line segments (4) and (5) are drawn from the points A and M so as to form an angle φ with the radiations OA and OM (the values of ψ and φ are α, δ in FIGS. 40 and 42, and ψ = π / 2-Θ-α, φ = π / 2-Θ-δ). Assuming that the intersections of (1) and (5) and (2) and (4) are F and B, respectively, the points B and F come on concentric circles.
Similarly, when the above operation is performed at points B and F, points C, J and G are determined, and points D, K and H are sequentially determined. That is, the rows F, G, H,... Of points taken in the upper right direction from the point A always form an angle ψ with the radial direction, and the points A, B, C, D, E form an angle φ with the radial direction. It is drawn as follows. Point A. Assuming that a line connecting F, G, and H is a new curve (1) and a line connecting points A, B, C, and D is a new curve (4), these two curves are equiangular with the radial direction. It becomes a line going to the center.
That is, each of these points is on a conformal spiral emanating from the center O. 58A, (1), (2) and (3) are counterclockwise spirals, and (4), (5) and (6) are clockwise spirals.
As shown in FIG. 58A, when the angle formed by the line segments AB, BC,... With respect to the central angle is set to 2Θ ′, the angle formed by the line segments AF, FG, GH is 2 (Θ−Θ ′). The folding condition is examined using an enlarged view of two rectangles on the left and right of the point F (FIG. 58B). These rectangles are congruent, and the line segments BF and FG form a corner 2 °. The relationship between お よ び, φ and α to δ is as shown in the figure. Since {OBF in FIG. 58A is an isosceles triangle having a vertex angle of 2 °, α + φ = π / 2−Θ and δ + ψ = π / 2−Θ, and
α + δ = π- (φ + ψ) -2Θ …………………… (29)
Get. From the inner angle relation of △ ABF or △ MFN,
β + γ = π− (φ + ψ) …………………… (30)
Get. The following expressions are established from Expressions (23) and (24).
β−α = δ−γ + 2Θ .................. (31)
Considering that the line segments BF and FN form an angle of 2 °, the above equation (3) holds.
That is, it is understood that the folding condition is automatically established when the folding line is drawn by the equiangular spiral.

[0028]
When φ = ψ is FIG. 39A and φ φ, FIG. 42 corresponds. Point B, the radius R ₁ of F is given by the following equation using the sine law radius of development view as R _0.
R ₁ / R ₀ = sin ｛2 (Θ−Θ ′) + ψ｝ = p (32)
Point of the second stage from the outer peripheral (C, J, G ...) and the third stage of the point (D, K, H ...) radius is given by the sequence ^{p 2,} p 3 ^....
FIG. 59 is an explanatory view of a development view of the conical wall with a folding line when the spiral of FIG. 58 is reversed.
In FIG. 59, as in FIG. 58, the radial direction and the angle ψ are taken upward from the point A to the right and the angle φ is taken upward to the left. These are (1) and (2), respectively. From point J, draw (3) in the same way as (1) and from point K, draw (4) in the same way as (2). Is point B. At this time, the angle formed by the line segment BC is 2 °.
Next, line segments BD and CD are drawn from points B and C in the opposite directions at similar angles ψ and φ, respectively. Intersection D is on radius OA. By repeating this, zigzag folding lines ACDFGI..., ABDEGH. Since ΔOBC is an isosceles triangle with a vertex angle 2Θ,
∠DBC = δ = π / 2−Θ−φ, ∠DCB = απ / 2−Θ−ψ
……………………… (33)
Is obtained. The following equation (34) is derived by using the outer angle relationship between ΔOBA and ΔOAC.
{CBA = γ = π / 2 + Θ− (φ + 2Θ−θ ^* ),
∠BCA = β = π / 2 + Θ− (ψ + θ ^* ) ……………… (34)
Expressions (15) and (16) are obtained from Expressions (33) and (34), and the folding conditions at all nodes are satisfied.
FIG. 41 corresponds to this case, and FIG. 39 can also be represented in this form.
FIG. 60 is an explanatory diagram of how to draw the developed view of FIG. 44A.
In FIG. 60, the line segments (1) and (2) are drawn from the points A and G at the same angle φ, and the line segments OB and OH taken symmetrically with respect to the perpendicular drawn from the point O to the base AG of △ OAG. Are assumed to be B and H.
Take φ in the opposite direction from points B and H, and let C and I be the intersections with OA and OG. By such operations, zigzag folding lines ABCDE... And GHLJK. At each node

[0029]
The folding condition is clarified in the description of FIG.
Further, it is easily understood that the developed view of FIG. 51A is a conformal spiral from the description of FIG.
FIG. 61 is an explanatory view of a pseudo-cone having an exploded view in which FIG. 44 is made into an equiangular spiral shape. FIG. 61A is an exploded view, and FIG. FIG.
Exploded views forming an isosceles trapezoid in which the folding lines are arranged along the spiral as shown in FIGS. 61 and 61B can also form a foldable conical wall.
FIG. 62 is a developed view of a folding conical wall with a folding line in which the circumferential spiral of FIG. 51A is raised one step at the right end.
When the developed view of FIG. 62 is a conical wall, the right edge and the left edge are connected so that the right end points A, B, C,... And the left end points D, E, F, D overlap. I do.
As described above, the folding condition at the node is automatically established by combining the equiangular spiral or the reversing type equiangular spiral, but the folding condition in the circumferential direction is the sum of the folding angles at the points in the circumferential direction. Must be set using FIG. 45 or the previous geometrical consideration so that is 2π.
Further, the nodes on these developments can be determined from the intersection of the concentric circles of the radii p, p ￥ t2 ￥ t, p ￥ t3… t.
5. Using the manufactured collapsible conical shell and its characteristic thickness of a polypropylene sheet having a thickness of 0.2 mm, the conical shell of FIG. 51B manufactured by the expanded view shown in FIG. 51A and the expanded figure shown by FIG. 56A. The state of folding of the 56B conical shell was observed. As a result, it was found that good folding was possible as predicted by the origami model.
6. Discussion Assuming mainly the case of N = 6, the creation of a conical structure that can be folded in the axial direction was geometrically studied using an origami model, and it was shown that this was possible. Here, since these conical shells are composed of folding lines, they become pseudo-conical, and it is difficult to extend the fan-shaped developed view to a conical shape obtained by joining.

[0032]
ζ = ∠FGJ
Given by
ζ = π-∠EGH-p = π- (π / 2 + Θ) -p = α-2θ
Therefore, the folding condition at the point G is expressed by the following equation (38) as β≡∠FGJ.
β = α-2θ ………………………………… (38)
If we define ∠JGO≡q,
q + β = (π / 2) −Θ
From the following equation (39) is obtained.
q = (π / 2-Θ)-(α-2θ)
= Π / 2- (α + Θ) + 2θ …………………………… (39)
From Expressions (37) and (39), p = q (this relationship at point G corresponds to the establishment of a mirror law with the radiation OE as a mirror surface).
Next, when ∠BJG≡r is set in △ OJG, r = q + 2θ is obtained. The folding condition at the point J is given by r = s (∠OJP≡s), considering the line segment OB as a mirror surface. Since ∠OJK = π / 2−Θ = ∠OJP + ∠PJK, if ∠PJK = γ, γ is given by the following equation (40).
γ = (π / 2-Θ) -s
= (Π / 2-Θ)-(q + 2θ)
= Π / 2-{-2θ- {π / 2- (α + Θ) + 2θ} = α-4θ (40)
If the “swing angle” of the zig / zag fold line in the radial direction is set to 2θ, the fold line BGJP in the radial direction becomes β = α−2θ, γ = α, where α is the angle at the point B on the outer side. A value obtained by subtracting the angle by 2θ, such as −4θ.
When the two main and sub radiations (OB and OG) are considered as mirror surfaces, the relation between the incident angle and the reflection angle is p = q = π / 2− (α + Θ) + 2θ = φ + 2θ,
r = s = π / 2− (α + Θ) + 4θ = φ + 4θ (41)
And the angle is increased by 2θ.
Assuming that the radius of the disk is OB = R ₀ , and the lengths of the line segments OG, OJ, OP are R ₁ , R ₂ , R ₃ .

[0034]
In the case of using a colored sheet or the like with a color, the shape becomes beautiful according to the amount of folding, and the visible color changes according to the shape. As for the disc-shaped folding structure S with a folding line, a large one can be used as an upholstery and a small one can be used as a body decoration such as a brooch.
FIG. 69 is an explanatory view of a development view of the disc-shaped folding structure with a folding line when the swing angle of the folding line of zig / zag in the radial direction is increased as approaching the center, and FIG. 69A is for explaining the folding conditions. 69B is an overall view of FIG.
When a zig / zag fold line is drawn at the same swing angle, the interval between the fold lines is sharply reduced as the position approaches the center. Therefore, consider increasing the swing angle gradually (FIG. 69A).
When the folding lines BG and GJ are drawn at the initial swing angle 2θ, p = q and r = p + 2θ. Next, when s = r from the point J and the swing angle is, for example, 4θ, the angle t in FIG. 69 becomes s + 4θ. At the point P, a line segment PQ is drawn at an angle t = u based on the mirror rule, and the point Q is determined. When the folding lines are sequentially obtained in accordance with the mirror surface rule, the angular relationship when the swing angles are 2θ, 4θ, and 6θ is given by the following equation (43).
p = q = π / 2− (α + Θ) + 2θ = φ + 2θ,
r = s = φ + 4θ, t = u = φ + 8θ (43)
Given by The line segment OG = R ₁ , the line segment OJ = R ₂ ... Can be formulated by the same procedure as that for obtaining the equation (42).
FIG. 70 is an exploded view of a disc-shaped folding structure with a folding line in the case where the swing angle of the folding line of zig / zag in the radial direction is increased toward the center and the folding line in the circumferential direction is also zig / zag. 70A is an enlarged view of a main part for explaining folding conditions, and FIG. 70B is an overall view.
In FIG. 70A, main radiations OA, OB... Of radii R ₀ and R ₀ ^* (R ₀ > R ₀ ^* ) are alternately drawn, and auxiliary radiations OF, OG. Here, F, G, and H are the intersections of the line segment drawn from the points A, B, and C so as to form an angle φ with the main radiation and the sub-radiation. In this way, when drawing according to the mirror surface rule, the folding condition is satisfied at all nodes.
64B, N = 36 (2Θ = 100), and FIGS. 69B and 70B are divided into N = 18. The folding line method was used up to the eighth stage from the outer periphery. Central part

[0036]
Means a folding method with lines.
Here, a method of folding a circular film using a conformal spiral will be described.
4.1 Basic Relational Expression FIG. 73 is an explanatory diagram of a folding line when a circular film or a partial circular film (sector-shaped film) is folded in the radial direction and the circumferential direction along an equiangular spiral. .
As shown in FIG. 73, the circular film is divided at equal angles by radial radiation from N centers and is replaced by N isosceles triangular elements (要素 OAM, △ OMN...) Having a vertex angle of 2Θ (2Θ ·). N = 2π). Each point is defined as shown in the figure. From the point A on the outer side, a straight line forming each line of the radiation and each φ is drawn, and an intersection of the radiation (OM) rotated by 2 ° at the central angle is defined as a point B.
With the point A as a starting point, a straight line forming φ with the radiation OA is drawn, and an intersection with the radiation OM rotated by 2 ° is set as B. Next, a straight line forming an angle χ with the radiation OM is drawn, and an intersection C with the radiation ON rotated by 2Θ is determined. Next, points D, E... Are determined by taking angles φ and χ alternately in the same procedure. This zigzag line is defined as (1). Here, the angle between the line segment AB and the base of the isosceles triangle is defined as β. That is, β≡90 ° −Θ−φ. The angle between the line segment BC and the MN (that is, the angle between the line segment BB 'drawn from B in parallel with the MN and the line segment BC) is defined as γ. γ = (90 ° −Θ) −χ. The value of γ is positive when C is on the same side as the center O with respect to the line segment BB ′, and negative when C is on the opposite side to the center O. When γ = 0, the line segments BC and MN are parallel.
Assuming that the radius of the circular plate is R ₀ and the sine theorem is used for △ OAB, the length of the radius of the point B (OB) ≡R ₁ is given by the following equation (44).
R ₁ / R ₀ = {sin φ / sin (φ + 2})｝ ≡p (44)
When the length of the radius of the point C (OC) is R ₂ and the sine theorem is used for △ OBC, R ₂ / R ₁ is represented by the following equation (45).
R ₂ / R ₁ = sinχ / sin (χ + 2Θ) ≡q (45)
That is, R ₂ / R ₀ is given by the following equation (46) using equations (44) and (45).
p · q = R ₂ / R ₀
= Sinφ · sinχ / {sin (φ + 2Θ) · sin (χ + 2Θ)}
............ (46)
That is, the points D, E, F ... radius dimensionless radius _{R 0} of the circular film of ^p 2 q, p

[0037]
^{2 q 2, p 3 q 2} ... p as given by the value obtained by multiplying alternating q.
Now, assuming that a line (2) connects points A, C, E, G,... Which give the lower limit of the zigzag line (1), the dimensionless radii of these points are 1, pq, (pq) ² , ( pq) ³ ,..., each of these points is given by the intersection of a conformal helix and a ray drawn every 4 °. The line (3) connecting the points B, D, F, H,... Giving the upper limit of the zigzag line is also given by the intersection of the conformal spiral and the radiation.
FIG. 74 is a basic explanatory diagram of a folding line when a circular film or a partial circular film (sector-shaped film) is formed along an equiangular spiral while being folded around the central axis while being wound around the central axis.
Next, as shown in FIG. 74, points P and Q that are advanced clockwise by an angle of an odd multiple of 2 ° (described later) from the start point A of the folding line (1) are determined, and from these points, points (1) and (1) are completely determined. Similarly, zigzag folding lines (4) and (5) are drawn.
At this time, the fold lines (1) and (5) are alternately determined with the mountain fold line, and the fold line (4) is alternately determined with the valley fold line.
Points on the folding line (1) are named I, J, and K, points on the folding line (4) are named R, S, and T, and points on the folding line (5) are named Q, U, and V as shown in the figure. The points Q, R, I and U, S, J on the radiation, which are displaced counterclockwise by 2 °, are connected by straight lines, and they are connected to another folding line group (6), (7), (8). ).
As shown in FIG. 74, when points P, Q,... Are taken every five isosceles triangular elements, the number of zigzags n (one zigzag once, n = 1) is changed to zigzag when n = 2. Since it is repeated twice, it proceeds counterclockwise through five isosceles triangles (for example, if zigzag is repeated twice along the folding line (4) from point P in FIG. 74, it reaches point R, and from point Q Intersects with the folding line (6) that has come out. If the isosceles triangle passing through the folding line (6) is included, it means that it has advanced counterclockwise through five isosceles triangles.)
The dimensionless radii of the points Q, R, I... Are 1, (pq) ² , (pq) ⁴ , and △ OQR and △ ORI in the figure have similar shapes.
That is, the new folding line groups (6) to (8) also become equiangular spirals toward the center O. Assuming that the angle between the QR of the fold line (6) and the PE of the fold line (9) forms radiation, ψ is α = (90 ° −Θ) −ψ. Let α be the angle between the outer edge (the base of the isosceles triangle element)

[0038]
.
The zigzag folding line (4) reaches the point R in the figure by repeating the zigzag n times (n = 2 in FIG. 74). At this time, the radius of the point R is given by (p · q) ⁿ .
On the other hand, since the angle formed by the spiral (6) emitted from the outer side point Q and the radiation is ψ, the value of the dimensionless radius giving the point R is represented by sinψ / sin (ψ + 2Θ). If this value is equalized with equation (46), the following equation (47) is obtained.
p ⁿ q ⁿ
= [Sinφsin} / {sin (φ + 2}) sin ({+ 2})}] ⁿ
= Sinψ / sin (ψ + 2Θ) ……………………………… (47)
The above equation (47) is the angular relationship to be satisfied between the spirals (1), (4), and (5) which turn clockwise and move toward the center, and the spirals (6) to (8) which cross them and rotate counterclockwise. Is given.
4.2 Folding Condition As described above, consider a case where the conformal spiral is bent every 2 °. Assuming that a point S in FIG. 74 composed of the valley fold line 3 and the mountain fold line 1 and a point U composed of the mountain fold line 1 are representative points, conditions for folding at these points will be considered.
FIG. 75 is an enlarged view of a main part of FIG.
FIG. 75 is an enlarged view of FIG. 74 around points S and U. At the point S, since {OSJ =}, {SJR = {+ 2}. Since ∠ORS = φ, considering △ JSR, ∠JSR = π − (− + 2Θ) −φ. Assuming that an extension of the line segment RS is SS ', the following equation is obtained.
If {USQ = {+ 2} is used, {TSU = π − {−} USQ = π − {−} − 2}. When ∠S′SJ = ∠TSU is set according to the folding condition, the following equation (48) is obtained as the folding condition at the point R.
2ψ + φ + χ = π-4Θ ……………………… (48)
As is clear from FIG. 75, the angle relationship of the point U is the same as that of the point S, and therefore the expression (48) is a folding condition. That is, when Expression (48) holds, the folding condition holds at all nodes.
FIG. 76 shows a circular film or a partially circular film (sector-shaped film) wound around a central axis.

[0039]
It is explanatory drawing of the folding condition at the time of forming the folding line to fold along an equiangular spiral.
As shown in FIG. 76, when the χ value is larger than π / 2−Θ, that is, when the folding line is directed upward at points B, D. Conditions are given.
4.3 Regarding the continuity of the spiral group in the circumferential direction, the folding condition was obtained. However, these spiral groups are equally distributed around the central axis, and conditions for maintaining the continuity of the spiral are derived. It is assumed that the zig / zag spiral (folding line (1)) starts m times from the outer peripheral point every n n isosceles triangle elements.
At this time, these start points rotate (2n + 1) · (2Θ) around the center (n: an integer). That is, the relationship between the number N of isosceles triangle elements and these values is given by (2n + 1) m = N. In the case of a circular film, it is necessary to equally divide the central angle 2π by (2n + 1) m.
That is, the division angle (vertical angle of the isosceles triangle element; 2 °) for satisfying the continuity is given by the following equation (49).
2Θ = 2π / ｛(2n + 1) · m｝ ……………………… (49)
Only by dividing the circular membrane in this way, the condition that the continuity of the m spiral groups is satisfied in the entire area of the membrane is achieved.
By using φ = π−2 {− {− 4} obtained from Expression (48) for Expression (47), the following Expression (50) is obtained.
(Pq) ⁿ
= [Sin (2ψ + χ + 4Θ) ・ sinχ / ｛sin (2ψ + χ + 2Θ) sin (χ + 2Θ)｝] ⁿ
= Sinψ / sin (ψ + 2Θ) ……………………………………… (50)
By giving 2Θ and χ value that are divided so as to satisfy Expression (49), ψ that satisfies Expression (50) can be calculated by numerical calculation. Further, the φ value is also obtained by the equation (48), and a developed view is drawn by a spiral folding line satisfying the folding condition at all the nodes.
4.4 When bending the sub-fold line at an arbitrary rotation angle (φ = φ)

[0040]
In the above, a development view is obtained in which the circular film is equally divided into N isosceles triangular elements having a vertex angle of 2 °, and the folding line is bent every time these elements are passed. In the case of FIG. 76, in the special case where the m spirals are always bent upward at an equal angle (φ = χ), a configuration of another folded development is possible.
FIG. 77 is an explanatory diagram of folding conditions when the main fold line is bent at an equal angle to radiation.
Points A, B, C and A ', B' on the outer circumference of the circle are determined as shown in FIG. A fold line (1) rising rightward is drawn from point A, and a fold line (2) rising leftward is drawn from point B. (1) has a central angle of 2θ ₁ (the angle of the string AA ′), and (2) has a central angle of 2θ ₂ (the angle of the string A′B). 1) is at an angle ψ (angle α with the outer side AI) with the radiation from the center, and the folding line (2) is at an angle φ with the radiation (angle β with the outer side BI).
The folding condition at point D is considered below.
∠ADA '= φ + 2θ ₁ , ∠BDA' = ψ + 2θ ₂
It becomes. If the extension point of BD is I,
{ADI = π-{(φ + ψ) +2 (θ ₁ + θ ₂ )}
It becomes.
Since ∠FDO = φ and ∠GDO = ψ,
{FDG = φ +}
It becomes.
When folding lines (2), (1), and (3) are mountain folds, GD ((4)) is a valley fold line, and the folding condition at point D is as follows. 51) is obtained.
φ + ψ = π / 2−Θ or (α + β) = π / 2 (51)
When the OD and _{R 1,} the use of sine theorem △ OAD, we obtain the following expression (52).
R ₁ / R ₀ = sinψ / sin (ψ + 2θ ₁ ) (52)
On the other hand, the following equation (53) is obtained for △ OBD.
R ₁ / R ₀ = sin φ / sin (φ + 2θ ₂ ) (53)
Both of these values give the radius of the point D. If these values are equalized and ψ = π / 2-φ-Θ is used, the following equation (54) is obtained.

[0041]
sin (β−θ ₁ ) / sin (β + θ ₁ )
= Sin (π / 2−θ ₂ −β) / sin (π / 2 + θ ₂ −β) (54)
When θ ₁ and θ ₂ are given, φ that satisfies Expression (53) is determined by numerical calculation. Ψ is obtained from Expression (51), and by using these values, a developed view that satisfies the folding condition at all nodes is obtained.
4.5 Application to Manufacturing of Conical Shell Assume that the zigzag spiral (folding line (1)) consists of m lines in FIG. . In the case of a disc, (2n + 1) · m · (2Θ) = 2π, but if the value of (2n + 1) · m · (2Θ) is smaller than 2π, a cone develops, and in this case also the folding is performed. Is possible.
5. FIGS. 78 to 80 show a developed view obtained by the above-described theory and a folded example thereof.
FIG. 78 shows an example of folding around the center with two zigzag spirals (m = 2) as folding lines, where n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 20 °.
FIG. 79 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 78 is an example of a folded development view when γ = 0 °, showing an example in which the angle of the folding line with respect to the radiation is different from FIG. 78.
FIG. 80 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 10, the number of isosceles triangular elements N = (2n + 1) m = 42, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
In FIGS. 78 to 80, 2 ° = 20 °, 20 °, and 180 ° / 21, respectively, and these values and the γ value determined by χ (γ = ° −90 ° + Θ) are respectively expressed as γ = π / 9, Given 0 and 0, the ψ value satisfying the equation (50) was obtained by numerical calculation. When this ψ value is substituted into Expression (48), φ is determined.
From α + ψ = 90 ° -Θ and β + φ = 90 ° -Θ, the values of α and β in FIGS. 78 to 80 can be obtained. For example, regarding FIG. 78, α = 69.763..., Β = 20.474.

[0043]
FIG. 85 shows an example of folding around the center using four zigzag spirals (m = 4) as folding lines, where n = 7, the number of isosceles triangular elements N = (2n + 1) m = 60, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
FIG. 86 shows an example in which three zigzag spirals (m = 3) are used as folding lines and folded around the center, where n = 8, the number of isosceles triangular elements N = (2n + 1) m = 51, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
FIG. 87 shows an example in which one zigzag spiral (m = 1) is used as a fold line and folded around the center, where n = 10, the number of isosceles triangle elements N = (2n + 1) m = 21, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 0 °.
When four main fold lines in FIG. 85 are spirals, the main fold lines are folded in a rectangular shape, and when three main fold lines are spirals in FIG. 86, the main fold lines are folded in a triangular shape. In the case of one spiral shown in FIG. 87, the spiral is wound around the central axis.
When γ = 0 ° and α and β values are obtained in the same manner as described above, the following is obtained.
In FIG. 85, γ = 0 °, α = 75.432..., Β = 29.132.
86, γ = 0 °, α = 76.233..., Β = 27.533.
In FIG. 87, γ = 0 °, α = 76.714..., Β = 26.572.
FIG. 88 shows an example in which four zigzag spirals (m = 4) are used as folding lines and folded around the center, where n = 7, the number of isosceles triangular elements N = (2n + 1) m = 60, It is a figure which shows the example of the development view of the disk-shaped folding structure with a folding line in case of (gamma) = 0 degree.
FIG. 89 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 88 in a half-folded state and a state in which the amount of folding is small.
FIG. 90 is a perspective view of the disc-shaped folding structure with a folding line having the developed view of FIG. 88 in a half-folded state and a state in which the amount of folding is large.
FIG. 91 is a perspective view showing a state in which the disk-shaped folding structure with a folding line having the developed view of FIG. 88 is completely folded.
The disc-shaped folding structure S with a folding line shown in FIGS. 88 to 91 has a circular hole Sa formed at the center in the developed view shown in FIG. Is the circular hole Sa in the unfolded state shown in FIG.

[0049]
CD, BE, etc. are 60 ° with respect to the lines AD, CB. When the valley fold line CD is folded, the AB portions come into contact, and △ ACE and △ BCE are joined. Bonding the joints creates a structurally stable core material (FIG. 104A) composed of square fold lines.
3.2 Honeycomb Core Model The honeycomb core is representative of a lightweight structure.
FIG. 105 is an explanatory diagram of a method of manufacturing a honeycomb core from one plate, FIG. 105A is a developed view, and FIG. 105B is a view of a honeycomb core manufactured from a plate having the developed view of FIG. 105A.
In FIG. 105A, a dotted line is a valley fold line, and a mountain fold line indicated by a dashed line has a cut C (cut portion). When the joining portions AB on both sides of the valley fold line in FIG. 105A are bonded to every other valley fold line and spread on both sides, a mesh-shaped honeycomb core shown in FIG. 105B can be manufactured. When this manufacturing method is used, there is a characteristic that the honeycomb core becomes a cylindrical honeycomb core.
4. 4.1 Production of core material 4.1 Production method of core material A 0.2-0.3 mm phosphor fine copper plate or a steel plate is cut along the folding lines shown in FIGS. Alternatively, two molds joined by hinges are manufactured, and a thin paper to be processed or an aluminum alloy plate (up to 0.08 mm) is inserted between the molds and bent to perform the bending process, as shown in FIGS. 101B to 102B. Such a product can be manufactured instantly.
By bonding only the bonding regions S1 and S2 of FIG. 102B, not bonding S3 and S4, but bonding a thin film on one side (or bonding the other way) to a cylindrical surface, Thus, it is possible to manufacture a lightweight and highly rigid pipe.
FIG. 106 is a view showing a folding line forming apparatus for manufacturing the core material shown in FIG. 103A.
In FIG. 106, a kraft film F is bonded on both sides of a large number of square parts (metal thin plates) P1 and parallelogram parts P2 separated by folding lines.

[0067]
In the structure with a folding line according to the present invention having the above-described configuration, a plurality of nodes, which are intersections of the mountain fold line (M) and the valley fold line, are arranged at a predetermined interval, and the mountain fold line ( M) and the number of valley fold lines have a plurality of fold lines (M, V) formed so that the difference between the number of valley fold lines and the number of valley fold lines is two. It is possible to provide an unknown, foldable circular sheet-like structure with a fold line.
The folding line forming die of the present invention can have the following constituent requirements (F01) and (F02).
(F01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and is foldable along the linear part connection part is provided. A pair of fold line forming members provided, wherein the fold line is a plurality of mountain fold lines (M) where the one surface side forms a mountain fold and one or more valleys which form a valley fold when viewed from one surface side of the fold linear molding. A plurality of nodes, which are intersections of the mountain fold line (M) and the valley fold line, are arranged at predetermined intervals and intersect at one node, and a valley fold line A pair of fold line forming members having the plurality of fold lines (M, V) formed so that the difference from
(F02) A folded linear molded connecting member that movably supports or connects the pair of folding line forming members between an overlapped state and an open state.
In the folding line forming mold of the present invention having the above-described configuration, the sheet-like member is folded by simultaneously folding the pair of folding line forming members in a state where the sheet-like member is sandwiched between the pair of folding line forming members. The ridge fold line (M) and the valley fold line required for the above can be formed.
The folding line forming method of the present invention can have the following constituent features (G01) and (G02).

[0071]
The present inventor has shown in a development view a cylindrical structure in which a spiral portion (1) rises one step every time the connecting portion turns into a spiral shape.
FIG. 23 corresponds to FIG. 17 in which the whole of FIG. 17 is inclined by ψ = π / 6, and three diamond patterns in oblique directions are formed.
24 is an explanatory view of a pseudo cylindrical body having a development view equivalent to that of FIG. 23. FIG. 24A is a development view, and FIG. 24B is a fold manufactured when both ends of the development views of FIGS. 23 and 24A are joined. It is a figure showing the half-fold state of a cylinder.
FIG. 25 is an explanatory view of a pseudo cylindrical body k having a development view obtained by inclining FIG. 14 by π / 6. FIG. 25A is a development view, and FIG. 25B is manufactured when both ends of the development view of FIG. 25A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 26 is an explanatory view of a pseudo-cylindrical body having a development view in which FIG. 15 is inclined by π / 6. FIG. 26A is a development view, and FIG. 26B is manufactured when both ends of the development view of FIG. 26A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 27 is a developed view obtained by tilting FIG. 16 by π / 6.
FIG. 28 shows the spiral type shown in FIG. 19, which is obtained by cutting along a straight line connecting points A and D in FIG. The angle (up to 0.193π) shown in FIG. 28 indicates the angle between the cutting line and the horizontal line. In this case, the angle of the valley fold line is limited because the shape of the triangular element is given. Become.
FIG. 29 is an explanatory view of a spiral-shaped folding cylinder having a folding line generalized from FIG. 24, FIG. 29A is a developed view, and FIG. 29B is manufactured when both ends of the developed view of FIG. 29A are joined. It is a figure which shows the half-fold state of a folding cylinder.
FIG. 30 is a development view in the case where the value of β is changed for each one of the six development steps of FIG. 29 by three steps.
FIG. 31 is a development view of a repetitive spiral type obtained by inverting the spiral mountain fold line and the valley fold line of FIG. 29 for each stage. This development can also be obtained by matching points A and B in FIG.
FIG. 32 is a view showing a portion cut by two parallel straight lines AB 'and C'D of the developed view of the cylindrical body shown in FIG. 21 so that A and B' and D and C 'overlap. By connecting the left and right end edges of FIG. 32 to the

[0072]
FIG.
FIG. 33 is an exploded view of a collapsible cylinder having an arbitrary-shaped quadrilateral element (part).
FIG. 34 is an explanatory diagram of a method for maintaining continuity when both ends of a developed view are joined.
FIG. 35 is a diagram showing the angular relationship between the folding lines satisfying the folding condition when the valley fold line is symmetrically inserted in the case of one node 6 fold line, and shows the folding condition in the case of FIGS. FIG.
FIG. 36 is a diagram showing an angle relationship between folding lines satisfying the folding condition when the valley folding lines (V1) and (V2) are alternately inserted between the mountain folding lines (M1), (M2) and (M3). 58 is an explanatory diagram of folding conditions in the case of FIGS. 56B and 57 described later.
FIG. 37 shows the case of one node 4-fold line. The folding conditional expression is obtained by the same procedure as above.
FIG. 38 is an enlarged view of a main part of a development view in a case where a development view of a cone whose main folding line is parallel to the outer side of the development view is composed of N isosceles triangles having a vertex angle of 2 °.
FIG. 39 is an explanatory view of a pseudo-cone wall having a development view of a pseudo-cone wall with a folding line obtained by using the value obtained by Expression (14). FIG. 39A is a development view, and FIG. 39B is a development view of FIG. 39A. It is a perspective view of the half-fold state of the conical wall with a folding line which has a.
FIG. 40 is an enlarged view of a main part of a development view of a conical wall with a fold line when divided into inequilateral triangular elements by a fold line.
FIG. 41 is a development view of a conical wall with a fold line when divided into inequilateral triangular elements by a fold line, where N = 3, 2Ｎ = π / 9, α = π / 9, δ = π / 6. (Θ ^* = about 0.0688π).
FIG. 42 is a development view of a conical wall with a fold line when it is divided into a trapezoidal triangular element by a fold line having an angle α at the upper right and an angle δ at the upper left at the point F in FIG. , Δ values are the same as those in FIG. 41.
FIG. 43 is an enlarged view of a main part of a development view of a conical wall with a fold line in the case of dividing by a trapezoidal element instead of dividing by the isosceles triangular element of FIG.
FIG. 44 is a view of the conical wall with a fold line, which is divided into an equilateral trapezoidal shape by a fold line and folded into a regular N pyramid, when N = 6 and φ ^* = π / 36, 2Θ = π / 12 in FIG. 43 described above.

[0073]
44A is an explanatory view of a pseudo-cone wall having an open view, FIG. 44A is a developed view, and FIG. 44B is a perspective view of a state in which the conical wall with a folding line having the developed view of FIG. 44A is half-folded.
FIG. 45 is a view showing a development view of a conical wall with a folding line composed of N isosceles triangular elements (vertical angle 2 °), in which only one step is written out as a curved strip portion.
FIG. 46 is an exploded view of a conical wall with a fold line having a simple, spiral exploded view consisting of three isosceles triangular elements.
FIG. 47 is a top view when the development view of FIG. 46 is folded.
48 is an explanatory diagram of a practical model obtained by modifying the model described in FIGS. 45 and 46. FIG. 48A is an explanatory diagram of a modification method, and FIG. 48B is an enlarged view of a main part of FIG. 48A.
FIG. 49 is a view showing a state in which the figure ABGHFE formed by the folding line in FIG. 48A is sequentially folded along folding lines AF and BF. FIG. FIG. 49B is a view showing a state after the mountain fold is further performed at B′F (original line segment BF) in the state of FIG. 49A.
FIG. 50 is a view showing a portion corresponding to the first-stage band plate and a portion corresponding to the second-stage band shown in FIG. 48A.
FIG. 51 is a developed view in the case where N = 6, γ + ψ ^* = π / 3, ψ ^* = π / 6, and γ = π / 6 in the conical wall with a folding line having the folding lines shown in FIGS. 51A is an explanatory view of a pseudo-conical wall having (2Θ = π / 18), FIG. 51A is a developed view, and FIG. 51B is a perspective view of a folded-conical wall having the developed view of FIG. .
FIG. 52 is a development view in the case where N = 6, γ + ψ ^* = π / 3, ψ ^* = π / 4, and γ = π / 12 in the conical wall with fold lines having the fold lines shown in FIGS. (2Θ = π / 6).
FIG. 53 is a developed view in the case where the number of steps in the developed view of FIG. 51A is reduced and the value of ψ ^* is increased for each step.
FIG. 54 is a developed view showing the same conical wall as the folded conical wall having the developed view of FIG. 53.
FIG. 55 shows the valley fold line of the second step in FIG.

[0074]
FIG.
FIG. 56 is an explanatory view of a pseudo-cone having a development view in which the FIG. 51 is formed into a repetitive spiral type. FIG. 56A is a development view, and FIG. It is a perspective view of the state which carried out.
FIG. 57 is a developed view (N = 6) of the repetitive spiral type obtained as 2Θ = π / 6, Δt * ￥ t = π / 6, γ = π / 6.
FIG. 58 is an explanatory view of a development view of a foldable conical wall having a folding line along a conformal spiral, FIG. 58A is an overall explanatory view, and FIG. 58B is an enlarged view of a main part of FIG. 58A.
FIG. 59 is an explanatory view of a development view of the conical wall with a folding line when the spiral of FIG. 58 is reversed.
FIG. 60 is an explanatory diagram of how to draw the developed view of FIG. 44A.
FIG. 61 is an explanatory view of a pseudo-cone having an exploded view in which FIG. 44 is made into an equiangular spiral shape. FIG. 61A is an exploded view, and FIG. FIG.
FIG. 62 is a developed view of a folding conical wall with a folding line in which the circumferential spiral of FIG. 51A is raised one step at the right end.
FIG. 63 is an explanatory diagram of the simplest folding method for origami.
FIG. 64 is an explanatory view of a development view of a disc-shaped folding structure with a folding line. FIG. 64A is an enlarged view of a main part for explaining folding conditions, and FIG. 64B is an overall view.
FIG. 65 is an enlarged view of a development view of the disc-shaped folding structure with a folding line shown in FIG. 64B.
FIG. 66 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 65 in a half-folded state and a small amount of folding.
FIG. 67 is a perspective view of the disc-shaped folding structure with a folding line having the development view of FIG. 65 in a half-folded state and a state in which the amount of folding is large.
FIG. 68 is a perspective view showing a state in which the disk-shaped folding structure with folding lines having the developed view of FIG. 65 is completely folded.
In FIG. 69, the swing angle of the folding line of Zig / Zag in the radial direction is increased as approaching the center.

[0075]
FIG. 69A is an enlarged view of a main part for explaining folding conditions, and FIG. 69B is an overall view.
FIG. 70 is an exploded view of a disc-shaped folding structure with a fold line when the swing angle of the fold line of Zig / Zag in the radial direction is increased toward the center and the fold line in the circumferential direction is also Zig / Zag. 70A is an enlarged view of a main part for explaining folding conditions, and FIG. 70B is an overall view.
FIG. 71 is an explanatory view of a conventionally known winding method in which the intersection of the spiral folding lines is on the Archimedes spiral.
FIG. 72 is a view showing a new folding line considered by the present inventor. FIG. 72A is a folding line in which the folding line (1) in the radial direction has one bending point and the spiral is reversed at this bending point in FIG. FIG. 72B is a diagram showing a line, and FIG. 72B is a diagram in which the outside of the bending point of FIG. 72A is replaced by a method of folding in a radial direction.
FIG. 73 is an explanatory diagram of fold lines when forming a fold line for folding a circular film or a partial circular film (sector-shaped film) in a radial direction and a circumferential direction along an equiangular spiral.
FIG. 74 is an explanatory diagram of fold lines when forming a fold line along a conformal spiral while folding a circular film or a partial circular film (sector-shaped film) or the like around a central axis and folding the film in the circumferential direction.
FIG. 75 is an enlarged view of a main part of FIG.
FIG. 76 is an explanatory diagram of folding conditions when forming a fold line along a conformal spiral while folding a circular film or a partial circular film (sector-shaped film) around a central axis.
FIG. 77 is an explanatory diagram of folding conditions when the main fold line is bent at an equal angle to radiation.
FIG. 78 shows an example of folding around the center with two zigzag spirals (m = 2) as folding lines, where n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 14 is a diagram illustrating an example of a folded development view when γ = 20 °.
FIG. 79 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 4, the number of isosceles triangle elements N = (2n + 1) m = 18, FIG. 78 is an example of a folded development view when γ = 0 °, showing an example in which the angle of the folding line with respect to the radiation is different from FIG. 78.
In FIG. 80, two zigzag spirals (m = 2) are used as folding lines to fold around the center.

[0077]
FIG. 91 is a perspective view showing a state in which the disk-shaped folding structure with a folding line having the developed view of FIG. 88 is completely folded.
FIG. 92 is a developed view in the case where the number of spirals serving as main folding lines is large (m = 12).
FIG. 93 is a developed view composed of two types of conformal spirals based on FIG. 77. The number of divisions N = 12, θ ₁ = π / 180, θ ₂ = 29π / 180, and φ is approximately π / 18. When the developed view of FIG. 93 is folded, it is satisfactorily wound around the center in a vertically symmetric manner. FIG. 93 suggests that these fold lines are replaced by elastic deformation during winding because the sub-fold lines are fine.
FIG. 94 is an exploded view of a disc-shaped folding structure with fold lines in which mountain fold lines and valley fold lines are alternately provided.
FIG. 95 shows the development of a disk-shaped folding structure with fold lines in which mountain fold lines and valley fold lines are provided alternately, and the circumferential lengths of the valley fold line and the left and right mountain fold lines are different on the left and right. FIG.
FIG. 96 is a view in which a fan-shaped portion between adjacent mountain fold lines in FIG. 95 is removed.
97 is an explanatory diagram of the folding condition of the sheet-like member, FIG. 97A is a developed view before folding, and FIG. 97B is a diagram showing a state where the sheet-like member is folded along a folding line in FIG. 97A.
FIG. 98 is an explanatory diagram of a DCC (double corrugated core), FIG. 98A is a developed view of the DCC, and FIG. 98B is an external view of the half folded state.
FIG. 99 is an explanatory diagram showing the vertical folding line group of FIG. 98 as zig / zag.
100A is an explanatory view of a newly devised model of a core having a joint, FIG. 100A is a developed view, FIG. 100B is a plan view of the developed view of FIG. 100A in a half-folded state, and FIG. 100C is an expanded view of FIG. It is an external view of what folded the figure and made it three-dimensional.
FIG. 101 is an explanatory view of another model of a newly devised core having a joint. FIG. 101A is a developed view, FIG. 101B is a plan view of the developed view of FIG. 101A in a half-folded state, and FIG. 101C is FIG. 3 is an external view of a three-dimensional view obtained by folding the development view of FIG.
FIG. 102 shows another core devised by the present inventor that satisfies another folding condition.

[0078]
102A is a development view, and FIG. 102B is an enlarged view of a main part of FIG. 102A.
FIG. 103 is an explanatory view of a core formed by folding the developed view of FIG. 102A, FIG. 103A is a perspective view of the folded core, and FIG. 103B is a perspective view of a sheet bonded to the lower surface of the core of FIG. 103A. .
FIG. 104 is an explanatory view of a model devised by the present inventor that does not satisfy another folding condition of a core having a joint, FIG. 104A is a developed view, and FIG. 104B is an enlarged view of a main part of FIG. 104A.
FIG. 105 is an explanatory diagram of a method of manufacturing a honeycomb core from one plate, FIG. 105A is a developed view, and FIG. 105B is a view of a honeycomb core manufactured from a plate having the developed view of FIG. 105A.
FIG. 106 is a view showing a folding mold for manufacturing the core material shown in FIG. 103A.
FIG. 107 is an explanatory view of the manufactured aluminum core. FIG. 107A is a perspective view, and FIG. 107B is a developed view, which has the same shape as the developed view of the paper shown in FIG. 103A.
FIG. 108 is an explanatory diagram of an application example of the structure with a cylindrical folding line, and FIG. 108A is a developed view.
FIG. 109 is an explanatory view of an application example of a spiral cylindrical structure with a folding line. FIG. 109A is a development view, and FIG. .
FIG. 110 is a plan view of the folding line forming die according to the first embodiment of the present invention.
FIG. 111 is a perspective view of a paper or resin sheet on which a folding line is formed.
FIG. 112 is an explanatory view of a folding line forming die according to the second embodiment of the present invention, and is a perspective view of one of a pair of flexible dies for sandwiching both sides of a sheet-like member forming a folding line. FIG.
FIG. 113 is a plan view of a folding line forming die according to Embodiment 3 of the present invention.
FIG. 114 is an explanatory view of the use state of the folding line forming die of FIG. 113, and FIG.

[0080]
FIG. 127A is a side view in a half-folded state, and FIG. 127B is a side view in a substantially completely folded state.
FIG. 128 is an explanatory view of a method for manufacturing the coffee can A, and is an explanatory view of an inner mold (a mold having a folding line forming surface) disposed on the inner surface of the cylindrical member. FIG. FIG. 128B is a cross-sectional view in which a pair of inner second dies are inserted between the pair of inner first dies of FIG. 128A; FIG. 128C is a cross-sectional plan view showing a state where a cam rod is inserted into the center of the inner first and second molds of FIG. 128B, and FIG. 128D is a diagram showing a state where the cam rod of FIG. It is a figure showing the state where the inside 1st and 2nd metallic molds were pushed out by pushing out.
FIG. 129 is an explanatory diagram of a method for manufacturing the coffee can A. FIG. 129A shows a state before an outer mold K2 is clamped with an inner mold (a mold having a folding line forming surface) set on the inner surface of a cylindrical member. 129B is a view showing a state where the mold is clamped from the state of FIG. 129A.
FIG. 130 is an explanatory view of a coffee can as the eighth embodiment of the folded line structure of the present invention, and is a diagram showing a folded line structure (coffee can) having a cylindrical wall formed along a spiral.
FIG. 131 is an explanatory diagram of another embodiment of the method for manufacturing the coffee can A.
132 is an explanatory diagram of a small container as a structure with a folding line according to Embodiment 9 of the present invention. FIG. 132A is a perspective view of a lid of the small container, and FIG. 132B is a perspective view of the small container in an extended state.
133 is an explanatory view of the small container of the ninth embodiment, FIG. 133A is a perspective view of the folded small container, FIG. 133B is a sectional view taken along the line 133B-133B of FIG. 133A, and FIG. It is sectional drawing of the state which covered the container.
FIG. 134 is an explanatory diagram of the method of manufacturing the small container B, and shows a state in which a mold (a mold having a folding line forming surface) is closed.
FIG. 135 is an explanatory diagram of a paper pack as a structure with a folding line according to the tenth embodiment of the present invention, and is a perspective view of a used state in which the paper pack is extended.

[0082]
FIG. 156 is a developed view of the gusset of FIG. 155.
FIG. 157 is an explanatory view of a gusset (partition member inside a box) as a structure with a folding line according to Embodiment 18 of the present invention, and is a perspective view of the gusset taken out of the paper box.
FIG. 158 is a development view of the gusset of FIG. 157.
FIG. 159 is an explanatory diagram of a gusset (partition member inside a box) as a structure with a folding line according to a nineteenth embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 160 is a perspective view of the gusset shown in FIG.
FIG. 161 is a developed view of the gusset of FIG. 159.
FIG. 162 is an explanatory view of a gusset (partitioning member inside a box) as a structure with a folding line according to a twentieth embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 163 is a perspective view of the gusset of FIG.
FIG. 164 is a developed view of the gusset of FIG. 163.
FIG. 165 is an explanatory diagram of a gusset (partition member inside a box) as a structure with a folding line according to a twenty-first embodiment of the present invention, and is a perspective view showing a state where the gusset is housed in a paper box.
FIG. 166 is a perspective view of the gusset of FIG.
FIG. 167 is a developed view of the gusset of FIG. 166.
168 is an explanatory view of the foldable passage cover, FIG. 168A is a perspective view of a half-folded state, and FIG. 168B is a perspective view of a completely folded state.
FIG. 169 is a developed view of a foldable passage cover as a structure with a folding line according to Embodiment 22 of the present invention.
FIG. 170 is an explanatory view of a foldable passage cover as a structure with a fold line according to Embodiment 23 of the present invention. FIG. 170A is a perspective view of a half-folded state, and FIG. 170B is a perspective view of a completely folded state.
FIG. 171 is a development view of the foldable passage cover of FIG. 170.
FIG. 172 is an explanatory view of a lamp shade as a structure with a fold line according to Embodiment 24 of the present invention. FIG. 172A is a development view of a sheet-like member which is a material for manufacturing the lamp shade, and FIG. 172B is a sheet of FIG. FIG. 5 is a perspective view of a lampshade formed by manufacturing a pseudo cone by joining left and right sides of a shaped member into a half-folded state.

[0083]
FIG. 173 is an explanatory diagram of a Christmas card as a structure with a fold line according to Embodiment 25 of the present invention. FIG. 173A is a plan view of the folded Christmas card, and FIG. 173B is a plan view of FIG. 173A opened. FIG. 173C is a diagram viewed from obliquely above the arrow 173C in FIG. 173B.
174A is an explanatory view of a hat as a structure with a folding line according to Embodiment 26 of the present invention. FIG. 174A is a perspective view of the hat, FIG. 174B is a sectional view taken along the line 174B-174B of FIG. 174A, and FIG. It is the figure seen from arrow 174C of 174B.
FIG. 175 is an explanatory view of the hat of Example 26. FIG. 175A is a plan view of the folded state of the hat, and FIG. 175B is a view seen from the arrow 175B of FIG. 175A.
176 is an explanatory view of a hat as a structure with a fold line according to Embodiment 27 of the present invention. FIG. 176A is a perspective view of the hat, FIG. 176B is a sectional view taken along the line 176B-176B of FIG. It is the figure seen from arrow 176C of 176B.
FIG. 177 is an explanatory view of the hat of Example 27. FIG. 177A is a plan view of the folded state of the hat, and FIG. 177B is a view seen from the arrow 177B of FIG. 177A.
FIG. 178 is a perspective view of a rewindable hat as a structure with a folding line according to Embodiment 28 of the present invention.
FIG. 179 is a perspective view of the retractable hat of FIG. 178 in a state of being folded.
FIG. 180 is a perspective view of the retractable hat in a state further folded from the state of FIG. 179.
FIG. 181 is an explanatory view of the method of manufacturing the wind-up hat shown in FIGS. 178 to 180. FIG. 181A is a developed view of the flange portion A of FIG. 178, FIG. 181B is a developed view of the temporal portion B, and FIG. It is a development view of the crown part C.
FIG. 182 is an explanatory diagram of another method of manufacturing the wind-up hat shown in FIGS. 178 to 181.

[0092]
128D shows a state in which the inner first and second dies are pushed outward by rotating the cam rod of FIG. 128C to push the inner second mold outward. FIG.
FIG. 129 is an explanatory diagram of a method for manufacturing the coffee can A. FIG. 129A shows a state before an outer mold K2 is clamped with an inner mold (a mold having a folding line forming surface) set on the inner surface of a cylindrical member. 129B is a view showing a state where the mold is clamped from the state of FIG. 129A.
The inner mold K1 shown in FIGS. 128 and 129 includes a pair of inner first molds K1a, K1a arranged to face each other, and a pair of inner second molds K1b, K1b arranged therebetween. And a cam rod K1c inserted between the inner first and second molds K1a, K1a, K1b, K1b. On the outer surface of the inner first and second molds K1a, K1a, K1b, K1b, an uneven surface (FIG. 125, FIG. 126) forming the mountain fold line M and the valley fold line V of the coffee can A shown in FIG. (Not shown). The outer mold K2 has four outer divided molds K2a formed by dividing a cylindrical mold into four equal parts, and the inner surface of each outer divided mold K2a is provided with the above-mentioned FIGS. Are formed with a concave-convex surface (not shown) forming a mountain fold line M and a valley fold line V of the coffee can A shown in FIG.
As shown in FIG. 128C, when the inner mold K1 is set inside the aluminum cylindrical member that is a material for manufacturing the coffee can A, and the cam rod K1c is rotated by 90 ° in this state, the inner first and second molds are rotated. K1a, K1a, K1b, and K1b are pushed outward to the state shown in FIG. 128D.
In this state, by clamping the outer mold K2 of FIG. 129A to the state of FIG. 129B, the coffee can A having the folding lines M and V shown in FIGS. 125 and 126 can be manufactured.
The inner first and second dies K1a, K1a, K1b, K1b of the inner die K1 are provided with air vent holes (not shown) for discharging air in recesses formed on the outer surfaces thereof. By forming it between the concave portion on the outer surface and the inner surface, the coffee can A can be easily formed.

[0093]
(Example 8)
FIG. 130 is an explanatory view of a coffee can as the eighth embodiment of the folded line structure of the present invention, and is a diagram showing a folded line structure (coffee can) having a cylindrical wall formed along a spiral.
In the description of the eighth embodiment, the same reference numerals are given to the components corresponding to the components of the seventh embodiment, and the detailed description thereof will be omitted.
The eighth embodiment differs from the seventh embodiment in the following points, but has the same configuration as the seventh embodiment in other points.
In FIG. 130, in the coffee can A of the eighth embodiment, a part P, which is a portion formed (enclosed) by the folding lines M and V, is formed along a spiral having an inclination angle of 45 °.
As in the eighth embodiment, a cylindrical wall (a structure with a cylindrical folding line) A1 having a folding line along a spiral having an inclination angle of 20 ° to 30 ° or more is folded when it is compressed in the axial direction while being twisted. Since the cylindrical wall A1 of the coffee can A is plastically deformed once it is folded, the cylindrical wall A1 does not automatically return to its original shape. For this reason, when the coffee can A is used, it is compressed and folded in the axial direction while being twisted when being used, so that the coffee can A is kept in a small folded state.
FIG. 131 is an explanatory diagram of another embodiment of the method for manufacturing the coffee can A.
In FIG. 131, the inner mold K1 set inside the cylindrical wall A1 having the bottom wall A0 is fixed to the upper end of the liquid container V, and the cylindrical wall A1 is accommodated in the liquid container V in the liquid container V. Fill with liquid. A tube T is connected to the upper end of the liquid container V, and the inside of the tube T is also filled with liquid.
In this state, when impact pressure is applied to the liquid in the tube T by the piston P, a fold line is formed on the cylindrical wall A1 according to the unevenness of the surface of the inner mold K1.
(Example 9)
132 is an explanatory diagram of a small container as a structure with a folding line according to Embodiment 9 of the present invention. FIG. 132A is a perspective view of a lid of the small container, and FIG. 132B is a perspective view of the small container in an extended state.

[0094]
133 is an explanatory view of the small container of the ninth embodiment, FIG. 133A is a perspective view of the folded small container, FIG. 133B is a sectional view taken along the line 133B-133B of FIG. 133A, and FIG. It is sectional drawing of the state which covered the container.
In FIGS. 132 and 133, the small container B (see FIG. 132B) has a circular bottom plate 6, an upper end plate 7, and a foldable pseudo-cylindrical wall 8. The outer shape of the upper end plate 7 is circular, and a hexagonal opening 7a is formed in the center.
As shown in FIG. 132B, the pseudo-cylindrical wall 8 is formed with a number of mountain fold lines M having a convex outer surface and a number of valley fold lines V having a concave outer surface.
132B and 133, the pseudo-cylindrical wall 8 of the small container B of the ninth embodiment has a plurality of parts P1 and P2 which are portions (enclosed) formed by the folding lines M and V. The part P1 is triangular and one side thereof is foldably connected to the bottom plate 6, and the part P2 is triangular and one side thereof is foldably connected to the upper end plate 7. A mountain fold line M, M,... Is formed at a connection portion between the bottom plate 6 and one side of each of the six parts P1 so that the mountain fold lines M, M,. Connected endlessly.
A mountain fold line M, M,... Is formed at a connection portion between the upper end plate 7 and one side of each of the six parts P2, and the mountain fold lines M, M,. Connected endlessly.
Each of the endlessly connected mountain fold lines M, M,... Forms a continuous and closed polygon along a plane perpendicular to the axis of the pseudo cylindrical wall 8.
When the pseudo-cylindrical wall 8 of the small container B of the ninth embodiment is compressed in the axial direction while being twisted, the pseudo-cylindrical wall 8 is folded along the folding lines M and V to be in a state shown in FIGS. 133A and 133B.
A lid 9 (see FIGS. 132A and 133C) for opening and closing the hexagonal opening 7a at the upper end of the small container B includes a circular upper plate 9a, a short cylindrical wall 9b provided on the outer periphery of the upper plate 9a, and a cylinder. A pair of protruding portions 9c, 9c extending downward from the lower end of the wall 9b, a lower end locking portion 9d provided at the lower end of the protruding portions 9c, 9c, and a cylindrical wall 9b above the protruding portions 9c, 9c. And an upper locking portion 9e which protrudes slightly on the inner side surface of the upper surface.
When the small container B is not used, the small container B is folded as shown in FIG. 133B.

[0102]
Point 4 is a folding line.
In FIG. 169, the foldable passage cover 16 according to the twenty-second embodiment has a plurality of parts P1, P2, and P3 that are portions (enclosed) formed by the folding lines M and V. Part P1 is triangular, part P2 is equilateral trapezoid, and part P3 is trapezoidal.
The foldable passage cover 16 is folded in a state where the outer shape is reduced as shown in FIG. 168 during storage or transportation.
(Example 23)
FIG. 170 is an explanatory view of a foldable passage cover as a structure with a fold line according to Embodiment 23 of the present invention. FIG. 170A is a perspective view of a half-folded state, and FIG. 170B is a perspective view of a completely folded state.
FIG. 171 is a development view of the foldable passage cover of FIG. 170.
In the description of the twenty-third embodiment, the same reference numerals are given to the components corresponding to the components of the twenty-second embodiment, and the detailed description thereof will be omitted.
The embodiment 23 is different from the embodiment 22 in the following points, but is configured similarly to the embodiment 22 in other points.
As in the case of the twenty-second embodiment, the foldable passage cover 16 shown in FIG. 170 is a passage portion where a person passes, such as a passage portion of a connecting portion between vehicles of a railroad vehicle or a passage between a terminal bridge end of an airport and an aircraft entrance. Therefore, it is suitably used in a place where the distance between the structures at both ends of the passage is not fixed.
The foldable passage cover 16 shown in FIG. 171 has an outer shape excluding a fan-shaped central portion in a developed view. The folding passage cover 16 is formed with a number of mountain fold lines M having a convex outer surface and a number of valley fold lines V having a concave outer surface when used in a half-folded state. is there. Further, each node satisfies the folding condition.
In FIG. 171, the foldable passage cover 16 according to the twenty-third embodiment has a plurality of parts P1, P2, P3, which are portions formed (enclosed) by the fold lines M and V.

[0103]
P4. The part P1 is a triangle, and the parts P2 to P4 are all quadrilaterals.
The foldable passage cover 16 according to the twenty-third embodiment is folded into a state in which the outer shape is reduced as shown in FIG.
(Example 24)
FIG. 172 is an explanatory view of a lamp shade as a structure with a fold line according to Embodiment 24 of the present invention. FIG. 172A is a development view of a sheet-like member which is a material for manufacturing the lamp shade, and FIG. 172B is a sheet of FIG. FIG. 5 is a perspective view of a lampshade formed by manufacturing a pseudo cone by joining left and right sides of a shaped member into a half-folded state.
The lamp shade 17 shown in the half-folded state shown in FIG. 172B is a member used as a lamp umbrella in an extended state, and is made of a sheet-like resin.
In the developed view of the lamp shade 17 shown in FIG. 172A, the transparent resin sheet for manufacturing the lamp shade 17 of FIG. 172B has a shape excluding the central portion of the fan shape. An adhesive margin 17a is provided on one of both sides of the resin sheet to be joined to each other. After forming the fold line on the resin sheet in the expanded state by using the same member as the fold line forming die shown in the first or third embodiment, the glue margin 17a has elasticity at the time of curing. An adhesive is applied to adhere to the other of the two sides. At this time, a foldable pseudo-conical wall can be manufactured using the transparent resin sheet.
The foldable pseudo-cylindrical wall of the transparent resin sheet has a large number of mountain fold lines M having a convex outer surface and a large number of concave valley lines V having a concave shape in a half-folded state.
At the node, which is the intersection of the mountain fold line M and the valley fold line V, a total of six fold lines of four mountain fold lines M and two valley fold lines V intersect. Then, the number of mountain fold lines M intersecting at each node = 4, the number of valley fold lines V = 2, and the difference is 2 (= 4-2). That is, the folding line pattern of the foldable pseudo-cone wall in the twenty-fourth embodiment is one section.

[0105]
174A is a perspective view of the hat, FIG. 174B is a sectional view taken along the line 174B-174B of FIG. 174A, and FIG. 174C is a view seen from the arrow 174C of FIG. 174B.
FIG. 175 is an explanatory view of the hat of Example 26. FIG. 175A is a plan view of the folded state of the hat, and FIG. 175B is a view seen from the arrow 175B of FIG. 175A.
174 and 175, the hat C (see FIG. 174) has a donut-shaped collar 13 and a foldable crown 14 provided on the upper surface of the central portion of the collar 13. The crown 14 has a hexagonal upper surface portion 14a and a side surface portion (pseudo-conical wall) 14b formed by twisting a hexagonal pyramid.
As shown in FIG. 174B, a large number of mountain fold lines M having a convex outer surface and a large number of valley fold lines V having a concave surface are formed on the side surface (pseudo-cone wall) 14b.
At a node, which is the intersection of the mountain fold line M and the valley fold line V, a total of four fold lines of three mountain fold lines M and one valley fold line V intersect. Then, the number of mountain fold lines M intersecting at each node = 3, the number of valley fold lines V = 1, and the difference is 2 (= 3-1). That is, the folding line pattern of the side surface portion (pseudo-conical wall) 14b of the twenty-sixth embodiment is a one-node four-fold line.
174 and 175, the side portion 14b of the hat C of the twenty-sixth embodiment has a plurality of parts P1 and P2 which are portions formed (enclosed) by the folding lines M and V. The part P1 is triangular and one side thereof is foldably connected to the collar 13. The part P2 is triangular and one side thereof is foldably connected to the upper surface 14a. A mountain fold line M, M,... Is formed at a connection portion between the collar 13 and one side of each of the six parts P1 so that the mountain fold lines M, M,. Connected endlessly.
A mountain fold line M, M,... Is formed at a connection portion between the upper surface member 14a and one side of each of the six parts P2, and the mountain fold lines M, M,. Connected endlessly.
The endlessly connected mountain fold lines M, M,... Are perpendicular to the axis of the side surface portion (pseudoconical wall) 14b when the side surface portion (pseudoconical wall) 14b is extended and folded. It forms a closed polygon in a simple plane.
The side head 14b of the hat C of this embodiment 26 is compressed in the axial direction while twisting.

[0106]
175A and 175B.
The angle between the mountain fold line M and the valley fold line V formed at the connecting portion between the collar 13 and one side of the part P1 is set to an angle larger than 45 °. For this reason, even if the rigidity of the side portion 14b is small, it is easy to maintain the extended state due to the rigidity when it is extended once.
When the hat C is not used, when the hat C is folded as shown in FIG. 175B, the space required for housing the hat C can be reduced.
(Example 27)
176 is an explanatory view of a hat as a structure with a fold line according to Embodiment 27 of the present invention. FIG. 176A is a perspective view of the hat, FIG. 176B is a sectional view taken along the line 176B-176B of FIG. It is the figure seen from arrow 176C of 176B.
FIG. 177 is an explanatory view of the hat of Example 27. FIG. 177A is a plan view of the folded state of the hat, and FIG. 177B is a view seen from the arrow 177B of FIG. 177A.
In the description of the twenty-seventh embodiment, the same reference numerals are given to components corresponding to the components of the twenty-sixth embodiment, and a detailed description thereof will be omitted.
The embodiment 27 is different from the embodiment 26 in the following points, but is configured similarly to the embodiment 26 in other points.
In FIG. 176A, on the temporal part (pseudo-conical wall) 14b, a plurality of parts P1 to P5 of a trapezoidal shape are formed by a large number of one-node four-fold lines. Each fold line is formed by joining and stitching the ends of the fabric. The mountain fold and the valley fold of the fold line are determined by the joining state of the ends of the fabric. When the end protrudes outward, a mountain fold line M is formed. When the end protrudes inward, the valley fold line is formed. V is formed. The parts P1 to P5 of the isosceles trapezoid are sequentially reduced in size from the part P1 arranged at the bottom to the part P5 arranged at the top.
Each of the isosceles trapezoidal parts P1 has one bottom side foldably connected to the collar 13, and one bottom side of the part P5 is foldably connected to the upper surface 14a. At the connection portion between the collar 13 and one side of each of the six parts P1, a mountain fold line M and a valley fold line V are formed so as to be connected alternately, and are connected alternately.

[0110]
The coordinates of the center position of r are assumed to be r = 0, j = 1, 2,..., 10, and a circle having a radius equal to the coordinates rj (rj = r1 × (11−j) / 10) of the position equally divided in the radial direction. FIG. 8 is a diagram showing the shape of a part (conical wall) (j) formed when the image is divided into 10 parts according to FIG.
FIG. 188 is a diagram showing the part number (j) of FIG. 187, the shape and length Lj of the bus, and the inclination θj.
FIG. 189 shows divided parts (J: J = 1, 2,...) Obtained by dividing the developed view of the parts (1), (2),..., (10) shown in FIG. FIG. 189A is a diagram showing that each part (j) is composed of 16 divided parts (J), and FIG. 189B is a diagram connecting the divided parts (J) in the radial direction. FIG.
Consider a curved strip ABCD having a curvature of width L at the outer periphery on a sector (outer radius R *) having a central angle Θ as shown in FIG. 186A. When the left and right ends AB and CD of the strip are joined, a truncated cone as shown in FIG. 186B is obtained. Assuming that the radius of the bottom of the truncated cone is R 'and the apex angle of the conical shell obtained by extending the truncated cone is 2θ, the outer circumference of the bottom of the truncated cone is equal to the outer circumference of the strip,
2πR '= R * ・ Θ ………………………………… (59)
Get. From FIG. 186B, since sin θ = R ′ / R *, Θ is given by the following equation (60).
Θ = 2πsin θ ……………………………………… (60)
As shown in FIG. 187, a curve passing through a gentle origin such as a parabola is represented by Z = f (r) on the ZX plane, and a thin film-like rotating shell obtained by rotating this around the Z axis is considered. . The radius of the upper end of the container-shaped rotary shell obtained by this rotation is r1. This rotating shell is divided into n parts on a plane perpendicular to the Z axis, and the rotating shell is approximated by n frusto-conical elements using the relationship in FIG. The intersection of the dividing plane and the shell forms a circle. The radii of the circle are r2, r3,... The n frustoconical elements are named sequentially (1), (2), (3),..., And the angles corresponding to the 切 り values in FIG. Θ3 ...
Since the inner diameter of the element (1) is equal to the outer diameter of the element (2), and the inner diameter of the element (2) is equal to the outer diameter of the element (3), the following equation (61) holds for the i-th and j + 1-th elements.

[0111]
2πrjΘj = 2πrj + 1Θj + 1 ... (61)
Now, assuming that the rotary shell is a paraboloid, Z = C (r / r0) {t2} t, n = 10, and the cutting radius is r2 = 0.9r1, r3 = 0.8r1, r4. = 0.7r1,... Is considered as a simple case. FIG. 188 shows a cross-sectional shape after division when C = 0.8, cut on the ZX plane, and each element is approximated by a truncated cone as described above. The length Lj (corresponding to L in FIG. 186) of each of the n truncated cone elements (1), (2), (3),... when they are cut open and expanded is easily calculated. Further, since the angle θj (θ in FIG. 186B) formed by these elements with the Z axis is also obtained, the Θj value of each element can be calculated by using the equation (60). The width of the element (1) is W1 and its outer peripheral length is 2πr1. The ratio of the width to the length is set as κ1 as the aspect ratio (κ1 = W1 / 2πr1). When this strip element is drawn on a circle having a radius Ro, the width W1 = κ1Θ1 ・ Ro = (W1 / 2πr1) Θ1 ・ Ro = W1 ｛Θ1 / (2πr1)｝ Ro, where the apex angle Θ1. That is, the dimensionless width W1 / Ro when expressed on the radius Ro circle is given by W1Θ1 / (2πr1). The other elements are generally given by the following equation (62), with αj≡Wj / (2πrj).
Lj / Ro = αjΘj ………………………………… (62)
If the outer radius of the sector j is (Rj) o and the inner radius is (Rj) i,
Lj = (Rj) o- (Rj) i (63)
And (Rj) iΘj = (Rj + 1) oΘj + 1. That is, in FIG. 189A, (R1) iΘ1 = (R2) oΘ2. Using this relationship and equations (59) to (63), Θj, Lj, Wj, and (Rj) i, (Rj) o values can be calculated in the order of elements (1), (2),. FIG. 189A shows a developed view of each element (j) obtained by using these values.
The numerical values in FIG. 188 are as follows.

[0113]
By supplying air to H1 and H2 to inflate them, the expanded state shown in FIG. 190 is maintained.
In this embodiment 30, when the film thickness constituting the shell is large, the winding may be cramped at the central portion. Therefore, in order to avoid this, when dividing the FIG. Is divided unequally.
That is, after dividing into eight equal parts, this is further divided into two parts at a central angle ratio of 0.475: 0.525, and eight sets (16 elements) of curved fan-shaped elements are alternately joined. The curved surface is shown in FIG. Here, when the left side of the element having a small central angle is folded into a valley and the right side is folded into a mountain, the element is wound while being shifted downward around the central axis. This is shown in FIGS. 191 and 192. This winding method has an advantage of alleviating the above-mentioned degree of cramp.
These models can be used to form parabolic surfaces of parabolic antennas, as well as large windable / unfoldable tents.
Industrial Applicability Above, the embodiments of the present invention have been described in detail, but the present invention is not limited to the embodiments, but falls within the scope of the present invention described in the claims. Various changes can be made. Modified embodiments of the present invention are exemplified below.
(1) In Examples 1 and 2, the folding line forming mold has a pair of foldable folding line forming members (flexible molds), and the sheet-like member is sandwiched between the pair of folding line forming members. In the state, a pair of fold line forming members are simultaneously folded to form a fold line in the sheet-like member. Good. When one fold line forming member is used, the fold line forming member may be folded in a state where the sheet-like member is attracted to one surface side. As a method of adsorbing the sheet-shaped member, for example, it is possible to adsorb the sheet-shaped member on one surface side by opening a ventilation hole in a part of the folding line forming member and reducing the pressure on the other surface side. Become.
In addition, a folding line forming member using magnetized material parts and a flexible magnetic rubber

Claims (20)

A structure with a folding line, comprising the following constituent requirements (A01) to (A05):
(A01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and that can be folded along the linear part connection part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(A02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(A03) a first mountain fold line, a second mountain fold line, and a third mountain fold line radially extending from one node, and the third mountain fold line is disposed between the first mountain fold line and the second mountain fold line; A plurality of fold lines having one node and four fold lines formed by a first valley fold line arranged on the opposite side to the mountain fold line;
(A04) The node is defined as the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line. One of the first mountain fold line and the second mountain fold line is the X axis. The angle formed by α and the angle formed by the other mountain fold line with the first valley fold line, and the plurality of fold lines formed so that α = γ,
(A05) The foldable structure having the quadrangular part other than the parallelogram. 2. The structure with a folding line according to claim 1, comprising the following constituent requirements (A06).
(A06) The structure with a fold line, wherein the part and the part connection portion provided with the fold line are formed of different members. The structure with a folding line according to claim 1, comprising the following constituent requirements (A07):
(A07) The structure with a fold line constituted by an integrally molded product with a fold line. A structure with a folding line, comprising the following constituent requirements (A01) to (A04), (A08):
(A01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and that can be folded along the linear part connection part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(A02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(A03) a first mountain fold line, a second mountain fold line, and a third mountain fold line radially extending from one node, and the third mountain fold line is disposed between the first mountain fold line and the second mountain fold line; A plurality of fold lines having one node and four fold lines formed by a first valley fold line arranged on the opposite side to the mountain fold line;
(A04) The node is defined as the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line. One of the first mountain fold line and the second mountain fold line is the X axis. The angle formed by α and the angle formed by the other mountain fold line with the first valley fold line, and the plurality of fold lines formed so that α = γ,
(A08) The structure with a folding line having the quadrangular and triangular parts. A structure with a folding line, comprising the following constituent requirements (A01) to (A05), (A09):
(A01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and that can be folded along the linear part connection part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(A02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(A03) a first mountain fold line, a second mountain fold line, and a third mountain fold line radially extending from one node, and the third mountain fold line is disposed between the first mountain fold line and the second mountain fold line; A plurality of fold lines having one node and four fold lines formed by a first valley fold line arranged on the opposite side to the mountain fold line;
(A04) The node is defined as the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line. One of the first mountain fold line and the second mountain fold line is the X axis. The angle formed by α and the angle formed by the other mountain fold line with the first valley fold line, and the plurality of fold lines formed so that α = γ,
(A05) The foldable structure having the quadrangular part other than the parallelogram.
(A09) When the fold line is extended, the shape becomes a flat plate, and when the fold line is bent along the mountain fold line and the valley fold line, the outer shape is reduced and becomes a flat plate shape having irregularities on the surface. The structure with a fold line, which can be folded and extended in a flat plate shape so that the outer shape becomes a three-dimensional structure with a further reduced size when completely folded along the valley fold line. A structure with a folding line, comprising the following constituent requirements (A01) to (A04), (A010), and (A011):
(A01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and that can be folded along the linear part connection part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(A02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(A03) a first mountain fold line, a second mountain fold line, and a third mountain fold line radially extending from one node, and the third mountain fold line is disposed between the first mountain fold line and the second mountain fold line; A plurality of fold lines having one node and four fold lines formed by a first valley fold line arranged on the opposite side to the mountain fold line;
(A04) The node is defined as the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line. One of the first mountain fold line and the second mountain fold line is the X axis. The angle formed by α and the angle formed by the other mountain fold line with the first valley fold line, and the plurality of fold lines formed so that α = γ,
(A010) A cylindrical wall or a conical wall having a cylindrical wall or a conical wall when the fold line is extended, and having an uneven outer shape when the fold line is bent along the mountain fold line and the valley fold line. Forming a cylindrical wall or a cone wall having a thickness having irregularities whose outer shape is further reduced in a completely folded state along the mountain fold line and the valley fold line,
(A011) The structure with a folding line having a plurality of folding lines that are continuous in a plane perpendicular to the axis of the cylindrical wall or the conical wall. A structure with a folding line, comprising the following constituent requirements (A01) to (A04), (A012), and (A013):
(A01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and that can be folded along the linear part connection part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(A02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(A03) a first mountain fold line, a second mountain fold line, and a third mountain fold line radially extending from one node, and the third mountain fold line is disposed between the first mountain fold line and the second mountain fold line; A plurality of fold lines having one node and four fold lines formed by a first valley fold line arranged on the opposite side to the mountain fold line;
(A04) The node is defined as the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line. One of the first mountain fold line and the second mountain fold line is the X axis. The angle formed by α and the angle formed by the other mountain fold line with the first valley fold line, and the plurality of fold lines formed so that α = γ,
(A012) A cylindrical wall or a conical wall which forms a cylindrical wall or a conical wall when the fold line is extended, and has an uneven outer shape when bent along the mountain fold line and the valley fold line of the fold line. Forming a cylindrical wall or a cone wall having a thickness having irregularities whose outer shape is further reduced in a state of being completely folded along the mountain fold line and the valley fold line,
(A013) The structure with a folding line, wherein the parts have a polygonal shape of a quadrangle or more. A structure with a fold line, comprising the following constituent requirements (B01) to (B04):
(B01) A linear fold line that has a plurality of polygonal parts and a linear part connecting part that connects outer sides of the parts to each other and that can be folded along the linear part connecting part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where one surface side forms a mountain fold and one or more valley fold lines that form a valley fold when viewed from one surface side of the structure with a fold line. A structure with a fold line having:
(B02) A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(B03) Between the first mountain fold line, the second mountain fold line, the third mountain fold line, and the fourth mountain fold line extending radially from one node, and between the first mountain fold line and the second mountain fold line A first valley fold line formed and arranged on the opposite side to the third fold fold line and the fourth fold fold line; and a first valley fold line disposed between the third fold fold line and the fourth fold fold line; A second valley fold line disposed on the opposite side to the first fold fold line and the second fold fold line, the first fold fold line and the fourth fold fold line being adjacent to each other, and The plurality of fold lines having one node and six fold lines in which the third mountain fold line is adjacently arranged;
(B04) The node is defined as the origin O, the X axis is taken in the direction of the extension of the first valley fold line, and the angles formed by the first fold fold line and the second fold fold line with the first valley fold line are respectively defined. α and β, angles between the third mountain fold line and the fourth mountain fold line with the second valley fold line are γ and δ, respectively, and an angle between the X axis and the second valley fold line is θ. In some cases, the plurality of folding lines formed so that β−α = δ−γ + θ. 9. The structure with a fold line according to claim 8, comprising the following constituent requirements (B05):
(B05) When the fold line is extended, the shape becomes a flat plate, and when the fold line is bent along the mountain fold line and the valley fold line, the outer shape is reduced and becomes a flat plate shape having irregularities on the surface. The structure with a fold line, which can be folded and extended in a flat plate shape so that the outer shape becomes a three-dimensional structure with a further reduced size when completely folded along the valley fold line. 9. The structure with a fold line according to claim 8, comprising the following constituent requirements (B06).
(B06) A cylindrical wall or a conical wall having a cylindrical wall or a conical wall when the fold line is extended, and having an uneven outer shape when bent along the mountain fold line and the valley fold line of the fold line. And a fold line that is foldable and extendable to form a thick cylindrical wall or conical wall having irregularities whose outer shape is further reduced when completely folded along the mountain fold line and the valley fold line. Attached structure. A structure with a folding line, comprising the following constituent requirements (C01) to (C04):
(C01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and that can be folded along the linear part connection part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(C03) When the folding line is extended, a cylindrical wall is formed, and when the folding line is bent in accordance with the mountain fold line and the valley fold line, a cylindrical wall having a reduced outer shape is formed. The structure with a fold line, which forms a thick cylindrical wall having irregularities whose outer shape is further reduced in a completely folded state along the fold line and the valley fold line,
(C04) The structure with a folding line having a folding line that is continuous along a plane perpendicular to the axis of the cylindrical wall and forms a closed polygon. A structure with a fold line, comprising the following constituent requirements (C01) to (C03), (C05):
(C01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and that can be folded along the linear part connection part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(C03) When the folding line is extended, a cylindrical wall is formed, and when the folding line is bent in accordance with the mountain fold line and the valley fold line, a cylindrical wall having a reduced outer shape is formed. The structure with a fold line, which forms a thick cylindrical wall having irregularities whose outer shape is further reduced in a completely folded state along the fold line and the valley fold line,
(C05) The structure with a folding line, wherein the part has a polygonal shape of a quadrangle or more. A structure with a folding line, comprising the following constituent requirements (C01) to (C03), (C06), and (C07):
(C01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and that can be folded along the linear part connection part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(C03) When the folding line is extended, a cylindrical wall is formed, and when the folding line is bent in accordance with the mountain fold line and the valley fold line, a cylindrical wall having a reduced outer shape is formed. The structure with a fold line, which forms a thick cylindrical wall having irregularities whose outer shape is further reduced in a completely folded state along the fold line and the valley fold line,
(C06) The structure with a fold line, wherein the fold lines are all formed along a spiral, and the parts are only obtuse triangles formed by dividing a parallelogram into two parts by diagonals.
(C07) A structure with a folding line having the above-described configuration having the obtuse angled triangular part whose one base angle is 35 ° or more. A structure with a folding line, comprising the following constituent requirements (D01) to (D03):
(D01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of the parts to each other and that can be folded along the linear part connection part is A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(D02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(D03) When the fold line is extended, a conical wall is formed, and when the fold line is bent in accordance with a mountain fold line and a valley fold line, a conical wall having an unevenness whose outer shape is reduced is formed. The above-mentioned structure with a folding line, which forms a thick conical wall having irregularities with a further reduced outer shape when completely folded along the folding line and the valley folding line. The structure with a folding line according to claim 14, comprising the following constituent requirements (D04) and (D05).
(D04) The first mountain fold line, the second mountain fold line, and the third mountain fold line are disposed between the first mountain fold line and the second mountain fold line, and are on the side opposite to the third mountain fold line. The plurality of fold lines having one node and four fold lines formed by the first valley fold line disposed at
(D05) The node is defined as the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line. One of the first mountain fold line and the second mountain fold line is the X axis. The plurality of fold lines formed so that α = γ, where α is the angle formed by the angle and γ is the angle formed by the other mountain fold line with the first valley fold line. The structure with a folding line according to claim 14, comprising the following constituent requirements (D06) and (D07).
(D06) a first mountain fold line, a second mountain fold line, a third mountain fold line, a fourth mountain fold line, and the third mountain fold line formed between the first mountain fold line and the second mountain fold line A first valley fold line disposed on the opposite side to the fold line and the fourth fold line, and a first fold line and a second fold line disposed between the third fold line and the fourth fold line; A second valley fold line disposed on the opposite side to the mountain fold line, the first mountain fold line and the fourth mountain fold line being adjacent, and the second mountain fold line and the third mountain fold line being adjacent Said plurality of fold lines having one node 6 fold lines arranged in
(D07) The node is defined as the origin O, the X axis is taken in the direction of the extension of the first valley fold line, and the angles formed by the first fold fold line and the second fold fold line with the first valley fold line are respectively defined. α and β, the angles between the third mountain fold line and the fourth mountain fold line with the second valley fold line are γ and δ, respectively, and the angle between the X axis and the second valley fold line is θ and The plurality of fold lines formed so that β−α = δ−γ + θ. The structure with a folding line according to claim 14, comprising the following constituent requirements (D08) and (D09).
(D08) First mountain fold line, second mountain fold line, third mountain fold line, and fourth mountain fold line, and first valley fold formed between the first mountain fold line and the second mountain fold line And a second valley fold line disposed between the second fold line and the third fold line, wherein the fourth fold line is the first fold line and the third fold line A plurality of fold lines having one node and six fold lines disposed between the second fold line and the second mountain fold line,
(D09) The node is defined as the origin O, the X axis is taken in the direction of the extension of the fourth mountain fold line, and the angles formed by the first mountain fold line and the second mountain fold line with the first valley fold line are respectively defined. θ1 and θ2, angles formed by the second mountain fold line and the third mountain fold line with the second valley fold line are respectively θ3 and θ4, and an angle formed between the X axis and the first mountain fold line is α ^*. The plurality of fold lines formed so that α ^* = θ2 + θ4 and β ^* = θ1 + θ3, where β ^* is the angle between the X axis and the third mountain fold line. A structure with a fold line, comprising the following constituent requirements (E01) to (E04):
(E01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of each part to each other and that can be folded along the linear part connection part is provided. A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A structure with a fold line having:
(E02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is two. The plurality of fold lines formed in;
(E03) The structure with a fold line formed of a sheet-like member having a fold line formed along a spiral (E04) The fold line has a circular sheet shape in a state where the fold line is extended, and a mountain fold line of the fold line And in the state of being bent in accordance with the valley fold line, the outer shape is a disk shape having unevenness reduced, and in the state of being completely folded along the mountain fold line and the valley fold line, the outer shape is further reduced in unevenness. The structure with a fold line having a shape having: A mold for forming a fold line, comprising the following constituent requirements (F01) and (F02):
(F01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of each part to each other and that can be folded along the linear part connection part is A pair of fold line forming members provided, wherein the fold line includes a plurality of mountain fold lines where one surface side forms a mountain fold and one or more valley fold lines which form a valley fold when viewed from one surface side of the fold linear molding. A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at a predetermined interval, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is 2. A pair of fold line forming members having the plurality of fold lines formed as described above,
(F02) A folded linear molded connecting member that movably supports or connects the pair of folding line forming members between an overlapped state and an open state. A folding line forming method characterized by comprising the following constituent requirements (G01) and (G02):
(G01) A linear fold line that has a plurality of polygonal parts and a linear part connection part that connects outer sides of each part to each other and that can be folded along the linear part connection part is provided. A fold line structure provided, wherein the fold line is a plurality of mountain fold lines where the one surface side is a mountain fold and one or more valley fold lines that are a valley fold when viewed from one surface side of the fold line structure. A plurality of nodes that are intersections of the mountain fold line and the valley fold line are arranged at predetermined intervals, and the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is 2 A sheet-like member sandwiching step of sandwiching a foldable integral-structure sheet-like member between a pair of fold line forming members having the plurality of fold lines formed as described above.
(G02) a fold line forming step of simultaneously folding the pair of fold line forming members sandwiching the sheet member along the mountain fold line and the valley fold line to form a fold line in the sheet member.

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