WO2001081821A1

WO2001081821A1 - Structure with folding lines, folding line forming mold, and folding line forming method

Info

Publication number: WO2001081821A1
Application number: PCT/JP2000/007348
Authority: WO
Inventors: Taketoshi Nojima
Original assignee: Taketoshi Nojima
Priority date: 2000-04-20
Filing date: 2000-10-20
Publication date: 2001-11-01
Also published as: JPWO2001081821A1; WO2001081821A9; JP3824540B2

Abstract

A structure (PET bottle, for example) (A) with folding lines, having a plurality of polygonal parts (P) and linear part-connectors for mutually connecting the outer sides of respective parts (P), with foldable linear folding lines (M, V) provided along the linear part-connectors, wherein the folding lines (M, V) consist of a plurality of ridged folding lines (M) ridge-folded at one surface side of the structure when viewed from the one surface side and more than one furrowed folding lines (V), with respective folding lines satisfying folding requirements. A novel folding method, wherein a wall-shaped structure is divided into polygonal planar parts (P) by many folding lines, and folding lines (M, V) at boundary portions between respective planar parts are mad foldable; and a novel folding line forming mold and a folding line forming method.

Description

Description Folded line structure, fold line forming die, and fold line forming method

TECHNICAL FIELD The present invention relates to a structure with a fold line, a mold for forming a fold line, and a method for forming a fold line, which can be folded between a folded state in which the outer shape becomes smaller and an expanded state in which the outer shape becomes larger. 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. The present invention relates to a folding structure with a folding line, wherein a folding line at a boundary portion of the folding line can be folded.

INDUSTRIAL APPLICABILITY The present invention is applicable to a plate-shaped object with a fold line and a cylindrical object and a cone-shaped object with a fold line that can be folded in the axial direction. For example, plate members such as a rigid floor or bottom wall, It can be used for various containers with cylindrical walls such as pet bottles, objects with conical walls such as lamp shades, outer space structures, and architectural structures. Background Art Research on the development of folding and deployable structures is technically related to the construction of antennas and solar cell structures for deployment in outer space, or, conversely, to the study of plastic buckling using the folding method. Evolved. In addition, these studies have also been applied to research aimed at elucidating the growth and motor functions of living things, such as the mechanism of folding of insect wings and leaves.

2. Description of the Related Art 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 fold structure having a foldable fold line is known. The thing is not known conventionally.

The conventional foldable structures with foldable lines are mainly the development of space structures. The following technologies (J01) and (J 02) are known.

(J 01) Planar folding structure

As the planar folded structure, Miu a a r i r using the origami fold line

(Refer to the concept of a deployed space structure [Kiyo Miura, Journal of the Japan Society of Mechanical Engineers, Vol. 90, No. 828, published in January, 1987, P1394-140]) Conventionally known. Miuraori divides a planar structure into a number of parallelograms formed by fold lines, and has a flat plate shape with an expanded outer shape when the fold line is extended, and a reduced outer shape when folded. Moreover, it becomes a flat plate shape having unevenness with an increased thickness.

(J 02) 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 Considerat ions (S. D. Guest, S. Pel legrio, Journal of Ap lied Mechanics, DECEMBER 199 4, Vol. 61/773 ~ 777)

(b) The Folding of Triangulated Cylinders, Part II: The Folding Process (S. D. Guest, S. Pellegrio, Journal of Applied Mechanics, DECEMBER 1994, Vo

(1.61 / 778 ~ 783)

(c) The Folding of Triangulated Cylinders, Part III: Experiments (S.D.Guest, S. Pellegrio, Journal of Applied Mechanics, MARCH 1996, Vol. 63 / 77〜83)

The documents (a) to (c) by SD Guest, S. Pellegrio et al. Disclose that a cylindrical wall is divided into a number of triangular plate walls by a number of folding lines including a folding line formed along a spiral. It is described that a foldable cylindrical wall can be formed by connecting the boundary portions of the triangular plate walls in a foldable manner. In addition, in the above-mentioned 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 lengths of the sides of the triangle indicated by the numerical calculations, 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) have extended fold lines. When unfolded, it becomes a cylinder, and when folded, it becomes a cylinder that contracts in the axial direction.

(Problems of conventional technology)

In the above-mentioned conventional planar folding structure and cylindrical folding structure, the condition of the folding line that can be folded is not known, so the used folding line 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 plate wall formed by the fold line has a base angle of about 3 degrees. It is only a triangle similar to a 0 ° isosceles triangle.

In such a narrow range that is empirically known, even if the research on the use of the folded structure such as the planar folded structure and the cylindrical folded structure is performed, a new folding line of the folded structure is obtained. It seems that it is not easy to find and find folding structures using new folding lines.

The inventor of the present invention has found that if the conditions for the foldable fold line of a fold line formed with a fold line become clear, the discovery of a new method of folding the fold structure, and the invention and use of a new fold structure will become necessary. I thought it would be easier.

Therefore, the present inventor conducted a study (a study of 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.

In addition, research on folding structures that can be folded along conventional folding lines is often performed using origami models that use origami, but folding lines that can be folded are complex. Therefore, it takes time to form a foldable fold line. In particular, it takes time to form a fold line on a sheet that is more rigid 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.

The following is a description of what was learned from the study of the folding method described above. (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 folding line of a sheet-like member.

(A) The plane wall and the quasi-cylindrical wall and the conical wall formed by a large number of divided plane walls are formed by a large number of divided plane walls of a predetermined shape divided by a large number of linear folding lines. be able to. 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 folding line is a shape which has been studied in the past (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) The plate with the folding line is half-folded or completely folded with the sheet-like member sandwiched by two plates with the same folding line that can be folded, thereby easily folding the sheet-like member. It is possible to form lines.

Next, the details of the research results are explained.

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 discuss a foldable cylindrical structural model. After the description, the folding performance of a cylinder manufactured using a polymer sheet is described.

In addition, a model for fabricating a foldable conical structure, which has not been reported so far, was geometrically determined using the concept of origami, and then these models were developed by combining equiangular spirals. Analytically clarify that the figure is represented.

(1) Flat folding structure with fold lines

1. How to fold

FIG. 1 is a fold line explanatory diagram showing a typical 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, the fold lines formed by mountain folds are represented by solid lines (Ml, M2, M3), and the valley fold lines are represented by broken lines (VI). The number of mountain folds and valley fold lines joining the nodes is NM, respectively. , NV . It is well known that the following equation holds between NM and NV at a node.

I NM- NV I = 2 (1) If NT is set as the total number of folding lines, then NT = NM + NV. Equation (1) is converted to, for example, NM—NV

= 2 and NT = 2 (1 + NV), which means that the number of fold lines that make up 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 (Ml) and (M2) are performed, a valley fold (VI) occurs. If the angle between the mountain fold (Ml), (M2) and the X axis is α,) 3, the angle between the fold line (VI) and (Μ2) is

It is given by 7 ~ a (2). Equation (2) is the relational expression of the angle when completely folded along the fold lines (1) to (4) in the Y-axis direction.

By this operation, the strip of paper is folded in half, and the axial direction to the right of the node is folded by 2α (when o is β) or 2; 8 (when α> ι8).

When α = 8, the axial direction is not bent in the 折り -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 becomes a Μ shape when the mountain fold (or the valley fold) is continuously performed.

In this 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 a method of folding to produce a cylindrical structure that can be folded in the same direction and folded in the Y-axis direction. Is roughly divided into "cylindrical cage".

2 flat fold

2.1 Miura aori (prior art)

To consider the possibility of structure construction, consider the simplest case of "one-node four-fold line".

Figure 2 is an illustration of the folding structure called "Miuraror ', which was devised by Miura for deployment of space structures.

In FIG. 2, the folding line of the folding structure is composed of three horizontal folding lines ((1) to (3)) and three zigzag folding lines (mountain, valley, mountain fold line, (4; ) To (6)). In folding lines (1) to (3), mountain folds and valley folds are alternately performed so that the expression (1) is satisfied. 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 figure, and the node can be completely folded in the Υ-axis direction in the figure.

At this time, it also contracts in the X-axis direction depending on the angle α, and the amount of contraction 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 on the left and right of the node. This characteristic of the 4-fold line method makes it possible to fold flat paper periodically from Υ = + ∞ to 10∞. FIG. 3 is a diagram in which the horizontal fold lines shown in FIG. 2 are zigzag at equal angles.

In FIG. 2, at each node, the fold lines (4) to (6) are symmetrical to the horizontal fold lines (1) to (3). Even if the zigzag operation is performed, the folding condition in the 方向 -axis direction in Equation (2) is satisfied, and the flat paper in FIG. 3 is completely folded in a new shape. When this fold is made into a half-folded state, it is possible to make the flat paper three-dimensional, that is, to have an "apparent" thickness, and it is possible to produce a highly rigid and lightweight flat plate.

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 or disk can be folded in the radial direction.

Fig. 4 is a diagram showing an example of a foldable line of a part (sector-shaped part) of a disk formed by six sector-shaped elements having a vertex angle of 26).

In FIG. 4, the circumferential folding lines (1) to (5) are bent by 2®. The radial fold lines (7), (8), (9) ... are provided zigzag within the angle Θ, and the outer sides A, B, C ... make an angle αθ with the outer side.

At this time, since the angle / 3 in FIG. 4 is αΟ + Θ due to the periodicity of these fold lines, the angle α の between the circumferential fold line (1) and the radial fold line is α Taking _ Θ satisfies the folding conditional expression (2). In other words, 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- 2 Θ…, the folding condition is satisfied at all the nodes, It is possible to draw an exploded view that can fold the plate in the radial direction.

In addition, like the fan-shaped plate, a circular plate is also developed in a development view that can be folded in the radial direction. can do.

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 to the fold lines (1) to (6) at all nodes. FIG. 3 is a diagram plotted symmetrically. As shown in Fig. 5, when the fold lines (7) to (9) are plotted at all nodes at equal angles and symmetrically with respect to the fold lines (1;) to (6), the folding condition is satisfied at each node. It can be folded in the Y-axis direction.

Here, α 1 and β 1 (initial values) can be freely selected.

FIG. 6 is a diagram showing an example of a folding line taking into account the periodicity of the folding method of FIG.

In FIG. 6, horizontal fold lines (1) to (6) indicate a fold line group having micro-squares 0 alternately with the horizontal direction. The zigzag of the vertical fold lines (7), (8),… becomes more pronounced downward.

FIG. 7 is a diagram 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 the 6-fold line method and the 4-fold line method of symmetrical fold lines are combined with the horizontal fold line, flat paper can be folded in a zigzag manner as in Miuraori shown in Fig. 2. .

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, in the case of one node and six fold lines, there is a combination in which two valley fold lines are inserted at symmetrical positions of four mountain fold lines. The angle relationship that satisfies the folding condition in the folding method frequently used in this specification is shown below.

The mountain fold line is (Ml), (M2), (M3), (M4), the valley fold line is (VI), (V2), and the extension of the fold line (VI) is the X axis. The angle between (Ml) and (VI), (M2) and (VI) is α, β, the angle between (Μ3) and (V2), the angle between (M4) and (V2) is α, and <5 Assuming that the angle between, (V2) and the X axis is 0, the folding condition is expressed by the following equation (3).

β-= δ-τ + θ (3) The following expression (3) holds that the expression (3) holds, which is proved as follows using the expression (4) described later. In the case of the 6-fold line method shown in Fig. 8, the conditions for folding in the Y-axis direction at node A are derived. Take the X-Y axis as shown in the figure with node A as the origin. Pl, p2, 3, the angle between the fold lines (Ml), (VI), (M2) and the vertical line (P) to the X axis, the vertical line (Q) and the fold lines (M4), (V2), ( M3) is Q1, a2, d3, ΐ1 = π / 2_α, ρ2 = π / 2, ρ3 = c / 2 + j8, α1 = π2 + (5 + 6> , Q 2 = π / 2 + θ, <ι3 = πΖ2 ー + 0

The vector pointing in the same direction based on the symmetric position (points 軸, Β) of the X axis in the region of X by the mountain fold (Ml), (Μ2), and valley fold (VI) is given by equation (4). If used, it forms an angle of PL = (-+ β + π / 2) after folding.

In the region of Χ> 0, the vector in the same direction from the points C and D is folded by mountain fold (Μ3), (Μ4), and ぴ valley fold (V2), and then QR = (δ-θ -Ύ + π 2). The points A and C and the points B and D are on the same plane, and these vectors point in the same direction. Therefore, if PL QR is put, equation (3) is obtained.

When (V2) matches the X axis, 0 = 0 and the following equation (3 ') holds.

β-a = δ-r (3 ')

In the case of the 6-fold line method, a mountain fold (or valley fold) is always formed on both sides of the center node. By repeating this folding method, the paper 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 6-fold line method, it is indispensable to combine this folding line method with the preceding 4-fold line method (see Fig. 2) (see Fig. 7).

(2) Cylindrical folding structure with folding lines

It is easy to guess that a continuous folding of a mountain at equal angles can produce a cylinder that can be folded vertically. In the following, we will consider making a foldable cylinder by such an operation.

1. Strips with expanded cylinders

Fig. 9 is a diagram for explaining the conditions in which both ends of the band plate are joined to form a cylinder when the band plate is folded along the fold line, and Fig. 9 Α shows the angle between the band plate, the fold line and the fold 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. As shown in Fig. 9A, consider the case where the strip is folded alternately between mountain folds and valleys, or when diffracting N in the same direction (N: even number). The angles between the N fold lines (1), (2),… and the X axis are S1, Θ2,-·, 0n, and the axis directions after the fold are XI, X2… I do. By the first folding operation (folding line (1)), the right side of (1) becomes the back side.

With this operation, the new axis (XI) is at an angle of 201 = ®2 with the X0 axis (see Figure 9B). When the second fold is performed at the fold line (2), the X2 axis makes an angle © 2 = 2 01—202 with the reference axis X0. By folding (3), the X3 axis becomes an angle of X0 and ®3 = 2 (θ1−Θ2 + 6> 3). By these series of folding operations, the front and back sides appear alternately, and by the folding operation N times, the angle ON (when N = even number) that the XN axis forms with the reference axis is expressed by the following equation.

ΘΝ = 2 {θ 1- Θ 2+ Θ 3 (4) When this strip is folded, the left and right edges of the strip are joined without any gap (closed). Then, it is given by the following equation (5).

ΘΝΖ 2 pit = η (5) Next, an example in which the left and right ends of the band strip folded so as to satisfy the above expression (5) will be described with reference to FIGS. 10 to 12 will be described.

FIG. 10 is an explanatory view of an example in which the above-mentioned expression (5) is satisfied and the folding direction is the same as the folding direction (either mountain fold or valley fold). Figure 10B shows the folded state of the strip in the folded state, (1), (2), (3), and (4), Figure 10B shows the state during folding, and Figure 10C shows the folded state. FIG.

Folding lines (1), (2), (3), (3), (1), (2), (3) 4) make an angle of 6 »1, Θ 2, Θ 3, 6 * 4 with respect to the X axis, 6» 1 = 6> 3 = 1 35 °, 6 »2 = 04 = 45 ° It is. 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 side of the fold line (1) of the X axis is the Χ0 axis, and the right X axis portion of each fold line (η) when η == 1, 2, 3, 4 is the X η axis (η = 1 to 4).

In Fig. 10 C, the angle between axis が 2 and axis Χ0 Θ2 is © 2 = 2 (Θ 1 ~ Θ 2) = 2 (1 35 ° — 45 °) = 2 X 90 ° = 1 800 ° = π. Also, the angle す 4 that the axis X4 makes with the axis X0 is ®4 = 2 (θ 1- Θ 2+ Θ 3- Θ 4) = 2 (1 35 ° — 45 ° + 1 35 ° — 45 °) = 2π. Therefore, η in the above equation (5) is η = (Θ4Ζ2π) = 1, and the axis Χ4 overlaps with the axis Χ0. 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 above formula (5) is satisfied and the folding direction is a regular hexagonal folding line along the folding line in the same direction (either mountain fold or valley fold), and FIG. Figure 1B shows the folded lines (1), (2), (3), (4), (5), and (6) of the folded strip, FIG. FIG. 1C is a view showing a folded state. In Fig. 11A, the fold lines (1) to (6) of the strip extending in the X-axis direction, which is the reference axis, in the same direction form angles 6> 1 to 6> 6 with respect to the X-axis. 6 * 1 = 6 * 3 = 6 »5 = 13 35 °, 02 = 04 = 06 = 45 °. That is, the fold lines (1) to (6) are formed zigzag at 30 ° (= πΖ6) with respect to the X axis.

In Fig. 11, the angle Θ6 between the axis X6 and the axis X0 は 6 is 26 = 2 (θ 1- Θ 2+ Θ 3- Θ 4 + 05-06) = 2 (1 50 ° — 30 ° + 150 °) — 30 ° + 150 ° — 30 °) = 2 Χ 2π. Therefore, η in the above equation (5) is η = (®6Ζ2π) = 2, and the axis Χ6 overlaps the axis Χ0. 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 formula (5) is satisfied and the folding direction is folded in a regular octagon by a folding line in the same direction. FIG. , (2),..., (8), FIG. 12Β is a diagram showing a state of being folded, and FIG. 12C is a diagram showing a state of being folded.

In Fig. 12 (2), the fold lines (1) to (8) of the strip extending in the X-axis direction, which is the reference axis, are bent in the same direction at angles 6 to 1 to 6 to the X-axis, respectively. 01 = 03 = 6 »5 = 6 * 7 = 1 57.5 °, 6> 2 = 04 = 6> 6 = 6> 8 = 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 formed by the axis X8 with the axis Χ0 Θ 8 is 6) 8 = 2 (6 »1-6 → 2 + 03-04 + Θ 5- Θ Q + Θ 7-Θ 8) = 2 (1 57.5 ° — 22.5 ° + — + 1 57.5 °-22.5 °) = 3Χ2π Therefore, η in the above equation (5) is η = (Θ8 / 2π) = 3, and axis Χ8 overlaps with axis Χ0 In this case, both ends of the strip are joined without any gap. It is.

From the description of FIG. 10 to FIG. 12, the band plate is folded in the same direction by the folding line in the same folding direction (either mountain fold or valley fold) to form a regular N-gon (N is an even number). It can be seen that when folding, zigzag fold lines (1), (2),..., (N) at an angle of 0 = π / Ν with respect to the reference axis X should be formed at equal intervals.

FIG. 13 is an explanatory view of an example in which the above formula (5) is satisfied and the folding direction is alternately reversed (reversed in the mountain fold direction and the valley fold direction). Α shows the folded lines (1) to (12) of the unfolded strip, FIG. 13B to FIG. 13F show the folded state, and FIG. 13G shows the folded state. In Fig. 13A, the fold lines (1), (3),..., Shown by solid lines, are folded in the same direction (for example, the mountain fold direction) of the strip extending in the X-axis direction, which is the reference axis. (11) has angles 6> 1, 6 »3,..., 011 with respect to the X axis, respectively, where 01 = 6/3 = — = 011 = 60 °. Also, fold lines (2), (4),... Shown by dotted lines that are folded in the opposite direction (for example, the valley fold direction) from the fold lines (1), (3),. ·, (12) make angles 02, Θ 4, ···, 012 with respect to the X axis, respectively, and 02 = 04 = ^ ·· = 012 = 30 °.

The imaginary line (13) shown in FIG. 13 is a line overlapping the fold line (1) when the band plate is folded.

In Fig. 13, the angle 実 12 that the axis X12 forms with the axis X0 as a solid line is © 12 = 2 (θ 1-Θ 2 + Θ 3—— + Θ 12) = 2 (60 ° — 30 ° + 60 °) — + 60 ° — 30 °)

= 2 Χ π. Therefore, η in the above equation (5) is η = (012 / 2π) = 1, and the axis X12 overlaps the axis Χ0. In this case, both ends of the strip are joined without any gap. 2. A cylinder with a fold line whose main fold line is a horizontal fold line group

Consider the upper and lower ends of the strip of paper (Fig. 9 Α) as horizontal fold lines, and ΥAssume some of these steps in the axial direction. The parallel horizontal fold lines (group) are named main fold lines.

The main fold line using the 4-fold line method and the 6-fold line method is composed of a group of horizontal fold lines. ΥFigures 1-4 to 1 show the development of a model for manufacturing a cylinder that can be folded in the axial direction. Figure 6 shows the results.

When manufacturing a cylinder that is folded in a square cross-section by the 1-node 4-fold line method, As is well known (as can be seen from the description of FIGS. 9A and 9B), a square plate can be formed by bending a band-shaped plate in the same direction at equal intervals of π · (Ν−2) ΖΝ. Here, π · (Ν−2) ΖΝ is the size of the interior angle of a regular square.

Fig. 14 shows a typical case where the strip-shaped plate shown in Fig. 9 折り is bent in the same direction at equal intervals by τΓ · (Ν-2) / を to form a square and Ν = 6. It is a figure which shows a development view.

Here, in consideration of the fact that the folding is performed by 20 when the folding angle is で in the above equation (4), the six zigzag mountain fold lines (1) to (6) that form an angle of 6 with the horizontal folding line are considered. ) Are introduced at equal intervals. At each mountain fold line, ττΖ3 is bent at a time, and finally a cylindrical structure that is folded in a hexagonal cross section is manufactured.

Fig. 15 is composed of trapezoidal elements with unequal sides by decomposing twice (ττΖ3) the angle between the mountain fold line and the horizontal fold line in Fig. 14 as α = 2πΖ9 and 0 = πΖ9. FIG.

In the case of folding into a regular hexagon, the division of the angle can be arbitrarily selected as long as the sum is CZ 3.

Fig. 16 shows the introduction of six sets of fold lines obtained by decomposing the mountain fold line in the Y-axis direction in Fig. 14 into a mountain fold line I of α = πΖ3 and a valley fold line II of β = π / 6. Fig. 16A is an exploded view of the cylinder produced according to Fig. 16A. Fig. 16A shows the half-folded state of the folded cylinder produced when both ends of the exploded view of Fig. 16A are joined. FIG. 16C is a perspective view of the same thing as FIG.

Fig. 16 A (Here, — As long as j3 = 7cZ6, the value of α can be freely selected.

Fig. 17 is a diagram in which points Α and の in Fig. 14 are matched and the mountain fold is removed from the horizontal fold line. The diamond pattern consisting of an isosceles triangle with a base angle of π / 6 in the horizontal direction (( It is a development view of 1) to (3)).

At this time, the cross-sectional shape at the horizontal fold line becomes an equilateral triangle, which corresponds to the diammond buckling model in the plastic buckling of a thin-walled cylinder.

Figure 18 is a developed view of a deformed diamond pattern composed of scalene triangular elements. FIG. 19 is an explanatory view of a pseudo-cylindrical body having a development view that is symmetrical and foldable one by one with respect to a horizontal folding line, FIG. 19A is a development view, and FIG. FIG. 19C is a view showing a half-folded state of a folding cylinder manufactured when both ends of the exploded view of FIG. 9 are joined, and FIG. 19C is a view of the same thing as FIG. The five types of developed views shown in FIGS. 14 to 17 are applicable to all horizontal folding lines, but the developed views shown in FIG. 19 can also be folded.

In FIG. 19, at the point A, the folding condition expression, the expression (3) is satisfied because of its symmetry, but the expression (3) is also satisfied at the point B.

FIG. 20 is a view showing an example of a developed view of the folding constituted only by the folding line similar to the point B in FIG.

FIG. 21 is a developed 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 foldable cylindrical body having a plurality of polygonal parts.

3-cylinder with fold line if the main fold line has a slope (spiral type)

Consider a case where the horizontal fold lines in FIGS. 14 to 21 are inclined.

In the above-mentioned documents (a) to (c), Guest et al. Considered a cylinder formed by a triangular divided flat plate, and was able to manufacture a cylindrical folded structure. The appropriate shape of the triangle was examined by numerical calculation. Fig. 22 shows the case where the connecting part of the divided flat plate made of the triangular split plate examined by Guest et al. Becomes spiral, and the spiral (1) rises one step each time it makes a round. The present inventor has shown a cylindrical structure in a developed view. They analyzed the characteristics of the cylinder shown in the expanded view in Fig. 22 when folded, using the angles (α, β) between the spirals as variables, but did not show the complete folding condition. I couldn't do it.

Fig. 23 corresponds to Fig. 17 in which the whole of Fig. 17 is inclined by = = π / 6, and three diamond patterns in the diagonal direction are configured, and the deployment of a foldable cylindrical structure FIG.

FIG. 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 both ends of the development views of FIG. 23 and FIG. 24A. When joined 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 k having a development view obtained by inclining FIG. 14/6, FIG. 25A is a development view, and FIG. 25B is an end view of the development view of FIG. 25A. It is a figure which shows the half-fold state of the folding cylinder manufactured at the time of joining.

FIG. 25A corresponds to a diagram in which FIG. 14 is cut along a horizontal line and a straight line GH inclined by πΖ6, and the cut line is 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 πΖ6. FIG. 26Α is a development view, and FIG. 26 6 is both ends of the development view of FIG. 26Α. FIG. 6 is a view showing a half-folded state of a folding cylinder manufactured when the two are joined.

FIG. 27 is a developed view in which FIG. 16 is inclined by πΖ6.

In the examples shown in Fig. 25 to Fig. 27, when the left end L and the right end R of the developed view are joined to form a cylinder, the pattern of the folding lines is generally not continuous. Details of the continuity of the development diagram will be described later.

Fig. 28 is the spiral type shown in Fig. 19, which is obtained by cutting along the straight line connecting points A and D in the figure. The angle (~ 0.193 volt) shown in Fig. 28 indicates the angle between this 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. Will be done.

FIG. 29 is an explanatory view of a spiral folding cylinder having a folding line, which is a generalized version of FIG. 24. FIG. 29Α is an expanded view, and FIG. 29B is an expanded view of FIG. 29A. It is a figure which shows the half-folded state of the folding cylinder manufactured when both ends are joined.

The folding condition does not depend on the value of 3 in Fig. 29A (see below).

FIG. 30 is a developed view in the case where the value of (3) is changed for each of the six developed steps shown in FIG.

As shown in Fig. 30, even if the value of) 3 is set independently for each stage, the folding condition can be satisfied.

Fig. 31 is a development view of the repetitive spiral type obtained by reversing the spiral mountain fold line and valley fold line of Fig. 29 2 for each stage. This development also matches points Α and の in Figure 16 Can also be obtained.

FIG. 32 is a view showing a portion cut by two parallel straight lines AB ′, C ′ D in the developed view of the cylindrical body shown in FIG. 21, wherein A and B ′ and D and C ′ are FIG. 32 is a development view of a foldable cylinder formed by connecting the left and right edges of FIG. 32 so as to overlap.

The cylindrical wall having the developed view shown in Fig. 32 can create a foldable cylindrical body having a plurality of polygonal parts.

Figure 33 is a developed view of a collapsible cylinder having a quadrangular element (part) of arbitrary shape.

In FIG. 33, when a straight line extending AF is assumed to be A E, the folding condition is Z B A E = ZD A C = Q !. The value of α can be arbitrarily determined as α = 180 ° / Ν (Ν is a positive integer). For example, when Ν = 8, α = 1800 ° / 8 = 22.5 °. Therefore, by setting ZBAE = ZDAC = a = 22.5 ° and setting the length of AE to an appropriate value, a foldable cylindrical body having a part of an arbitrary shape 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 line is not always satisfied at both ends of the development. When a development diagram is given with a trapezoidal element as in the case of Fig. 25 to Fig. 27, continuity can be maintained by properly selecting the upper base length Lu of the trapezoid in Fig. 14. it can.

FIG. 34 is an explanatory diagram of a method for maintaining continuity when both ends of the developed view are joined. In Fig. 34, N trapezoidal elements are drawn in the direction of the main fold line (angle) starting from the origin O, and point A is determined. Assuming that the height of the trapezoid is h, the length O A = N {

(h / t a η Θ) + Lu}. Draw m (even number) elements below the Nth trapezoidal element, and set point B as shown in the figure. In order for the development to be continuous for any given point, point B must be on the X-axis. Since A B = mh, the following expression (6) is obtained from t an -O AZO B.

Lu = {2 N— m · tan / / tan Θ} h / tan? /) (6) In other words, if Lu is properly determined by equation (6), the left and right ends of the development diagram in these cases Is obtained.

5. Verification of folding condition of cylinder with fold line

A typical example verifies whether the condition for closing in the circumferential direction (see equation (5)) is satisfied when the cylinder having the folding line described above is folded.

In the cylinder given in Fig. 25, consider the fold line of the strip (minimum width D) at the lowermost end of this development. There are 18 fold lines here, and the fold lines with the same inclination appear repeatedly every 6 lines from the left side, so they are composed of three sets of 6 fold lines. Using equation (4), the angle of rotation of the axis by these fold lines is given by 傾斜 (= π / 6) as the inclination angle.

ΘΝ = 2 {(α + Y) — Y + Y — Y + (+ Φ) — Y} X 3 = 1 2 α ... (7) Since α = πΖ6, Θ と = 2π in equation (4), which satisfies equation (5). Thus, it can be seen that the condition for closing is satisfied after folding.

In the case of Fig. 29 (9), the following equation is obtained by considering the rotation angles of the lowermost six parallelograms by the folding lines.

ΘΤ = 2 {(+ β)-β} X 6 = 1 2 α (8) If α = π / "6, then 条件 = 2 π and the closing condition (see equation (5)) is satisfied. As can be seen from Eq. (8), ΘΤ does not depend on the ternary value, that is, in the models of Figs. 29 to 31, the condition for folding into a square shape is α = π Ζ Ν. The angle in the figure; 8 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 of the valley fold line was set to π / Ν. However, as can be seen in the example in Fig. 25, the inclination angle of the main folding line is not limited to れば as long as the continuity of the developed view can be satisfied.

6. Fabrication of foldable pseudo cylinder

The present inventor 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 confirmed that this was possible. When the helical folding model shown in Fig. 25 and Fig. 27 is pressed by the material testing machine, the upper part of the cylinder is folded while rotating at the lower part stopped. The results of observing the progress of the folding show that the proposed model allows good folding, and that the load required for complete folding is extremely low, 20 to 4 ON. (Diameter of the cylinder before folding; about 100 mm).

7. Summary of Research on Cylindrical Body with Folded Line

In the above explanation, taking the example of N = 6 (—part N = 3,8), manufacturing a pseudo cylinder that divides the developed view into triangular elements, trapezoidal elements, or quadrangular shapes of arbitrary shape and folds it into a regular N-gon shape The law was explained. Unless the main fold line, which is difficult to satisfy the continuity at the left and right edges of the developed view, is composed of an odd number of trapezoidal elements, the fold angle at one node is (N-2) ΖΝ By doing so, it is possible to produce a folded structure for any Ν value (Ν≥3, integer).

If the angle of the fold line is selected so as to satisfy Equation (5), and the length of the fold line is appropriately selected, it is also possible to manufacture a fold structure that is not a square shape.

When a cylinder is made of a thin polymer sheet, it seems easy to mold it into the shape shown in Figure 16Β and Figure 24Β. Therefore, if molding is performed in such a shape, it is thought that it is possible to produce a foldable container like a potter.

When the valley fold line forms a spiral shape, expansion and contraction in the axial direction was generally easier than that of the horizontal type. This seems to need to be considered in improving the folding structure.

(3) Conical folding structure with folding line

1. Basic relations for folding

Figure 35 shows the angular relationship between the folding lines that are folded at these nodes when the conical wall that constitutes the foldable conical folding structure with folding lines has one contact, six folding lines, and one node and four folding lines. To Figure 37.

Fig. 35 shows the angular relationship between the fold lines satisfying the folding condition when the valley fold line is symmetrically inserted in the case of 1 node and 6 fold lines, in the case of Figs. 50 to 52 described later. FIG. 4 is an explanatory diagram of folding conditions.

If the angle between the inserted valley fold line is 0 and the angle α; ~ <5 as shown in Fig. 35, the following equation is obtained. (3) holds.

β-= δ-γ + θ (3) Figure 36 shows the case where the valley fold lines (Vl) and (V2) are inserted alternately between the mountain fold lines (Ml), (Μ2), and (Μ3). FIG. 9 is a diagram showing an angle relationship between folding lines satisfying folding conditions, and is an explanatory diagram of folding conditions in the case of FIGS. 56B and 57 described later.

In Figure 36, the angles between the X axis, which is an extension of the mountain fold line (M4), and (Ml) and (M3) are α * and 0 *, respectively, and the angle between each fold line is 0 □ _-04 And Take the X axis as the origin, with node 3 as the origin, as shown in Figure 36.

The conditions for folding in the Υ axis direction at node Ο are derived in the same manner as described above. In the region of X 0, the vector in the same direction at the symmetric position of the X axis (points B and C) rotates by the angle π (= Q _Z ) after folding by mountain fold (Μ4). Turn in the opposite direction.

Next, consider the vectors at points D and E in the region where X> 0. If the angle between the perpendicular (Q) to the X axis and the fold line (Ml), (VI), (M2), (V2), (M3) is QQ _s as shown in Figure 36, then q ι = T / 2 + *,

2 = π / 2 + α * — θ ι,

α 3 = π / 2 + *-(θ + 6> ₂ ),

Q 4 = π Ζ 2— * +. The angle Q ₂ formed by these vectors by this folding is given by the following equation (9).

Q _2/2

= τπ / 2 + a *-(θ _ζ + θ) (9)

Even after folding, the points Β and D are on the same plane, and the vector at this point points in the same direction, so if the Q ₂ value and π in the negative region are equal,

θ _ζ + θ

Get.

a * + ø… + ø

With, β Q _{ι +} β ₃

Therefore, the folding condition in this case is expressed by the following equation (10).

Fig. 37 shows the case of a 1-node 4-fold line. The folding condition is obtained by the same procedure as above.

Because

Q 2 = Q = π

And put

α = τ.

That is, when the mountain fold line (Ml) to (Μ3) is given, a valley fold (VI) occurs at a position of a τ value equal to the angle α between the X axis which is an extension of (Μ3) and (Ml).

2. Folded conical wall whose main fold line is parallel to the outer edge of the development

FIG. 38 is an enlarged view of a main part of the developed view in the case where the developed view of a cone whose main folding line is parallel to the outer side of the developed view is composed of Ν isosceles triangles having a vertex angle of 2 °.

The valley fold line (dashed line) in Fig. 38 is called the main fold line. The vertex is 0, the points on the outer side are A, Β, C, and D. From these points, a straight line that forms an angle α with the outer side is plotted, and the intersection points are Ε, F, and G.

From the points から, F, and G, draw a line at an angle α with the line segments E F and FG in the same manner as above, and let their intersection points be Η and I. With this construction, the development is divided by two kinds of isosceles triangle elements. From the symmetry, Ο, Η, Β and なし, I, C form a straight line, and a symmetric diamond pattern is obtained on the left and right of the straight line ΟF. The straight line OF is perpendicular to the outer side BC. The folding lines that make up node F correspond to those in Figure 35.

Let ZCFG = ZBFE =) 3, and in consideration of the symmetry at the node F, set δ in Fig. 35 and ァ a to | 3. Since the angle between the valley fold lines E F and F G is 2 ®, if we put 0 = 2 式, the equation (1 0) becomes

J3-α = Θ (1 1). Since Δ〇 F Ε and FG FG are isosceles triangles with a vertex angle of 2 （(base angle π / 2 Θ), the following equation (1 2) is obtained if ZHFI = *. Τ * + 2 α =;-2 Θ (1 2)

When folded at the node F, the angle between the valley fold lines EF and FG becomes α2α. If it is folded in a square shape, the angle formed by the valley fold line is (Ν−2) ΖΝ · π, so the following equation (13) holds.

Τ *-2 α = (Ν-2) / Ν · π (1 3)

The α and 0 values satisfying the folding condition from the above equations (11) to (13) are given by the following equation (14).

α = π no 2 Ν — ® / 2, β = α + Θ = π / 2 Ν + @ / 2 (1 4)

Considering the case of Ν = 3, 2 Θ = TCZ6, α = π / 8 and β = 57C / 24 are obtained from the equation (14).

Fig. 39 is an explanatory diagram of a pseudo-cone wall having a development diagram of a pseudo-cone wall with a fold line obtained by using the values obtained by equation (14). Fig. 39A is a development diagram, and Fig. 39B is a development diagram. FIG. 39 is a perspective view of a half-folded state of the conical wall with a fold line having the developed view of FIG. 39A.

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, the points on the outer edge are A, B, C, D ..., and the line that forms an angle with the outer edge at each point is drawn on the upper right, and the line that forms the angle δ is drawn on the upper left. Be Ε, F, G (ZBOF = θ *). From these points, draw straight lines from the points EF and FG to the upper left at an angle α, and to the upper right at an angle δ, and let their intersections be Η and I.

Points Ο, Η, Β and Ο, I, C form a straight line. An asymmetric diamond pattern is obtained on the left and right of the straight line OF. Let ZBFE = / 9, ZCFGG = r, and let the intersection of EF and BC be J. AO BC and AO CD, ΔΟ EF and △ 〇 FG are isosceles triangles each having an apex angle of 2 °, and ZD C J = ZG F J = 2 ®, and ZO F J = ZO C J is obtained.

That is, the points O, F, C, and J are on the same circle, and ZCJF = ZFOC = 26>-. When attention is paid to ΔΒ F J, the following equation is obtained.

β-= 2 ®-θ * (1 5)

ZC FJ = _T — 2 得 obtained from the angular relation around point F can be obtained from the angular relation of AC FJ (5 = ZCFJ + (2 Θ-, the following equation (16) is obtained. Δ- End = 1 Θ * (1 6) Substituting 0 * of equation (16) into equation (15) and considering that the angle between the valley fold lines EF and FG is 2®, the following folding condition equation (1 Ί ') Be established. β-α = δ-τ + 2 Θ (1 7 ') As before, if ZH F 1 = a *, the angle between the valley fold lines EF and FG when folded at the node F is τ * _ ( α + <3). Considering the folding of a regular square, can this value be equal to (ΖΝ—2) ΖΝ · 兀, and obtained from the geometric relationship? Using (a + (5) = π-2 ®, the following folding condition (17) is obtained.

(+ δ) = π / Θ — Θ (17) If α and 5 that satisfy equation (17) are selected, a collapsible development diagram consisting of scalene triangular elements can be obtained.

Fig. 4 1 is an exploded view of a conical wall with a fold line when it is divided into a trapezoidal triangular element by a fold line, where Ν = 3, 2 ® = π / 9, α = π / 9, <5 = vit / 6 This is the development diagram (6> * = about 0.06888π).

FIG. 42 is a development view of a conical wall with a fold line when divided into a trapezoidal triangular element by a fold line having an angle α in the upper right and an angle δ in the upper left at the point F in FIG. 40. , a, and δ are developed views when the same values as in FIG. 41 are used.

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 resulting rectangle is a dashed parallelogram, with points F, I,… rotated about the center by an angle of 0 *. The folding condition at the node holds in the same way as 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. 38.

In Fig. 43, two straight lines (A C, B D) forming an angle α with A 点 from points A, 上の on the outer side are drawn symmetrically with respect to a straight line O I, and points C, D are determined so as to be the apex angle.

With ZDCE = r *, ZDCB = ZDCO + ZOCF, and ZDCO = TC "2 one φ * Ζ2, OCF = (π / 2-Θ) — When α is used, Γ * can be expressed by the following equation (18) Is done.

Γ * = π— (* / 2 + ® + a) (18)

Since line segment CF is a valley fold line, it is folded by folding at node C. The angle formed by the later mountain fold DC and 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 *-a = π-(* / 2 + Θ + 2) (1 9)

Considering the case of folding in a regular square, (Γ * _ 0!) And (Ν _ 2) / Ν · π are equalized, and the following equation (2 0 — 1) is obtained.

α = π / Ν-(* / 2 + Θ) / 2 (20-1)

Since ZHCF = 2 © and AB and CD are parallel, ZACCH = a, and β-ZACCF is expressed by the following equation (20—2).

β = + φ * ^ 2 + Θ

At the point / N + (φ2 + Θ) / 2 (20−2) point C, since ZACH = ZEAF = o ;, the conditional expression (17) for the folding is satisfied.

Fig. 44 shows a conical wall with a fold line, which is divided into equilateral trapezoids by a fold line and folded into a regular N pyramid, N = 6, φ * = π / 36, 2 Θ = fig / FIG. 44 is an explanatory view of a pseudo-conical wall having an exploded view in the case of 2, wherein FIG. 44 展開 is a developed view, and FIG. 44 Β is a half-folded conical wall with a fold line having the developed view of FIG. 44 前記. It is a perspective view of the state which carried out.

3. Folded conical wall whose main fold line is spiral

In Section 2 above, when the cone is formed, the development view in which the valley fold line is parallel to the bottom surface has been described. Here, we consider folding when the valley fold line, which is the main fold line, becomes spiral.

Fig. 45 shows the development of a conical wall with a folding line consisting of N isosceles triangular elements (vertical angle 2Θ), with only one step drawn out as a curved strip.

Here, it is assumed that mountain folds and valley folds are introduced periodically, and the angle between the fold line and the outer side A B,… is 77, 77 (0 ≤ (ζ, 77) ≤% / 2).

When this strip is bent at these fold lines, it will bend in the circumferential direction by = 2 (ζ-77) Ν. Originally, this strip was bent at an angle of 2 °, so that after folding, the ends of this strip should be joined without gaps so that φ + yu = 2π must be established. This corresponds to the circumferential folding condition, which is expressed by the following equation (21). φ + ip = 2 (ζ-7? + Θ) N = 27 C (2 1) Fig. 46 shows a polygonal conical wall with a simple helical development of three isosceles triangular elements. FIG. FIG. 47 is a top view when the developed view of FIG. 46 is folded.

In Figure 46, three radiations () to (3)) and a group of lines ((4), (5) —) parallel to the outer edge are mountain fold lines. The valley fold line forms the corner ο: with the outside. Considering that the angles β to δ in Fig. 46 are isosceles triangular elements (vertical angle 2Θ), the following equation holds.

β = π 2 + Θ-a = dash / 2 + Θ +

δ = π / 2 — Θ— α

The valley fold line that forms the spiral bends 2 ® every time it passes through one triangular element. Put 0 = 2Θ in the folding condition (1 7) 0! Substituting ~ δ, it can be seen that equation (17) holds for any α.

The α value is obtained under the condition of closing in the circumferential direction after folding, and when folding in a square shape, use ζ = α, 77 = πΖ 2— Θ in equation (2 1) and the following equation (22 is obtained.

a = {(N-2) / 2 N}-π (2 2) In Fig. 46, the three spirals (1) to (3) emerging from points A, F and G are the radiations in Fig. 46 It consists of a mountain-shaped fold line.

Although this model gives a typical spiral pattern, it is folded without any gaps up to the center of Fig. 46, so it is difficult to practically use it as a method for folding thick sheets or membranes. is there.

FIG. 48 is an explanatory diagram of a practical model obtained by deforming the model described in FIGS. 45 and 46, FIG. 48 is an explanatory diagram of the deforming method, and FIG. 48B is a diagram of FIG. It is a principal part enlarged view.

In FIG. 48A, the points C and D are rotated around the center O around the center by an angle 20 *, and moved to the points E and F, respectively. And ZCAE = ZBDF = ~ = Y * put. By this operation, the congruent rectangles ABFE, BGHF ... are periodically placed on the same circumference. be painted.

In FIG. 48B, the valley fold line is assumed to be A F, and the angles a to δ and D and Q are given as shown in the figure.

ΖΟΑΒ == ΖΟ ΒΑ = π / 2-©

Is obtained, the following equation is obtained.

ρ = π / 2-Θ + -ί) *, = π / 2 + Θ— τ—Y *,

δ = π / 2-@-(a + yutsu (2 3)

Since Z A C E = 7c / 2 — 0 *, we focus on A A E C and obtain Z A E C = / 2 — Yu *. Considering that △ 〇 CE and △ EF are isosceles triangles, using ZAEF = Q = — (ZOEC + ZOEF + ZAEC) obtained from the angular relationship around point E, we obtain the following equation (2 4) .

a = π / 2 + 2 θ * + TJ) * + ®, a = γ-2

(2.4) Fig. 49 is a view showing the state when the figure ABGHFE formed by the fold line in Fig. 48 前記 is sequentially folded at the fold lines AF and BF, and Fig. 49A shows a valley-folded AF. Fig. 49B shows the state of the subsequent rectangles ABFE and BGHF (hatched area; back side). Fig. 49B shows the state of Fig. 49A after mountain folding at B'F (original line segment BF). It is a figure showing a state.

When each point is determined as shown in FIG. 49B, ZAFB ′ = β and ZFΒ′Η = δ. By valley fold AF and mountain fold BF in one block, these two blocks are bent by the angle between the straight line AF in Fig. 49B and B'H ". This angle is adjusted as shown in the figure. Then, ゆ = 一兀 (2 (2 + * *) Using / 3 + δ = π: _ 2 (r + Ψ *) obtained from equation (2 3), the following equation (2 5) Get.

Y = 2 (α + Yutsu (2 5) Considering the folding in a regular N-gon shape, one of the inner angles is (N— 2) π / 、.

(Α + Yu = (Ν-2) π / 2 Ν (26).

Fig. 50 corresponds to the part corresponding to the first-stage strip shown in Fig. 48 It is a figure showing a part.

In FIG. 50, it is possible to newly draw the second stage based on points E, F, and H in the same procedure as that performed in FIG. 48. The rectangles 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 (2 3) and (2 4): 3 — α = π / 2 + ®—Y * + 2 6 »* —2 key and <5 _a = pit / 2 — ®—Y * — 2 key Get. That is, the following equation (27) is obtained.

β-= 6-r + (D-α) = δ-r + 2 (& + θ *) (27) The angle between the valley fold line (1) and (2) in Fig. 50 is 2 due to the periodicity. Θ Similarly, the angle between folding lines (2) and (3) is 20 *. In other words, considering that (1) and (3) form an angle of 2, Equation (27) shows that the conditional expression for folding at node F is satisfied. FIG. 51 shows において = 6, r + Ψ * = π / 3, ** = vert / 6, and τ = πΖ6 in the fold line conical wall having the fold lines shown in FIGS. 48 to 50. Explanatory drawing of the pseudo-conical wall having the developed view of the case (2Θ = π / 18), FIG. 51 1 is a developed view, and FIG. 51B is a conical wall with a folding line having the developed view of FIG. It is a perspective view in the state where it was folded in half. FIG. 52 shows N = 6, A + Y * = π / 3, Y * = π / 4, A = πΖ1 2 in the fold line conical wall having the fold lines shown in FIGS. Figure 2 is a development view (2 ® = π / 6).

FIG. 53 is a developed view when the number of steps in the developed view of FIG. 51A is reduced and the value of Y * is increased for each step.

In FIG. 53, in the case of a conical wall, Y * + α = 60 °. Yu * and α are split under the condition of Yu * + α = 60 °. It can be arbitrarily divided into Y and * values for each stage. In the case of a conformal spiral, the pattern becomes smaller as it goes toward the center.

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. 53 described above. In FIG. 54, the joining of both side edges is easier than in FIG.

Fig. 55 shows the second valley fold line in Fig. 50 in the opposite direction to that of the first tier at an angle τ. FIG.

Assuming that the intersection of this valley fold line and OA (O; center) is K, ΔΚ Ε ゆ becomes Y *, and the newly obtained rectangle EFIK is similar to that of the first row. The folding line at point F corresponds to Fig. 37. When the mountain fold line (1) in FIG. 37 corresponds to the mountain fold line F 1, 1 □ _ 10 in FIG. 37 becomes 0 ι = δ, θ _ζ = τ, 6 »α, 0; 3.

Since the line segments F H and FE in FIG. 55 form an angle 2 ®, and / 3 * in FIG.

α * = δ + r + 2 ®, β * = + β + 2 & (28-1)

Becomes

Using equations (2 3) and (2 4), α j8 * in the above equation becomes

α ^ = π / 2--*-® = β + γ

β * = π Ζ 2— ゅ * one Θ— 2 θ * = a + δ

(28-2). By using 0 ι = (5, θ _ζ = τ, θ _z = a, 6>; 3) in these expressions, the expression (10) is obtained, and the folding condition is satisfied.

Drawing a valley fold line in the opposite direction for each step in this way creates a repetitive, spiral-shaped folding structure.

FIG. 56 is an explanatory view of a pseudo-cone having a developed view in which FIG. 51 is made into a repetitive spiral type. FIG. 56A is a developed view, and FIG. 56B is a folding line having the developed view of FIG. It is a perspective view in the state where the attached conical wall was folded in half.

Figure 57 shows the expanded view (Ν = 6) of the iterative spiral type obtained with 2Θ = π / 6, * = πΖ6, and a = π / 6.

4. Analytical study using conformal spiral

The two patterns formed by the fold lines in the above development are similar and become smaller toward the center.

FIG. 58 is an explanatory view of an exploded view of a foldable conical wall having a fold line along a conformal spiral, FIG. 58 8 is an overall explanatory view, and FIG. 58B is FIG. FIG.

The exploded views shown in Fig. 39A and Fig. 42, as in the previous geometrical treatment, The angle formed by the pattern with respect to the center O is 2 mm, and it is generally represented as shown in Fig. 58A. This FIG. 58A is drawn as follows. First, draw the line segments (1) and (2) in the upper right direction so as to make an angle with the radiation OA, 〇I from the center O starting from the points A and I. Next, line segments (4) and (5) are drawn from points A and M in the upper left direction so as to form an angle φ with the radiation (Y and φ values are α and δ in Fig. 40 and Fig. 42, and φ = πΖ 2 — Θ— α, φ = πΖ 2 Θ Θ—5)). Assuming that the intersections of (1) and (5) and (2) and (4) are F and 各々, respectively, the points Β and F come on concentric circles.

Similarly, when the above operation is performed at points, and F, points C, J and G are determined, and points D, K and H are sequentially determined. That is, the sequence of points F, G, H ... taken from point A in the upper right direction always forms an angle with the radial direction, and the sequence of points A, B, C, D, E forms an angle φ with the radial direction. It is drawn as follows. If the line connecting points A, F, G, and H is a new curve (1) and the line connecting points A, B, C, and D is a new curve (4), these two curves are equal to the radial direction. A line going to the center while making an angle.

That is, each of these points is on a conformal helix emanating from the center O. In Fig. 58 A, (1), (2), and (3) are counterclockwise spirals, and (4), (5), and (6) are clockwise spirals. As shown in Fig. 58 A, if the angle between line segments AB, BC,… and the central angle is set to 2 2 ', the angle between line segments AF, FG, GH is 2 (Θ-は') It is. The folding conditions are examined using the enlarged view of the two rectangles on the left and right of point F (Fig. 58-8Β). These rectangles are congruent, and the line segments BF and FG form the angle 2 2. Y, φ and a! The angle relationship of ~ δ is as shown in the figure. Since AO B F in Fig. 8 Α is an isosceles triangle with a vertex angle of 2 ®, α + φ = π / 2 — Θ and δ + = = 兀

+ δ = π-(φ + Y)-2 Θ (2 9). From the internal angle relation of AA B F or AM F N,

β + Ύ = π-(+ ψ) (30). From equations (2 2) and (2 3), the following equation holds.

β-α = δ-τ + 2 Θ (31) Considering that the line segments BF and FG form an angle of 2 が, the above equation (3) holds. In other words, it can be understood that the folding condition is automatically established when a folding line is drawn with a conformal spiral. = ゅ corresponds to Figure 398, and ≠ corresponds to Figure 42. The radius of points B and F is the radius of the developed map R. Is given by the following equation using the sine law.

RiZR. = sin {2 (Θ-Θ ') + i>} = ρ (3 2)

The radius of the second stage point (C, J, G ~) and the third stage point (D, Κ, H ~) from the outer circumference are sequentially! ) ² , P ³ …

FIG. 59 is an explanatory view of a development view of a conical wall with a fold line when the spiral of FIG. 58 is reversed.

In FIG. 59, as in FIG. 58, the radial direction and the angle are taken upward from the point A and the angle Φ is taken upward. 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 B C is 2 °.

Next, draw the line segments BD and CD in the opposite direction from the point B> C at the same angles and respectively. Intersection D is on radius OA. When this is repeated, zigzag folding lines ACD F G I, AB F E GH… are obtained. Δ〇 Since B C is an isosceles triangle with a vertex angle 2Θ,

Z D B C = d = π Z 2 _ ® _ φ, α = Z D C B = π / 2 O

(33) is obtained. The following equation (34) is derived by using the outer angles of Δ〇 B A and ΔO A C, respectively.

Ζ Ο Β Α = τ = π / 2 + Θ- (Φ + 2 Θ— 6>

ZB CA = j3 = 7c / 2 + @-(+6>) (3 4) From equations (33) and (34), equations (15) and (16) are obtained, and all nodes The folding condition is satisfied.

Figure 41 corresponds to this case, and Figure 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, line segments (1) and (2) are drawn from points A and G at the same angle Φ, and line segments OB and OH are drawn symmetrically with respect to the perpendicular drawn from point O to the bottom AG of AOAG. Let B and H be the intersections with.

Take φ in the opposite direction from points B and H, and let the intersection with OA, 00 be I. With this operation, we get the zigzag fold lines ABCDE… and GHLJ…. At each node The folding conditions are 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. 50.

FIG. 61 is an explanatory view of a pseudo-cone having an exploded view in which FIG. 44 is made into a conformal spiral, FIG. 61A is an exploded view, and FIG. 61B is an exploded view of FIG. 61A. FIG. 4 is a perspective view of a state in which the conical wall with a folding line is half-folded.

As shown in FIG. 61 and FIG. 61B, a development view in which the folding lines form an isosceles trapezoidal shape arranged along a spiral 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 side 緣 and the left side edge are set so that the right end points A, B, C,… and the left end points D, E, F, D overlap. Connect. As described above, the folding condition at the node is automatically established when the equiangular spiral or the inverted type of the equiangular spiral is combined, but the folding condition in the circumferential direction is based on the circumference of the folding angle at each point. It must be set using Figure 45 or the previous geometric considerations so that the sum of the directions is two.

The nodes on these developments are ) The value can be determined and determined from the intersection of the concentric circles of the radii p, p ² , p ³ … and the radii.

5. Foldable conical shells produced and their characteristics

Using a 0.2 mm thick polypropylene sheet, the conical shell shown in Fig. 51B produced by the development shown in Fig. 51A and the production shown in Fig. 56 produced by the development shown in Fig. 56A B was observed to be folded. As a result, it was found that good folding is possible as predicted by the origami model.

6 Discussion

Assuming mainly 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, it is difficult to stretch them to a conical shape obtained by joining the fan-shaped exploded views together with the pseudo-conical shape. . It is thought that these structures can be manufactured by connecting thin metal plates etc. processed into triangular or trapezoidal elements with joints, etc. It seems possible.

In addition, the folding mechanism shown here is considered to be a basic model of a large structure such as a foldable dome roof and a tent structure. There are many issues that need to be overcome to achieve these, but adding another ingenuity to the proposed folding model would likely lead to new forms of processing and products.

7. Summary

In order to create a conical shell structure that can be folded in the axial direction, which has not been reported before, we proposed several new developments, verified geometric folding conditions, and Is 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 lines

Creating a disc-shaped folding structure with fold lines that can be folded radially or circumferentially by forming a fold line using the spiral of Archimedes and the spiral of Bernoul 1 i (conformal spiral) Can be.

1. Basic relationship

FIG. 63 is an explanatory diagram of the simplest folding method for origami.

In Fig. 63, one contact point (black dot) is composed of four fold lines. If 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 line (3) and ( 4) When the angles are equal, they can be folded.

This folding condition is interpreted as follows. The line segment that bisects the angle between the mountain fold line (2) and (3) is (Α), and the line perpendicular to this is (Β). The angle between the valley fold line (4) and the extension (5) of (1) is bisected by (によって) (at an angle of; 8). At this time, the angle between (1) and (A) is also 6; Considering (B) as a mirror surface, (2) and (3) can be regarded as incident light and (4) as reflected light.

In other words, the intersection of two orthogonal straight lines considered as a mirror surface is set as a node, and at this point, two zigZzag fold lines are made to enter and reflect at an equal angle, and intersect. The folding condition is satisfied at the point. This is called the "mirror rule" of the 4-fold line method. 2. How to fold in the radial direction

FIG. 64 is an explanatory view of a development view of the 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 zigZzag in the center direction by combining the zigZzag fold line (1) toward the center and (2) in the circumferential direction.

An isosceles triangle element with a vertex angle of 2 Θ (Α Ο Α Β, Δ Ο B C ···) N radius R. (2 Ν = 2 ττ, base angle = π ノ 2 — を). Draw another sub-radiation OF, OG, OH ... rotated by 2θ at the central angle from the main radiation OA, OB, OC ... constituting Δ Ο Α ,, AOBC…. A straight line is drawn from the points A, B, C ... on the outer side so as to form an angle with the main radiation, the intersections with the sub-radiation are F, G, H ..., and the radius from the center point 0 is.

Also, the points I, J, K ... on the concentric circles (radius R ₂ ) are taken on the original radiations OA, OB, OC. Draw a zigZzag fold line in the radial direction in this way. The fold lines in the circumferential direction, FG, GH ... and IJ, JK, rotate around the center at an angle of 2 ® due to symmetry.

If the point of intersection between the extension of the line segment OG and the outer circumference circle is point E, Δ Ο Ε となり is an isosceles triangle with a vertex angle of 2 、, and Ζ Ο Β Ε = (πΖ2) — 0.

Since Z O B C = (7Γ / 2) — ®, the following equation (35) is obtained.

Using ZOBGE = ci) as ZCBE = ©-0 (35) p ≡ ZBGE, and considering the external angle relationship of △ 〇BG, the following equation (36) is obtained.

p = +2 0 (3 6)

Z G B C = (π / 2) .- ®-≡ a

Is defined, and the following equation (37) is obtained by using the previous equation (36).

D = (% 2)-(+ &) + 2 Θ (37) Next, consider the folding condition at point G.

If the angle between the extension of line GH and line GB is ζ, then the folding condition at point G is ζ = ZFGJ

Given by

ζ = π— Z E G H _ p = dash— (π / 2 + Θ)-ρ = α-2 θ

Therefore, the folding condition at the point G is expressed by the following equation (38) as) 3 ≡Z F G J.

β =-2 θ (3 8) J G 0≡

Q + β = (π / 2)-Θ.

From the following equation (39) is obtained.

α = (πΖ2— Θ) — (α-2 Θ)

= i / 2-(a + @) + 29 (39) From Equations (37) and (39), p = ci (this relationship is the point G, and the mirror law with the radiation OE as the mirror surface) ).

Next, when A B J G≡ r is set in A O J G, r = Q + 20 is obtained. The folding condition at the point J is given by r = s, considering the line segment OB as a plane (ZOJP≡s).

Since ZO J K = 7t / 2 -0 = ZO J P + Z P J K, put ZP J K≡ r

, R is given by the following equation (4o).

γ = (π / 2-Θ)-s

= (π / 2-Θ)-(Q + 2 θ)

= π / 2-®-2 θ-{π / 2 _ (α + ©) + 2 θ} = a-4 θ (40) Take the “swing angle” of the zigZzag fold line in the radial direction to 20 And the fold line BGJP… in the radial direction is the value obtained by subtracting the angle by 20 as β = o-2θ and γ = a-4θ, where the angle at point B on the outer edge is the angle.

When the two primary and secondary radiations (Ο Β and OG) are considered to be specular, the relationship between the angle of incidence and the angle of reflection is

p = Q = vit / 2-(α + Θ) + 2 Θ = + 2 Θ.

r = s = π / 2 (α + Θ) + 4θ = + 4θ (4 1), and the angle is increased by 20.

Disc radius OB = R. , The lengths of the line segments OG, OJ, OP are R _lt R ₂ , R ₃ When the sine theorem is used for △ OBG, △ 〇 GJ ..., the following equation (42) is obtained.

R. ~ R α = 8ϊη φ / sin (+ 2 θ),

R ₂ ZR. = sinci) "sin ((i) + 40),

After obtaining the primary and secondary radiation groups from the center, give R a_Z R ₀ , R ₂ / R. If we draw concentric circles of… and make these intersections nodes, we can obtain a developed view that satisfies the folding condition at all nodes.

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 disk-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 disk-shaped folding structure with a folding line having the developed view of FIG. 65 in a half-folded state and a large amount of folding.

FIG. 68 is a perspective view showing a state in which the disk-shaped folding structure with a folding line having the developed view of FIG. 65 is completely folded.

The disc-shaped folding structure S with fold lines 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 an intersection of the mountain fold line M and the valley fold line V, a total of four folds 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 and the number of valley fold lines V = 1 and the difference is 2 (= 3-1). In other words, the folding line pattern of the foldable circular colored sheet is one node and four folding lines. The fold lines are formed along a plurality of conformal spirals so as to satisfy the folding condition of the circular sheet.

The disc-shaped folding structure S with folding lines shown in Fig. 65 to Fig. 68 has a foldable color. When it is made up of colored sheets or the like that are colored, the shape becomes beautiful according to the amount of folding, and the visible color changes according to the shape. As for the disc-shaped folded 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 broach.

Fig. 69 is an exploded view of a disk-shaped folding structure with a folding line when the swing angle of the folding line of zigZzag in the radial direction is increased as approaching the center.Fig. 69A shows the folding conditions. FIG. 69B is an enlarged view of a main part for explanation.

When the zigZzag fold line is drawn at the same swing angle, the interval between the fold lines sharply decreases as it approaches the center, so consider increasing the swing angle gradually (Fig. 69A).

If we draw the fold lines BG and GJ at the initial swing angle of 20, p = (i = r = D + 20 at i. Then, from point J, s = r, and take the swing angle of 40, for example. , And the angle t in Fig. 69 becomes: Draw a line segment PQ at the point P based on the mirror rule based on the mirror rule, and determine the point Q. When the folding line is sequentially obtained according to the mirror rule, the swing angle becomes The angle relationship at 20, 4θ, 6 ° is given by the following equation (43).

p = d = vat / 2 — (α + Θ) + 2 θ = + 2 θ,

τ = 5 = φ + 4θ, and t = u = φ + 8θ (43). The line segment OG = R, the line segment OJ = R ₂ … can be formulated by the same procedure as that used to find equation (8).

Figure 70 shows the development of a disc-shaped folding structure with a folding line when the swing angle of the zig / zag folding line in the radial direction is increased toward the center and the circumferential folding line is also zigZzag. FIG. 70A is an enlarged view of a main part for explaining folding conditions, and FIG. 70B is an overall view.

In Figure 70A, radius R. And R. * (R.> R. *) alternately depict the main radiation O A, O B ... and draw the sub-radiation OF, OG ... shifted from them by 20. Here, F, G, and H are the intersections of the lines drawn from points A, B, and C at an angle to the main radiation and the sub-radiation. Thus, when drawing according to the mirror surface rule, the folding condition is satisfied at all nodes.

FIG. 64B is divided into N = 36 (20 = 100), FIG. 69B, and FIG. 70B into N = 18. The folding line method was used up to the eighth step from the outer circumference. Central part In the center, alternately laying valley folds and valley folds at the center to avoid the blank area in the center.

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, consider eliminating the radial folding line zig / zag.

In Fig. 71, the blank area in 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 fold line A F ((1)) is C. Draw a line segment CD so as to be symmetrical to the folding line (1) (ZACD = 2 TT / N :).

In this way, if N fold lines are drawn from the vertices of a regular N-gon so as to be symmetrical each time they intersect with the fold line, an evenly spaced spiral pattern is obtained. It is easy to see that the intersection of the radial fold line and this spiral fold line is on the Archimedean spiral centered on the center.

This is the basic form of the folding (winding) method proposed by Guest and others.

FIG. 72 is a diagram showing a new folding line considered by the present inventor. FIG. 72A is a diagram in FIG. 71 in which the radial folding line (1) has one bending point. Fig. 72B is a diagram in which the outside of the bending point in Fig. 72A is replaced by a method of folding in the 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 in which the Archimedes spiral is combined with the developed view in FIG. 64B is created.

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 minute, so that the folding angle becomes extremely small at the time of winding. This can be replaced by elastic deformation. For winding of polymer films or fabrics with low elastic modulus, only the main fold line is sufficient, and the introduction of the Archimedes spiral is practically formal.

4. Folding method by conformal spiral style

The folding method using the conformal spiral style is a straight fold formed along the conformal spiral. 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 fold lines when a circular film or a partial circular film (sector-shaped film) or the like is folded in the radial and circumferential directions along a conformal spiral.

As shown in Fig. 73, the circular film is divided at equal angles by radial radiation from the center of N lines, and this is replaced with N isosceles triangular elements (ΔΟΑΜ, Δ の-) with a vertex angle of 2 ® (2 Θ · Ν = 2π). Each point is defined as shown in the figure. From the point 上の on the outer perimeter, draw a straight line forming the radiation and each Φ, and define the intersection point of the radiation (OM) rotated by 2 で at the central angle as point B.

Starting at point A, draw a straight line that forms φ with the radiation OA, and let the intersection with the radiation OM, which has been rotated 2 °, be B. Next, a straight line that forms an angle と with the radiation OM is drawn, and an intersection C between the radiation ON which is rotated by 2® is determined. Next, take the angles Φ and χ alternately in the same procedure to determine points D, Ε. This zigzag line is referred to as (1). Here, the angle between the line segment ΑΒ and the base of the isosceles triangle is defined as. That is, J3≡90 ° — ®_φ. The angle between line segment BC and MN (that is, the angle between line segment BB 'drawn from B in parallel with MN and line segment BC) is defined as a. = = (9 0 ° — Θ) — Defined by χ. The value of Τ is positive when C is on the same side as the center O with respect to the line segment B B ′, and negative when C is on the opposite side of the center O. When τ = 0, the segments BC and MN are parallel. R for the radius of the circular plate. When the sine theorem is used for △ 〇 AM, the length (OB) of the radius of the point B is given by the following equation (44).

{βϊηφ / sin (+ 2 Θ)} ρ ρ. ·-· (44) Also, when the length of the radius of the point C (OC) is R ₂ and the sine theorem is used for △ 〇 BC, the following equation is obtained. 4 5).

That is,. Using equations (4 4) and (4 5), the following equation (46) is obtained.

D · Q = R ₂ / o

= Ξϊηφ · sinx / {sin ( + 2 Θ) / sin (χ + 2 Θ)} (4 6) In other words, the point D, E, F ... radius dimensionless radius R0 of circular film of [rho ² ( ΐ, D It is given by a value obtained by alternately multiplying p and Q like ² Q ² , P ³ Q ² ….

Now, as a line (2) connecting points A, C, E, G,… that gives the lower limit of the zigzag line (1)

, The dimensionless radius of each point is given by 1,: PQ, (PQ) ² , (PQ) ³ ,…, so each of these points is an equiangular helix and the radiation of every 4 mm. Given at the intersection. The line (3) connecting the points B, D, F, H ... that gives the upper limit of the zigzag line is also given by the intersection of the conformal helix and the radiation.

Fig. 74 shows a basic explanation of the folding line when forming a folding line along the equiangular spiral while folding a circular film or a partial circular film (sector-shaped film) around the central axis while winding it around the central axis. It is.

Next, as shown in Fig. 74, points P and Q that are advanced clockwise by an angle that is an odd multiple of 2 （(described later) from the start point A of the folding line (1) are defined. Draw zigzag fold lines (4) and (5) in exactly the same way as.

In this case, fold lines (1) and (5) are alternately set as mountain fold lines, and fold line (4) is alternately set as valley fold lines. Points on fold line (1) are I, J,:, fold line (4) The upper point is named R, S, T, and the point on the fold line (5) is named Q, U, V as shown in the figure, and the points Q, R, I and The points U, S, and J are connected by a straight line, and these are set as another folding line group (6), (7), (8).

As shown in Fig. 74, if points P, Q ... are taken every five isosceles triangular elements, the number of zigzags n (one zigzag once, n = l) becomes zigzag when n = 2. Is repeated twice, so go counterclockwise through five isosceles triangles. (For example, if zigzag is repeated twice along the fold line (4) from point P in Fig. 74, point R will be reached. Intersects the fold line (6) from Q. If you include an isosceles triangle that passes through the fold line (6), you have advanced counterclockwise through five isosceles triangles.)

The dimensionless radii of points Q, R, I… are 1, (PQ) ² , (p α), and 厶 QR and AOR I in the figure are similar.

That is, the new folding line groups (6;) to (8) also become conformal 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) -1Φ. Equivalent to the outer edge (the base of the isosceles triangle element) The zigzag folding line (4) repeats the zigzag n times to reach the point R in the figure (n = 2 in FIG. 74). At this time, the radius of the point R is given by (P · d) ⁿ .

On the other hand, since the angle formed by the spiral (6) coming from the outer point Q with the radiation is fluctuating, the value of the dimensionless radius giving the point R is expressed by sin / sin (y + 2Θ). If this value is equalized with equation (46), the following equation (47) is obtained.

p ⁿ q ⁿ

= [sin φ sin% / {sin (+ 2 Θ) sin (% + 2 Θ)}] "-

= sin // sin (+2 2) (4 7) The above equation (4 7) crosses the spirals (1), (4), (5) toward the center while turning clockwise, and It gives the angular relationship to be satisfied by the spirals (6) to (8) rotating clockwise.

4.2 Folding conditions

As described above, consider a case in which a conformal spiral is bent every time 2 passes. Consider the point S in Fig. 74 consisting of the valley fold line 3 and the mountain fold line 1 and the point U consisting of the mountain fold line 1 as representative points, and consider the folding conditions at these points.

FIG. 75 is an enlarged view of a main part of FIG. 74.

Figure 75 shows an enlarged view of Figure 2 near points S and U. At point S, ZO S J = i /), so that Z S J R = i /) + 2 ®. Since ZO R S-φ, considering A J S R, Z J S R = 7T — (Y + 2 ®) — φ. Assuming that an extension of the line segment J S is S S ′, Z S ′ S R = 7C—Z J S R = Y + 2 Θ + Φ.

If ZU S Q = Y + 2 ® is used, ZTU S = 7C — χ— ZU S Q = 7C— χ—Yu _ 2 ®. If Z S 'S R-ZTU S is placed according to the folding condition, the following (48) is obtained as the folding condition at the point R.

2 ψ + + χ = π- 4 Θ (4 8) As can be seen from FIG. 75, since the angular relationship of point U is the same as that of point S, equation (4 8) is a folding condition. That is, if equation (48) holds, the folding condition holds at all nodes.

Figure 76 shows a circular or partial circular membrane (fan-shaped membrane) wound around the central axis. FIG. 7 is an explanatory view of folding conditions when forming a folding line along an equiangular spiral. The relational expression of equation (48) is, as shown in FIG. If it is larger, that is, the folding condition is given by equation (48) even if the folding line is directed upward at points 点, D….

4.3 Continuity of spiral group in circumferential direction

In the above, the folding conditions were determined, but these spiral groups are equally distributed around the central axis, and the conditions for maintaining the continuity of the spiral are derived. Consider the case where the spiral (folding line (1)) of zigZzag starts m lines from the outer peripheral point every η number of isosceles triangular elements. In this case, these start points are (2 n + l) (2Θ) Rotate (n: 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 into (2n + l) m.

That is, the division angle (vertical angle of the isosceles triangle element; 2Θ) for satisfying the continuity is given by the following equation (49).

2 ® = 2 vit / {(2 n + 1) · m} (4 9) Only by dividing the circular membrane in this way, the condition that the continuity of m spiral groups is satisfied in the entire region of the membrane Achieved.

By using φ = π−2 Yuichi χ _ 4 られる obtained from equation (48) in equation (47), the following equation (50) is obtained.

(Q) ^η

= [sin (2 ゆ + χ + 4Θ) · sin% / {sin (2ψ +%-2Θ) sin (χ + 2Θ)}] "

= sin? /) / sin (Y + 2Θ) (50) By giving 2Θ and χ values divided to satisfy equation (49), the equation that satisfies equation (50) can be calculated by numerical calculation. . In addition, a value of 0 is also obtained by the equation (48), and a development diagram with a spiral folding line that satisfies the folding condition at all nodes is drawn. 4.4 When folding the minor fold line at an arbitrary rotation angle (= χ) Above, the circular membrane was equally divided into N isosceles triangular elements with an apex angle of 2 °, and a developed view was obtained by folding the fold line after passing each of these elements. In the case of Fig. 76, in the special case where m spirals are always bent upward at the same angle (Φ = Χ), it is possible to construct another folded development.

FIG. 77 is an explanatory diagram of folding conditions when the main folding line is bent at an equal angle to radiation.

Points A, B, C and A ', B' on the circumference of the circle are defined as shown in Fig. 77. Draw an upward fold line (1) from point A and an upward fold line (2) from point B. (1) The central angle is 2θ (angle of the string AA '), and (2) is the central angle of _2θz (angle of the string A'B). (1) is at an angle with the radiation from the center (the angle α with the outer edge AI), and the fold line (2) is with the radiation at an angle φ (the angle with the outer edge Ι 3) 3).

Consider the folding condition at point D below.

ZADA '= φ + 26> BD Β' = φ + 2 θ _ζ

Becomes延長 If the extension point of D is Η,

ZADH = 7C _ {(Φ + _{yu) + (θ ^ + θ 2} )}

Becomes

Ζ F D Ο = φ, Z G D O =

Ό G = φ + -φ

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 when Z AD Η and ZFDG are equidistant. 5 1) is obtained. φ + Y = π Ζ 2 — 2 Θ, or (a +) = π / 2 (5 1)

'Assuming that OD is R, if the sine theorem is used for AOAD, the following equation (52) is obtained.

/ sin (Y + 6 »J (5 2)

On the other hand, the following equation (53) is obtained for △ 〇BD.

R iZ R. = sin (i) Zsin (+ θ _z ) (5 3)

Both of these values give the radius of the point D. If these values are equalized and the above φ = π / 2 — Yuichi 2 ® is used, the following equation (54) is obtained. sin () 3 _ 0 / sin {β + Θ

= sin (/ 2-0 ₂ -j3) / sin (πΖ 2 + 0 ₂ —… (5 4)

Given Θθ, Φ that satisfies Equation (53) is determined by numerical calculation. Equation (51) gives the displacement, and using these values yields a development that satisfies the folding conditions at all nodes.

4.5 Application to the manufacture of conical shells

In Fig. 74, it is assumed that the zigzag spiral (folding line (1)) consists of m lines, and the angle formed by the departure point on the outer edge is (2n + l) · (2Θ). In the case of a disc, (2 n + l)-m-(2 Θ) = 2 pits, but if this (2 n + l)-m-(2 Θ) value is smaller than 2 π, the cone unfolds As shown in the figure, folding is possible in this case as well.

5. Examples of folding products

FIGS. 78 to 80 show a developed view obtained by the above-mentioned theory and an example of its folding.

Figure 78 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 triangular elements N = (2 n + 1 FIG. 7 is a diagram illustrating an example of a folded development view when m = 18 and a = 20 °.

Figure 79 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 4 and the number of isosceles triangular elements N = (2 n + 1 ) m = 1

FIG. 8 is an example of a folded development view when a = 0 °, showing an example in which the angle of the fold line with respect to the radiation is different from FIG.

Figure 80 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 10 and the number of isosceles triangle elements N = (2n + 1) is a diagram showing an example of a folded development view when m = 42 and a = 0 °.

In Fig. 78 to Fig. 80, 2 Θ = 20 °, 20 °, and 180 ° / 21 respectively, and τ determined by these values and χ (r = Z-90 + Θ)値 = π

Given values of 9, 0 and 0, a numerical value that satisfies the equation (50) was obtained by numerical calculation. Substituting this shift value into equation (4 8) determines φ.

From α + · = 90-Θ,; 3 + ψ = 90-Θ, the values of α and j8 in Fig. 78 to Fig. 80 can be determined. For example, in FIG. 78, α = 69.763 6 °, 0 = 20.474−. It is.

In the examples of FIGS. 78 to 80, the circular membrane whose main fold line is composed of two spirals is folded into a new plane. In the state of the side surface after folding in FIGS. 78 and 79, when the ァ value increases, the central part is folded in a shape protruding upward. This is advantageous when manipulating the unfolding of the structure. Comparing Fig. 79 and Fig. 80, the larger the number of divisions, the smaller the folding.

Figure 8 1 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 triangular elements N = (2 n + 1 FIG. 7 is a diagram showing an example of a development view of a disc-shaped folded structure with a fold line when m = 18 and r = 0 °.

FIG. 82 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 small amount of folding.

FIG. 83 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 and a large amount of folding.

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.

The disc-shaped folding structure S with fold lines shown in FIGS. 81 to 84 is obtained by combining the circular sheet (the disc-shaped fold structure with fold lines) developed as shown in FIG. When folded by V, in the half-fold state where the amount of folding is small, the state is as shown in FIG. 82. When the amount of folding is increased, the state shown in FIG. 83 is obtained. Figure 84 is almost folded, and when fully folded, it folds into a plane.

Since the shapes of the folding lines M and V of the disc-shaped folding structure S with folding lines in FIGS. 81 to 84 are different from those in FIGS. 65 to 68, colors in which foldable colors are applied are provided. When constituted by the attached sheets and the like, a shape change and a color change different from those in FIGS. 65 to 68 can be obtained.

As for the disc-shaped folding structure S with fold lines, similarly to the disc-shaped fold structure S with fold lines, a large one can be used as an upholstery and a small one can be used as a professional. And so on.

Figures 85 to 87 show developments in the case of three spirals, four spirals, and one spiral. Figure 85 shows an example in which four zigzag spirals (m = 4) are used as folding lines and folded around the center, where n = 7 and the number of isosceles triangular elements N = (2 n + 1 ) m = 6

It is a figure which shows the example of the fold development figure in case of 0, a = 0 degree.

Figure 86 shows an example in which three zigzag spirals (m = 3) are used as folding lines and folded around the center, where n = 8 and the number of isosceles triangular elements N = (2 n + 1 ) m = 5

FIG. 4 is a diagram showing an example of a folded development view when 1, a = 0 °.

Figure 87 shows an example in which one zigzag spiral (m = 1) is used as a folding line and folded around the center, where n = l0, the number of isosceles triangle elements N = (2n + 1) A diagram showing an example of a folded development view when m = 21 and a = 0 °.

When the main fold line in FIG. 85 has four spirals, it is folded so as to be wound in a square shape, and when the main fold line in FIG. 86 has three spirals, it is folded so as to be wound in a triangular shape. In the case of one spiral in Fig. 87, the spiral is folded around the central axis.

When T == 0 ° and α,] 3 values are obtained in the same manner as above, the following is obtained.

In Fig. 85, τ = 0 °, ο; = 75.432 °, 0 = 29.132- °.

In Figure 86, τ = 0 °, Q! = 76.23 3 °, 0 = 27.53 3 °.

In FIG. 87, τ = 0 °, 0! = 76.7 1 4— °, and 26.572− °.

Fig. 8 8 shows an example of folding around the center using four zigzag spirals (m = 4) as folding lines, where n = 4, the number of isosceles triangular elements N = (2n + 1 FIG. 7 is a diagram showing an example of a development view of a disc-shaped folded structure with a fold line when m = 60 and τ = 0 °.

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 small amount of folding.

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 folded structure S with a fold 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 in Fig. 88? From then on, the inner diameter becomes smaller as it is folded in FIG. 89, FIG. 90, and FIG.

The disc-shaped folding structure S with fold lines shown in FIGS. 88 to 91 is a circular sheet (the disc-shaped fold structure with fold lines) developed as shown in FIG. When folded by V, in the half-fold state where the amount of folding is small, the state becomes as shown in FIG. 89, and when the amount of folding is increased, the state shown in FIG. 90 is obtained. In the fully folded state, the state is as shown in FIG.

The shape of the folding lines M and V of the disc-shaped folding structure S with folding lines in FIGS. 88 to 91 is different from that of FIGS. 65 to 68 and FIGS. 81 to 84. Therefore, in the case of a foldable colored sheet or the like, a shape change and a color change different from those in FIGS. 65 to 68 and FIGS. 81 to 84 are obtained.

Fig. 92 is a developed view when the number of spirals as main folding lines is large (m = 12). In Fig. 92, m = 12 and n = l, and the disk is divided into 36 equal parts. This is the case. Given α = 25 °, α and / 3 are obtained in the same manner as described above.

α = 55.270 · °, = 44.46 · °.

If the number of divisions of the central angle is doubled by this folding, the folding efficiency will be reduced by half, but the number of folding lines will increase and it is not suitable for engineering. This is rather interesting from a modeling perspective.

FIG. 93 is a developed view based on the above-mentioned FIG. 77, which is configured by two kinds of conformal spirals. The number of divisions Ν = 1 2, θ ^-πΖ ΐ β,, 0 ₂ = 2 9 vertices 18 0, and (|) is the same. When the developed view in Fig. 93 is folded, it is wrapped around the center symmetrically up and down. The one shown in FIG. 93 suggests that these fold lines are replaced by elastic deformation during winding because the sub-fold lines are fine.

Based on the development of Fig. 93, a circular stainless steel plate (thickness t = 0.05 mm, radius R = 140 mm) was cut into 12 pieces along the main fold line, and this was The ones joined by craft film were produced. This can be wound like the one shown in 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 a development view of a disc-shaped folding structure with fold lines in which mountain fold lines and valley fold lines are alternately provided.

In FIG. 94, the disc-shaped folded structure S with a fold line has a mountain fold line M along an equiangular spiral toward the center from a point obtained by equally dividing the outer periphery thereof into N (N is a positive integer 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 bisected toward the center.

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 self-deployed because it is deployed by elastic deformation. Since the fold lines at the center are fine, it is necessary to engineeringly combine with the folding method such as Guest, except for soft and thin cloth and rubber, etc. Fig. 95 shows mountain fold lines and valleys. It is a development view of a disc-shaped folding structure with a folding line in which folding lines are provided alternately, and the circumferential length of the valley folding line and the mountain fold lines on the left and right sides thereof are different on the left and right.

In FIG. 95, the disc-shaped folded structure S with a fold line has a mountain fold line M along an equiangular spiral toward the center from a point obtained by equally dividing the outer periphery by N (N is a positive integer and N≥4). A valley fold line V is formed along the equiangular spiral from a point where the equally divided outer periphery is further divided into two at an appropriate division ratio. The equiangular spiral in Fig. 95 is wound counterclockwise from the center to the outer periphery, and the angle between the valley fold line V and the right-hand ridge fold line M is β Let α be the angle formed by α>) 3.

In this case, when folded 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 the fan-shaped portion between the adjacent mountain fold lines in FIG. 95 is removed. A conical wall is formed by connecting the outer sides の of both ends in the circumferential direction in Fig. 96 so as to overlap. This conical wall can also be folded along the mountain fold line Μ 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) Application of folding structure with folding line

Based on the results of the above-mentioned folding method for flat plates and cylinders, we will explain the results of basic research aimed at their practical application in engineering. Here, mainly, I will describe.

(a) Modeling of a folding method for creating a high-rigidity, high-strength core material by bending a flat plate in a zigzag manner and making it three-dimensional, and a processing method therefor.

(b) A cylindrical deployment structure model with a simple mechanism devised based on the axial folding characteristics of the cylinder.

The former considers not only the creation of high-strength materials for aerospace, but also the realization of reuse of waste paper, etc.

1. Folding and non-folding conditions

FIG. 97 is an explanatory view of the folding condition of the sheet-like member, FIG. 97A is an expanded view before being folded, and FIG. 97B is a view showing a state of being folded along a folding line of FIG. 97A. .

Consider the circular thin flat paper shown in Fig. 97A, the center is set to 0, the line segments OA, OC, and OD are mountain-folded, and OB is valley-folded. The angle between these line segments is set as Q: ~ δ as shown in Fig. 97A.

Now, Ο 谷 is folded in a valley, the coordinate axes are determined as shown in Figure 97 9, and the line segment OA is taken on the X axis. The coordinates of points B, C, and D are (one cos j3, sinj3, O ), (X, y, ζ), (― cos, sin α, Ο).

If the angle between the line segments Ο Β and Ο C is τ and the angle between the line segments OD and OC is << 5 and α + β + γ + δ = 2 π. Χ y ζ 1, then the point C The ζ coordinate of is given by the following equation (55).

(1 ζ ² ) sin (-β)

= cos ² r + cos ² δ — 2 cos r cos δ cos (a — β) (5 5)

Since the coordinates of point C are determined by equation (55), the angle between plane OBC and the bottom surface (x_y surface) can be obtained. If z = 0 in equation (55), the condition is folding. When z is set to 0 and δ is eliminated from the right side and compared with the left side, the following equation (56) is obtained.

cos ² (a + β + τ) + cos ² γ = cos ² α + cos ² β,

cos τ = cos cos β (56) The relationship that satisfies these two equations (55) and (56) is given by the following equations (57) and (58) available.

+ γ = π (57) β + Τ = π (58) Since equation (58) is a condition for folding a circular plane into two, as a folding condition, here, equation (57) is adopt.

Structures made under the conditions that satisfy the folding conditions have low stability, and structures that do not satisfy the folding conditions tend to have high stability as structures. Therefore, this report mainly uses the unfolding condition for (a) and the folding condition for (b).

2. Modeling of core material

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 duouble corrugated core (DCC) based on the flat plate folding method (raiura ori).

FIG. 98 is an explanatory diagram of a DCC (duouble corrugated core), and is an expanded view of the DCC.

FIG. 99 is a diagram showing the vertical folding line group of FIG. 98 as zig / zag.

These nodes are composed of four fold lines, and the folding conditions are satisfied at all nodes. Therefore, when subjected to surface pressure, these cores are structures that can be pushed and spread on the original plane, and are unstable.

In order to avoid this, it is indispensable 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 technology seems to govern the success or failure of this structure.

Figure 100 is an explanatory view of the newly devised model of the core with a joint. Figure 100A is a developed view, and Figure 100B is a half-folded view of the developed view of Figure 100A. The top view of the thing, Fig. 100 (is an external view of a three-dimensional view obtained by folding the development of Fig. 10 OA. Fig. 101 is an explanatory diagram of another model of a newly devised core with a joint. And Figure 10 1A is a developed view, Fig. 10 IB is a plan view of the developed view of Fig. 101A in a half-folded state, and Fig. 101C is a three-dimensional view of the developed view of Fig. 101A folded down. It is an external view of a thing.

It can be seen that these have large joints, with the A part on the top and the B part on the bottom. Here, the nodes are composed of four or five fold lines.

FIG. 102 is an explanatory view of a model that does not satisfy another folding condition of a core having a joint devised by the present inventors. FIG. 102A is a development view, and FIG. 102B is a view of FIG. 102. It is a principal part enlarged view of A.

FIG. 103 is an explanatory view of a core produced by folding the developed view of FIG. 102A, FIG. 103A is a perspective view of the folded core, and FIG. 103B is FIG. FIG. 4 is a perspective view of a core bonded to a lower surface of a core.

The folding line shown in FIG. 102A does not satisfy the folding condition, and is considered so that the folding line becomes a square when the plate is made three-dimensional. In Fig. 102B, the vertical fold lines AC, DF, A'C ', D'F' and the diagonal fold lines DB, EC, A'E ', B'F', etc. are 45 degrees. .

When the valley fold line D—B is folded, the A—E parts come into contact, and AAB D and AED B join. All joints similar to the joints S 1 and S 2 are denoted by S 1 and S 2. When the valley fold line A'-E 'is folded, the members B'-D' come into contact, and AD'A'E 'and Δ' 'A'E' are joined. The joints similar to the joints S 3 and S 4 are all denoted by S 3 and S 4.

By bonding the joints S 1 and S 2 and bonding the joints S 3 and S 4, a structurally stable core material (FIG. 103A) composed of square fold lines is created. Is done. The core shown in FIG. 103B in which a sheet is bonded to the lower surface of the core can withstand a large compressive force. ·

FIG. 104 is an explanatory view of a model that does not satisfy another folding condition of a core having a joint devised by the present inventors. FIG. 104A is a developed view, and FIG. 104B is a view of FIG. 104A. FIG.

The folding line shown in Fig. 104A does not satisfy the folding condition, and is considered so that the folding line becomes a square when the plate is made three-dimensional. In Figure 104 B, vertical folding For lines AD and CB, CD, BE, etc. are at 60 °. When the valley fold line C—E is folded, the sections A—B come into contact, and ΔΑ CE and ΔΒ CE join. Bonding the joints creates a structurally stable core material (Fig. 104A) consisting of square fold lines.

3.2 Honeycomb core model

The honeycomb core is representative of a lightweight structure.

FIG. 105 is an explanatory view of a method for manufacturing a honeycomb core from one plate, FIG. 105A is a developed view, and FIG. 105B is a manufactured from a plate having the developed view of FIG. It is a figure of the eight strength Mukoa.

In FIG. 105A, a dotted line is a valley fold line, and a dashed mountain fold line has a cut C (cut portion). When the joints A and B on both sides of the valley fold line in Fig. 105A are bonded to every other valley fold line and spread out on both sides, the mesh-shaped honeycomb core shown in Fig. 105B is manufactured. be able to. When this manufacturing method is used, there is a characteristic that the honeycomb core has a cylindrical shape.

4. Fabrication of core material

4.1 Manufacturing method of core material

A 0.2-0.3 mm phosphor copper plate or a steel plate was cut along the fold lines shown in Figs. 101-102, and these were joined up and down with a craft film or joined with hinges. When two dies are manufactured, a thin paper to be processed or an aluminum alloy plate (~ 0.08 mm) is inserted between them, and bending is performed. Fig. 101B to Fig. 102B Products such as those shown in can be instantaneously manufactured.

Only the bonding areas S 1 and S 2 of FIG. 102B are bonded, and S 3 and S 4 are bonded without bonding, but bonded to a thin film on one side thereof (or bonded in reverse) By winding this into a cylindrical shape, it becomes 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 number of square parts (metal thin plates) P1 and parallelogram parts P2 separated by folding lines are bonded to both sides of the craft film F and folded. A line forming die K is configured. The folding line forming die K has a pair of foldable flexible dies K 1 and K 2 which are symmetrically formed with respect to the central axis L. The flexible molds (folding molds) Kl 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 made from the next time. Become. Therefore, when the flexible mold K1 is folded on 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 resin sheet becomes It is sandwiched between a pair of flexible molds K 1 and K 2. If the flexible molds K1 and K2 are simultaneously folded along the folding line in this state (the flexible molds K1 and K2 overlap), a folding line is formed on the paper or resin sheet. 4.2 Core Materials Made

A paper core and an aluminum core were manufactured using the folding mold described above, using the model shown in Fig. 102, which is considered to be the closest to practical use. The paper core is 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.

The compressive strength of these products is about 0.4 to 0.8 MPa (specific gravity: 80 to 20 KgZm ³ ) for paper products, and about 1 to L. 5 MPa for aluminum products (about lOOK). gZ m ³ ) (cell size: 10 to 1 lmm, sample size: 50 to 50 mm).

5. Folding / unfolding model

In the section “(2) Cylindrical folding structure with fold line” described above, several examples of the folding method in the axial direction of the cylinder were described. Fig. 108 to Fig. 109 show developments of these representatives 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.

Cutting the valley fold line (dotted line) in Fig. 108 and joining A and B together to produce a cylinder results in a structure consisting of hexagonal members. By replacing the hexagonal member with a narrow plate, a truss structure that can expand and contract in the axial direction can be manufactured.

Fig. 109 is an explanatory view of an application example of a spiral-shaped cylindrical folding line structure, Fig. 109A is a development view, and Fig. 109B is configured based on Fig. 109A. Telescopic inflatable construction It is a figure showing structure. -In view of the above research results, the present invention has the following content (1) as an issue.

(1) A new folding line for a structure with folding lines, in which the wall-shaped structure is divided into polygonal flat walls by a large number of folding lines, and the folding lines at the boundaries between the divided flat walls can be folded. And a novel folding line-equipped structure using the novel folding line, a novel folding method, and a novel folding line forming mold and a folding line forming method. DISCLOSURE OF THE INVENTION Next, the present invention which has solved the above-mentioned problems will be described. Elements of the present invention are denoted by katakana in order to facilitate correspondence with the elements of the embodiments described later. Add the enclosed items.

The reason why the present invention is described in correspondence with reference numerals in the embodiments described later 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-mentioned problems, a structure with a folding line according to the first invention is characterized by comprising the following constituent requirements (A 01) to (A 05):

(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and the outer sides of the respective parts (P; P1, P2; P1 to P5) Linear fold lines having linear part connection parts connected to each other and foldable along the linear part connection parts

(M, V) provided with a fold line, wherein the fold line (M, V) is a plurality of mountain fold lines where the one surface side is a mountain fold when viewed from one surface side of the fold line structure. (M) and the fold line structure having at least one valley fold line,

(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 valley fold lines intersecting at one node The plurality of fold lines (M, V) formed so that the difference from

(A 03) The first mountain fold line (Ml) and the second mountain fold line (M2 ) And the third fold line (M3) is disposed between the first fold line (Ml) and the second fold line (M2) and opposite to the third fold line (M3). A plurality of fold lines (Ml to M3, VI) having one node and four fold lines formed by the first valley fold line (VI) arranged on the side

(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 (Ml) or the second mountain fold line (M2) When one mountain fold line forms an angle with the X-axis, α, and the other mountain fold line forms an angle with the first valley fold line (VI), α = α. The plurality of folding lines (Μ1 to Μ3, VI),

(# 05) The structure with a fold line having the quadrilateral parts (Ρ; Ρ1, Ρ2; Ρ1 to Ρ5) other than a parallelogram.

(Operation of the first invention)

In the structure with a folding line according to the first aspect of the present invention, the node is defined as the origin ο, the X-axis is taken in the direction of the extension of the third folding line (Μ3), and the first folding line ( Ml) or one of the second mountain fold lines (M2) has an angle a with the X axis, and the other mountain fold line has an angle with the first valley fold line (VI). , A plurality of polygonal parts (Ρ; Ρ1, Ρ2; Ρ1 to Ρ5) are formed by the plurality of fold lines (Μ, V) formed so that α = τ ”. For this reason, the structure with a fold 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 a folding line has parts (Ρ; Ρ1, Ρ2; Ρ1 to Ρ5) having a shape (a quadrilateral other than a parallelogram) different from the conventional shape, In a small folded state and a large extended state, a structure with a fold line different from the conventional shape can be manufactured.

(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 configuration requirement (Α06):

(Α06) The part and the part connection part provided with the fold line are formed by separate members. The above-mentioned structure with a folding line.

(Operation of Embodiment 1 of First Invention)

In the structure with a folding line according to the first embodiment of the first invention having the above configuration, since the part and the part connection part provided with the folding line are formed by different members, for example, It can be made of a rigid thin plate such as a metal plate, and the part connection part can be made of a hinge member. Therefore, a structure with a strong folding line can be provided.

(Embodiment 2 of the first invention)

The structure with a folding 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 a one-piece molded product with the folding line, the structure with the folding line is easily manufactured by integral molding. be able to. The fold line can be formed at the same time as molding.However, when the structure with a fold line is a sheet-like member, the fold line may be formed on an integrally formed sheet-like member. It is possible.

(Second invention)

The structure with a folding line according to the second invention is characterized by having the following constituent requirements (A01) to (A04), (A08).

(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and the outer sides of each of the packs (P; P1, P2; P1 to P5) A fold line structure having a linear part connection portion connected to each other and having a linear fold line foldable along the linear part connection portion, wherein the fold line is a fold line. A fold line structure 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 (V) which form a valley fold when viewed from one surface side of the line structure;

(A02) A plurality of nodes which are intersections of the mountain fold line and the valley fold line are arranged at predetermined intervals. The plurality of fold lines (M, V) formed so that the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is 2;

(A03) First mountain fold line (Ml), second mountain fold line (M2) and third mountain fold line (M3) extending radially from one node, and first mountain fold line (Ml) and second A one-node four-fold line formed by a first valley fold line (VI) arranged between the mountain fold lines (M2) and opposite to the third mountain fold line (M3); Multiple fold lines (Ml to M3, VI),

(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 (Ml) or the second mountain fold line (M2) When one mountain fold line forms an angle with the X-axis, α, and the other mountain fold line forms an angle with the first valley fold line (VI), α = α. The plurality of fold lines (Μ1 to Μ3, VI),

(A08) The foldable structure 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), the folded state is small and the shape 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 shape.

(Third invention)

A structure with a folding line according to a third invention is characterized by comprising the following constituent requirements (A01) to (A05), (A09),

(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and outer sides of the respective parts (P; P1, P2; P1 to P5) are mutually connected. A fold line having a linear part connection portion to be connected and a linear fold line foldable along the linear part connection portion, wherein the fold line is a fold line. A structure having a folding 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 (V) forming a valley fold when viewed from one side of the structure; (A 02) 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 (M1 to M3, VI) formed so that

(A03) a first mountain fold line (Ml), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (Ml) and the second mountain fold line (Ml) A one-node four-fold line formed by a first valley fold line (VI) arranged 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 (Ml) or the second mountain fold line (M2) When one mountain fold line forms an angle with the X axis, α, and the other mountain fold line forms an angle with the first valley fold line (VI), α = ァ. The plurality of folding lines (Μ1 to Μ3, VI),

(A05) The folded structure with the folding line, comprising the above-mentioned parts (P; PI, 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 the surface is formed into a flat plate shape with irregularities. The above-mentioned structure with folding lines, which can be folded and extended in a flat plate shape so that the outer shape becomes a three-dimensional structure further reduced in a state of being completely folded along the folding lines and the valley folding lines.

(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 quadrangular pads (P; P1, P2; P1 to P5) other than the parallelogram. Also, in the extended state of the large external shape, it is possible to manufacture a flat plate-like folded line structure having a shape different from that of the conventional flat plate-shaped folded line structure.

(4th invention)

The structure with a folding line according to the fourth invention is characterized by comprising the following constituent requirements (A01) to (A04), (A010) and (A011).

(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and the respective parts (P; P 1, P 2; P 1 to P 5) having a linear part connection part connecting outer sides thereof to each other, and having a linear part foldable along the linear part connection part. A fold line provided with a fold line, wherein the fold line is a plurality of mountain fold lines (M) and a valley fold where the one surface side is a mountain fold when viewed from one surface side of the structure with a fold line. The fold line structure having at least one valley fold line (V);

(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 2. The plurality of fold lines (M1 to M3, VI) formed as described above,

(A03) a first mountain fold line (Ml), a second mountain fold line (M2) and a third mountain fold line (M3) extending radially from one node, and the first mountain fold line (Ml) and the second mountain fold line (Ml) A one-node four-fold line formed by a first valley fold line (VI) arranged between the mountain fold lines (M2) and opposite to the third mountain fold line (M3); Multiple fold lines (Ml to M3, VI),

(A04) The node is defined as the origin O, the X-axis is taken in the direction of extension of the third mountain fold line (M3), and the first mountain fold line (Ml) or the second mountain fold line (M2) When one mountain fold line forms an angle with the X axis as α and the other mountain fold line forms an angle with the first valley fold line (VI) as Τ, α = Τ. The plurality of folding lines (Μ1 to Μ3, VI),

(A010) A cylindrical wall or conical wall is formed when the fold line is extended, and a cylindrical wall or cone having an uneven outer shape is formed when the fold line is bent in accordance with the mountain fold line and the valley fold line of the fold line. Forming a wall, and forming a thick cylindrical wall or conical wall 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 (Μ1 to Μ3, VI) that are continuous in a plane perpendicular to the axis of the cylindrical wall or the conical wall.

(Operation of the fourth invention)

The structure with the folding line of the fourth invention having the above configuration has a plurality of folding lines (Μ1 to Μ3, VI) continuous in a plane perpendicular to the axis of the cylindrical wall or the conical wall, so that the outer shape is In the small folded state and large extended state, the structure differs from the conventional structure with fold lines. A cylindrical or conical folding line-shaped structure having a different shape can be manufactured. (Fifth invention)

The structure with a folding line according to the fifth invention is characterized by comprising the following constituent requirements (A01) to (A04), (A012), and (A013).

(A01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and outer sides of the respective parts (P; P1, P2; P1 to P5) are mutually connected. A fold line having a linear part connection portion to be connected and a linear fold line foldable along the linear part connection portion, wherein the fold line is a fold line. A structure having a folding 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 (V) forming a valley fold when viewed from one side of the structure;

(A03) First mountain fold line (Ml), second mountain fold line (M2) and third mountain fold line (M3) extending radially from one node, and the first mountain fold line (Ml) and second A one-node four-fold line formed by a first valley fold line (VI) arranged between the mountain fold lines (M2) and opposite to the third mountain fold line (M3); Multiple fold lines (Ml to M3, VI),

(A04) The node is defined as the origin O, the X axis is taken in the direction of extension of the third mountain fold line (M3), and the first mountain fold line (Ml) or the second mountain fold line (M2) 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 (VI), α = α. The plurality of fold lines (Μ1 to Μ3, VI),

(A012) A cylindrical wall or cone having a cylindrical wall or a conical wall when the fold line is extended, and a concave or convex shape having a reduced outer shape when the fold line is bent along the mountain fold line and the valley fold line of the fold line. Forming a wall, and forming a thick cylindrical wall or conical wall having irregularities whose outer shape is further reduced in a completely folded state along the mountain fold line and the valley fold line; (A013) 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 fifth invention)

Since the structure with a folding line according to the fifth invention having the above-described configuration has polygonal parts (P; P1, P2; P1 to P5) of four or more quadrilaterals, the folded shape and the outer shape are small. In a stretched state with a large fold line and a large external shape, a cylindrical or conical fold line structure having a different shape from the conventional fold line structure can be manufactured.

(Sixth invention)

The structure with a folding line according to the sixth invention is characterized by having the following constituent requirements (B01) to (B04).

(B01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and the outer sides of the respective parts (P; P1, P2; P1 to P5) are mutually connected. A fold line having a linear part connection portion to be connected and a linear fold line foldable along the linear part connection portion, wherein the fold line is a fold line. A structure having a folding 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 (V) forming a valley fold when viewed from one side of the structure;

(B02) 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 2. The plurality of fold lines (M1 to M4, VI, V2) formed as described above,

(B03) a first mountain fold line (Ml), 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 third fold line formed between the first fold line (Ml) and the second fold line (M2) and opposite to the third fold line (M3) and the fourth fold line (M4). The first fold line (M1) and the second fold line (M2) are located between the first valley fold line (VI) and the third fold line (M3) and the fourth fold line (M4). ) And a second valley fold line (Ml) and a fourth fold fold line (M4) adjacent to the second valley fold line (M4). M2) and the plurality of fold lines (M1 to M4, VI, V2) having one node and six fold lines in which the third mountain fold line (M3) is arranged adjacently; (B04) The node is the origin O, the X axis is taken in the direction of the extension of the first valley fold line (VI), and the first ridge fold line (Ml) and the second ridge fold line (M2) are Let α and be the angles formed by the 1-valley fold line (VI), respectively, and define the angles formed by the third mountain fold line (Μ3) and the fourth mountain fold line (Μ4) with the second valley fold line, respectively? "And <5, and when the angle between the X axis and the second valley fold line is Θ, the plurality of fold lines (Μ1 to Μ4 , VI, V2).

(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 defined as the origin Ο, the X-axis is taken in the direction of the extension of the first valley folding line (VI), and the first mountain folding line ( Ml) and the second mountain fold line (M2) form angles α and; 3 with the first valley fold line (VI), respectively, and the third mountain fold line (M3) and the fourth mountain fold line (M3) If M4) is the angle between the second valley fold line and T and δ, respectively, and the angle between the X axis and the second valley fold line is 0, then-α = 6-a + 6> The parts (折り; Ρ1, Ρ2; Ρ1 to Ρ5) having shapes different from those of the related art can be used by the plurality of folding lines (Μ1 to Μ4, VI, V2) formed as described above, and Each part (Ρ; Ρ1, Ρ2; Ρ1 to Ρ5) 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.

In addition, in the folded state and the extended state, it is possible to provide a structure with a folding line having a shape different from that of the related art.

(Embodiment 1 of the sixth invention)

The structure with a fold line according to the first embodiment of the sixth invention is characterized in that, in the sixth invention, the following configuration requirement (Β05) is provided:

(Β05) When the fold line is extended, it becomes a flat plate, and when it is bent along the mountain fold line (Μ) and the valley fold line, the outer shape is reduced and it becomes a flat plate with uneven surface, In the state of being completely folded along the mountain fold line (Μ) and the valley fold line, the structure with the fold line that can be folded and extended into a flat plate shape so that the outer shape becomes a three-dimensional structure further reduced. .

(Operation of the First Embodiment of the Sixth Invention) In the structure with a folding line according to the first embodiment of the sixth invention having the above configuration, a flat plate-like structure with a folding line having a shape different from the conventional one is provided in a folded state having a small outer shape and an extended state having a large outer shape. can do.

(Embodiment 2 of the sixth invention)

The structure with a folding line according to the 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 concavities and convexities in which a cylindrical wall or a conical wall is formed when the fold line is extended, and the outer shape is reduced when the fold line is bent along the mountain fold line (M) and the valley fold line. Or, in the state of being completely folded along the mountain fold line (M) and the valley fold line, the outer shape is further reduced to form a thick cylindrical wall or a conical wall having irregularities with a further reduced unevenness. The extensible structure with a fold line.

(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, in the folded state having a small outer shape and the extended state having a large outer shape, a cylindrical or conical folding line structure having a shape different from the conventional shape is provided. Things can be provided.

(Seventh invention)

The structure with a folding line according to the seventh invention is characterized by having the following constituent requirements (C01) to (C04).

(C01) A plurality of polygonal parts (P; Pl, P2; P1 to P5) and outer sides of the respective parts (P; P1, P2; P1 to P5) are mutually connected. A fold line having a linear part connection portion to be connected and a linear fold line foldable along the linear part connection portion, wherein the fold line is a fold line. A structure having a folding 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 (V) forming a valley fold when viewed from one side of the structure;

(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 2. The plurality of fold lines (M1 to M4, VI, V2) formed as described above, (C03) Forming a cylindrical wall in a state where the fold line is extended, and forming a cylindrical wall having irregularities whose outer shape is reduced in a state where the fold line is bent according to a mountain fold line and a valley fold line of the fold line, The structure with a fold line, which forms a thick cylindrical wall 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,

(C04) The structure with a fold line having a fold line that forms a closed polygon that is continuous along a plane perpendicular to the axis of the cylindrical wall.

(Operation of the seventh invention)

The structure with a folding line according to the seventh invention having the above configuration has a plurality of folding lines (M1 to M4, VI, V2) that are continuous in a plane perpendicular to the axis of the cylindrical wall. In the extended state, and in the extended state of the outer shape, a cylindrical folded line structure having a shape different from that of the conventional folded line structure can be manufactured.

(Eighth invention)

The structure with a folding line according to the eighth invention is characterized by comprising the following constituent requirements (C01) to (C03), (C05):

(C01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and outer sides of each of the packs (P; P1, P2; P1 to P5) A fold line structure having a linear part connection portion connected to each other and having a linear fold line foldable along the linear part connection portion, wherein the fold line is a fold line. A fold line structure 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 (V) which form a valley fold when viewed from one surface side of the line structure;

(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 2. The plurality of fold lines (M, V) formed as described above,

(C03) Forming a cylindrical wall in a state where the fold line is extended, and forming a cylindrical wall having irregularities whose outer shape is reduced in a state where the fold line is bent according to a mountain fold line and a valley fold line of the fold line, The structure with a fold line, which forms a thick cylindrical wall 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,

(C05) The part (P; P1, P2; P1 to P5) is a polygon with a quadrangle or more The structure with a folding line having a shape.

(Operation of the eighth invention)

In the structure with a folding line according to the eighth aspect of the present invention, the parts (P; P1, P2; P1 to P5) have a polygonal shape of a quadrangle or more, so that the outer shape is small. In the folded state and the extended state of the outer shape, a cylindrical fold line structure having a conventional triangular part (P; P1, P2; P1 to P'5) is different from a cylindrical structure with a different shape. A folded line structure can be manufactured.

(Ninth invention)

The foldable structure according to the ninth invention is characterized by having the following constituent requirements (C01) to (C03), (C06), and (C07).

(C01) A plurality of polygons (P; P1, P2; P1 to P5) and outer sides of each of the parts (P; P1, P2; P1 to P5) And a linear part connecting portion that connects the linear parts to each other, and provided with a linear folding line that can be folded along the linear part connecting portion. The structure with a fold line having a plurality of mountain fold lines (M) that form a mountain fold and one or more valley fold lines (V) that form a valley fold when viewed from one surface side of the structure with a fold line ,

(C03) When the fold line is extended, a cylindrical wall is formed, and when the fold line is bent according to the mountain fold line and the valley fold line, a cylindrical wall having an uneven outer shape is formed, and the mountain 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 fold lines are all formed along the spiral, and the parts (P; P1, P2

P1 to P5) are the above-mentioned folded line structure, which is only an obtuse triangle formed by dividing a parallelogram into two parts by a diagonal line;

(C07) A structure with a folding line having the above-mentioned structure, which has 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 a folding line according to a ninth aspect of the present invention, the folding lines are all formed along a spiral, and the parts (P; P1, P2; P1 to P5) are parallelograms. Of the conventional oblique angle triangular structure formed by dividing the oblique angle triangle into two parts by a diagonal line, the obtuse angle triangular part having one base angle of 35 ° or more (P; P 1, P 2 P1 to P5), with a conventional cylindrical oblique triangular part having a base angle of about 30 ° (P; P1, P2; P1 to P5) with a cylindrical folding line A cylindrical fold line structure having a different shape from the structure can be manufactured.

(10th invention)

The tenth aspect of the present invention is characterized in that the folding line structure has the following constituent requirements (D01) to (D03).

(D01) A plurality of polygonal parts (P; P1, P2; P1 to P5) and the outer sides of the respective parts (P; P1, P2; P1 to P5) are mutually connected. A fold line having a linear part connection portion to be connected and a linear fold line foldable along the linear part connection portion, wherein the fold line is a fold line. A structure having a folding 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 (V) forming a valley fold when viewed from one side of the structure;

(D02) 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 The plurality of fold lines (M, V) formed so that

(D03) When the fold line is extended, a conical wall is formed, and when the fold line is bent in accordance with the mountain fold line and the valley fold line, a conical wall having an unevenness whose outer shape is reduced is formed. The above-mentioned structure with a folding line, wherein the outer shape is further reduced in a state of being completely folded along the fold line and the valley fold line to form a thick conical wall having a protrusion.

(Operation of the tenth invention)

The structure with a folding line according to a tenth aspect of the present invention having the above-described structure, forms a conical wall in a state where the folding line is extended, and has an outer shape in a state where the folding line is bent according to a mountain fold line and a valley fold line of the fold line. Forming a conical wall having reduced irregularities, wherein the mountain fold line and the valley fold are formed. When completely folded along the line, a thick cone wall with a concave cT whose outer shape is further reduced is formed.

That is, the tenth aspect of the present invention can provide a foldable conical foldable structure which is not conventionally known.

(Embodiment 1 of the 10th Invention)-The structure with a folding line according to the embodiment 1 of the 10th invention has the following constitutional requirements (D04) and (D05) in the 10th invention. Characterized by

(D04) The first mountain fold line (Ml), the second mountain fold line (M2) and the third mountain fold line (M3), and the first mountain fold line (Ml) and the second mountain fold line (M2) ) And a first valley fold line (VI) arranged on the side opposite to the third mountain fold line (M3). M1 ~ M3, VI),

(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 (Ml) or the second mountain fold line (M2) When one mountain fold line forms an angle with the X-axis, α, and the other mountain fold line forms an angle with the first valley fold line (VI), Τ, α == α. The plurality of fold lines (Μ1 to Μ3, VI).

(Operation of the First Embodiment of the Tenth Invention)

In the structure with a folding line according to the first embodiment of the tenth aspect of the present invention having the above-described configuration, in the folded state having a small outer shape and the extended state having a large outer shape, a conical folding line structure which has not been conventionally known. Things can be provided.

(Embodiment 2 of the 10th invention)

The structure with a folding line according to the second embodiment of the tenth invention is characterized in that, in the tenth invention, the following structural requirements (D06) and (D07) are provided.

(D06) a first mountain fold line (Ml), 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 (Ml) and A first valley fold line (VI) formed between the second fold line (M2) and opposite to the third fold line (M3) and the fourth fold line (M4); Third fold line (M3) and fourth fold line (M4) and a second valley fold line (V2) arranged on the opposite side to the first fold line (Ml) and the second fold line (M2). 1-node 6-fold line where the 1st fold line (Ml) and 4th fold line (M4) are adjacent and the 2nd fold line (M2) and 3rd fold line (M3) are adjacent The plurality of fold lines (M1 to M4, VI, V2) having

(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 (VI), and the first mountain fold line (Ml) and the second mountain fold line (M2) are The angles formed by the 1-valley fold line (VI) are α and J3, 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 And <5, and when the angle between the X-axis and the second valley fold line (V2) is set to 0, the plurality of plurality formed so as to be 0−α = δ_ · τ + 0. Fold line (Μ1 ~ Μ4, VI, V2).

(Operation of the Second Embodiment 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, in the folded state having a small outer shape and the extended state having a large outer shape, a conical folding line structure which has not been conventionally known. Things can be provided.

(Embodiment 3 of the 10th invention)

The tenth embodiment of the present invention is characterized in that the structure with a folding line according to the tenth embodiment has the following constitutional requirements (D08) and (D09).

(D08) The first mountain fold line (Ml), the second mountain fold line (M2), the third mountain fold line (M3) and the fourth mountain fold line (M4), and the first mountain fold line (Ml) The first valley fold line (VI) formed between the second fold line (M2) and the second fold fold line (M2) and the third fold line (M3) A second valley fold line (V2), and the fourth fold fold line (M4) is between the first fold fold line (Ml) and the third fold fold line (M3), and The plurality of fold lines having one node and six fold lines arranged on the opposite side of the two fold lines (M2)

(M1-M4, VI, V2),

(D09) The node is the origin O, the X axis is taken in the direction of the extension of the fourth fold line (M4), and the first fold line (Ml) and the second fold line (M2) are The angles between the valley fold line (VI) and the valley fold line (VI) are 01 and 02, respectively. The angle between the mountain fold line (M3) and the second valley fold line (V2) is 03 and 04, the angle between the X axis and the first mountain fold line (Ml) is, and the X axis and the When the angle formed with the three-fold fold line (〜3) is 3 *, the plurality of fold lines (Μ1 to * 1 to S3) are formed such that α * = 02 + 04; Μ4, VI, V2).

(Operation of the Third Embodiment of the Tenth Invention)

In the structure with a folding line according to the third embodiment of the tenth aspect of the invention, it is possible to provide a conical folding line with a conventionally unknown shape in a folded state having a small outer shape and an extended state having a large outer shape.

(11th invention)

The structure with a folding line according to the eleventh invention is characterized by having the following constituent requirements (E01) to (Ε04).

(E01) The linear shape having a plurality of polygonal parts (Ρ; Ρ1, Ρ2; Ρ1 to Ρ5), and linear part connecting portions connecting outer sides of the respective parts to each other. A structure with a fold line provided with a linear fold line (V, V) that can be folded along the connection part, wherein the fold line (Μ, V) is on one side of the structure with a fold line The structure with folding lines (Α; Β; C ;, 有する) having a plurality of mountain fold lines (Μ) whose one surface side is a mountain fold and one or more valley fold lines (V) of a valley fold as viewed from above

(Ε02) A plurality of nodes that are intersections of the mountain fold line (Μ) and the valley fold line are arranged at predetermined intervals, and the number of mountain fold lines (Μ) and the number of valley fold lines intersecting at one node The plurality of fold lines (Μ, V) formed so that the difference between

(Ε03) The structure with a fold line formed of a sheet-like member having a fold line formed along a spiral

(Ε04) When the fold line is extended, the shape is a circular sheet, and when the fold line is bent according to the mountain fold line (Μ) and the valley fold line, the shape is a disc-shaped shape having a reduced outer shape. The structure with a fold line, which has a shape having a thickness with irregularities whose outer shape is further reduced when the fold line is completely folded along the mountain fold line (線) and the valley fold line.

(Operation of the 11th invention) The structure with a folding line according to the eleventh aspect of the present invention having the above-described structure, wherein 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 a plurality of fold lines (M, V) formed so that the difference between the number of lines (M) and the number of valley fold lines is 2, the outer shape is smaller and the outer shape is larger. In the extended state, it is possible to provide a foldable circular sheet-like structure with a folding line, which is not conventionally known.

(First and second inventions)

The mold for forming a folding line according to the 12th invention is characterized by having the following constitutional 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. A pair of folding line forming members provided with a plurality of mountain fold lines (M) and a valley fold where the one surface side forms a mountain fold when viewed from one surface side of the folding line forming mold. 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. A pair of fold line forming members having the plurality of fold lines (M, V) formed so that the difference between the number and the number of valley fold lines is 2;

(F02) A folded linear molding 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 12th invention)

In the folding line forming mold according to the twelfth aspect of the present invention having the above structure, the pair of folding line forming members are simultaneously folded in a state where the sheet-like member is sandwiched between the pair of folding line forming members. It is possible to form the mountain fold line (M) and the valley fold line required for the G-shaped member.

(13th invention)

A folding line forming method according to a thirteenth aspect of the present invention includes the following constituent features (G01) and (G02): (G OD A linear fold line that has a plurality of polygonal parts and a linear part connection part connecting the outer sides of the parts to each other, and is foldable along the linear part connection part. A fold line, wherein the fold line is a plurality of mountain fold lines (M) and a valley fold where the one surface side forms a mountain fold when viewed from one surface side of the fold line structure. And 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. A sheet member having a foldable integral structure 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 valley fold lines is two. A sheet-like member sandwiching step,

(G02) The pair of fold line forming members sandwiching the sheet-like member are simultaneously folded along the mountain fold line (M) and the valley fold line, and a fold line is formed on the sheet-like member. Forming fold line forming process.

(Operation of the thirteenth invention)

In the folding line forming method according to the thirteenth aspect having the above-described configuration, in the sheet-like member holding step, the sheet can be folded between the pair of folding line forming members having the plurality of folding lines (M, V). An integrated sheet-like member is sandwiched.

Next, in the folding line forming step, the pair of folding line forming members sandwiching the sheet-like member are simultaneously folded along the mountain fold line (M) and the valley fold line, and the sheet-like member is folded. To form a fold line.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a fold line explanatory diagram showing a typical example of a fold line, which is a straight line to be folded of origami or a folding structure, and a node, which is an intersection of a plurality of fold lines.

Figure 2 is an illustration of the folding structure called "Miuraorai", which was designed by Miura for deployment of space structures.

FIG. 3 is a diagram in which the horizontal fold lines shown in FIG. 2 are zigzag at equal angles.

Figure 4 shows a part (sector) of a disk formed by six sector elements with an apex angle of 2Θ. It is a figure showing an example of a fold line which can be folded. '

Fig. 5 is a view of the horizontal fold lines shown in Fig. 2 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 a diagram drawn with angle and symmetry.

FIG. 7 is a diagram illustrating a one-node four-fold line method, a one-node six-fold line method, and illustrates an example of a folding method considered by the present inventors.

FIG. 8 is a diagram 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 diagram for explaining the condition where both ends of the band plate are joined to form a cylinder when the band plate is folded along the fold line, and Fig. 9A shows the band plate and the fold line and the fold line. FIG. 9B is a diagram showing a change in the orientation of the reference axis when folded along the fold line shown in FIG. 9A.

FIG. 10 is an explanatory view of an example in which the above expression (5) is satisfied and the folding direction is the same as the folding direction (either the mountain fold or the valley fold). Figure showing the folding lines (1), (2), (3), and (4) of the strip in the folded state, FIG. 10B shows the state in the middle of folding, and FIG. 10C shows the state in the 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 hexagon along a folding line in the same folding direction (either a mountain fold or a valley fold). Shows the folding lines (1), (2), (3), (4), (5), and (6) of the strip in the unfolded state, and FIG. 11B shows the state of being folded FIG. 11C is a view showing a folded state. '

FIG. 12 is an explanatory view of an example in which the above formula (5) is satisfied and the folding direction is folded in a regular octagonal shape by a folding line having the same folding direction. FIG. 12A is a folding line of the expanded strip (1). , (2),..., (8), FIG. 12B is a diagram showing a state of being folded, and FIG. 12C is a diagram showing a state of being folded.

Fig. 13 shows that the above formula (5) is satisfied and the folding direction is alternately reversed. FIG. 13A is a diagram illustrating folding lines (1) to (12) of a strip in an unfolded state, and FIG. FIG. 13B to FIG. 13F are views showing a state of being folded, and FIG. 13G is a view showing a state of being folded.

Fig. 14 shows a typical development when the strip-shaped plate shown in Fig. 9A is bent at equal intervals by π · (ΖΝ-2) Ν in the same direction to form a square, and Ν = 6. FIG.

Fig. 15 is a trapezoidal element of inequality, which is twice as large as the angle between the mountain fold line and the horizontal fold line in Fig. 14 (ττΖ 3) as α = 27cZ 9) 3 = π Ζ 9 It is a development view of the constructed pseudo cylinder.

Fig. 16 introduces six sets of fold lines obtained by decomposing the 山 -axis mountain fold line of Fig. 14 into α π 山 3 mountain fold line I and β = π Ζ 6 valley fold line II. Fig. 16A is an exploded view of the cylinder produced by the above method. Fig. 16A is a developed view, and Fig. 16Β is a half-folded state of the folded cylinder produced when the both ends of the developed view of Fig. 16Α are joined together. FIG. 16C is a perspective view of the same as FIG. 16B, but viewed from a different direction.

Fig. 17 is a diagram in which points A and B in Fig. 14 are matched to remove the mountain fold from the horizontal fold line. A diamond pattern consisting of an isosceles triangle with base angle ext / 6 in the horizontal direction (( It is a development view of 1) to (3)).

Figure 18 is a developed view of a deformed diamond pattern composed of scalene triangular elements.

FIG. 19 is an explanatory view of a pseudo-cylindrical body having a development view that is symmetrical and foldable one by one with respect to a horizontal folding line, FIG. 19A is a development view, and FIG. FIG. 19C is a view showing a half-folded state of a folding cylinder manufactured when both ends of the exploded view of FIG. 9 are joined, and FIG. 19C is a view of the same thing as FIG.

FIG. 21 is a development view of a foldable cylindrical wall having a plurality of polygonal parts (flat walls) formed by folding lines.

Figure 22 shows a series of triangular split plates studied by Guest et al. The inventor of the present invention has shown in a development view a cylindrical structure in which the spiral (1) rises one step each time the connecting portion turns into a spiral and the circuit goes around once.

Fig. 23 corresponds to Fig. 17 in which the whole is inclined by 7 = 6c / 6, and three diagonal diamond patterns are formed.

FIG. 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. 243 is a drawing of both ends of the development views of FIG. 23 and FIG. 24A. FIG. 4 is a diagram showing a half-folded state of a folding cylinder manufactured when joined.

FIG. 25 is an explanatory view of a pseudo-cylindrical body k having a developed view obtained by inverting FIG. 14 from above. FIG. 25A is a developed view, and FIG. 25B is both ends of the developed view of FIG. 25A. FIG. 6 is a view showing a half-folded state of a folding cylinder manufactured when the two are joined.

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. 26 2 is a development view, and FIG. 26 2 is both ends of the development view of FIG. 26Α. FIG. 6 is a view showing a half-folded state of a folding cylinder manufactured when the two are joined.

FIG. 27 is a developed view in which FIG. 16 is inclined by πΖ6.

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 the figure. The angle (~ 0.193π) shown in Fig. 28 indicates the angle between this 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. Will be done.

FIG. 29 is an explanatory view of a spiral folding cylinder having a folding line that is a generalized version of FIG. 24. FIG. 29 2 is an expanded view, and FIG. 29 9 is an expanded view of FIG. 29Α. It is a figure which shows the half-folded state of the folding cylinder manufactured when both ends are joined.

FIG. 30 is a developed view in a case where the value of β is changed for each one of the six developed steps of FIG. 29 in three steps.

FIG. 31 is a development view of a repetitive spiral type obtained by reversing the spiral mountain fold line and the valley fold line of FIG. 29 step by step. This development can also be obtained by matching points Α and の in Fig. 16.

FIG. 32 is a view showing a portion cut by two parallel straight lines AB ′, C ′ D in the developed view of the cylindrical body shown in FIG. 21, wherein A and B ′ and D and C ′ are By connecting the left and right edges of Fig. 32 so that they overlap, a foldable cylinder is obtained. FIG.

Fig. 33 is an exploded view of a collapsible cylinder having arbitrary shaped quadrangular elements (parts).

FIG. 34 is an explanatory diagram of a method for maintaining continuity when both ends of the developed view are joined. Figure 35 shows the angular relationship between the fold lines satisfying the folding condition when the valley fold line is symmetrically inserted in the case of one node and six fold lines. FIG. 14 is an explanatory diagram of a folding condition in the case.

Fig. 36 shows the angle relationship between the folding lines satisfying the folding condition when the valley fold lines (4) and (6) are inserted alternately between the mountain fold lines (2), (3) and (5). FIG. 57 is an explanatory diagram of folding conditions in the case of FIGS. 56B and 57 described later.

Figure 37 shows the case of one node and four fold lines. The folding condition is obtained by the same procedure as above.

FIG. 38 is an enlarged view of a main part of the developed view in the case where the developed view of a cone whose main fold line is parallel to the outer side of the developed view is composed of N isosceles triangles having an apex angle of 2®.

Fig. 4 1 is an exploded view of a conical wall with a fold line when it is divided into a trapezoidal triangular element by a fold line, where Ν = 3, 2 Θ = πΖ9, α = πΖ 9, and δ = πΖ6. (6 * = approximately 0.06887C).

FIG. 42 is an exploded view of a conical wall with a folding line when it is divided into a trapezoidal triangular element by a folding line having an angle α at the upper right and an angle δ at the upper left at the point F in FIG. , a, and the values are the same as those in FIG.

FIG. 44 shows 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, 1 [= 6, * = 71 in FIG. 43; no 36, 2 Θ = π / Exhibition in case of 1 2 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 the folded conical wall having the developed view of FIG.

FIG. 46 is a development view of a conical wall with a folding line having a simple, spiral development view composed of three isosceles triangular elements.

FIG. 47 is a top view when the developed view of FIG. 46 is folded.

FIG. 48 is an explanatory diagram of a practical model obtained by deforming the model described in FIGS. 45 and 46. FIG. 48A is an explanatory diagram of the deforming method, and FIG. 48B is a diagram of FIG. 48A. FIG.

FIG. 49 is a view showing a state in which the figure AB GHF E formed by the folding line of FIG. 48A is sequentially folded at folding lines AF and BF, and FIG. Fig. 49B shows the state of rectangles ABFE and BGHF (light black portion; back side). Fig. 49B shows the state shown in Fig. 49A, and the mountain was further folded at B'F (original line segment BF). It is a figure showing a state after.

FIG. 50 is a view showing a portion corresponding to the first-stage band plate shown in FIG. 48A and a portion corresponding to the second-stage band plate.

FIG. 51 shows the case where N = 6, a + Y * = πΖ3, Y * = π / 6, and a = π6 in the conical wall with a fold line shown in FIGS. 48 to 50. Is an explanatory view of a pseudo-cone wall having a developed view (2Θ = πΖΖ8) of FIG. 51, wherein FIG. 51 1 is a developed view, and FIG. 51B is a half view of a folded conical wall having the developed view of FIG. It is a perspective view in the state where it folded. FIG. 52 shows the case where N = 6, a + ゅ * = vault 3, Y * = πΖ4, and a = π / 12 in the fold line conical wall having the fold lines shown in FIGS. 48 to 50. This is the development of (2 ® = π / 6).

FIG. 53 is a developed view when the number of steps in the developed view of FIG. 51 is reduced and the value of * is increased for each step.

Fig. 55 shows the second valley fold line in Fig. 50 in the opposite direction to that of the first tier at an angle FIG.

Figure 57 shows the expanded spiral (螺 = 6) obtained when 2 Θ = π Ζ 6, π / 6, and = π / 6.

FIG. 60 is an explanatory diagram of how to draw the development view of FIG. 44 described above.

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. 6 IB is a folded view having the exploded view of FIG. 61A. It is a perspective view of the state where the conical wall with a line was folded in half.

FIG. 63 is an explanatory diagram of the simplest folding method for origami.

In Fig. 69, the swing angle of the folding line of Zig / Zag in the radial direction is increased as it approaches the center. FIG. 69A is an enlarged view of a main part for explaining folding conditions, and FIG. 69B is an overall view of the disk-shaped folding structure with folding lines.

Fig. 70 shows the development of a disk-shaped folding structure with a fold line when the swing angle of the fold line of ZigZZag in the radial direction is increased toward the center and the fold line in the circumferential direction is also ZigZZag. FIG. 70A is an enlarged view of a main part for explaining folding conditions, and FIG. 70B is an overall view.

FIG. 74 is an explanatory diagram of fold lines when a circular film or a partial circular film (sector-shaped film) is folded in a radial direction and a circumferential direction along a conformal spiral.

FIG. 75 is an enlarged view of a main part of FIG. 74.

FIG. 76 is an explanatory view of folding conditions 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 a conformal spiral. FIG. 77 is an explanatory diagram of folding conditions when the main folding line is bent at an equal angle to radiation.

Figure 78 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 4 and the number of isosceles triangular elements N = (2n + 1 FIG. 6 is a diagram showing an example of a folded development view when m = 18 and A = 20 °.

Figure 79 shows an example in which two zigzag spirals (m = 2) are used as folding lines and folded around the center, where n = 4 and the number of isosceles triangular elements N = (2 n + 1 ) FIG. 78 is an example of a folded development view in the case of m = 18 and τ = 0 °, showing an example in which the angle of the fold line with respect to the radiation is different from that of FIG.

Figure 80 shows two zigzag spirals (m = 2) as fold lines and folds around the center. FIG. 9 is a diagram illustrating an example of folding, showing an example of a folded development view in a case where n = 10, the number of isosceles triangle elements N = (2n + 1) m = 42, and a = 0 °.

Fig. 8 1 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 triangular elements N = (2 n + 1 FIG. 7 is a diagram showing an example of a development view of a disc-shaped folded structure with a fold line when m = 18 and _T = 0 °.

Figure 85 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 = (2 n + 1 ) m = 6

Figure 86 shows an example in which three zigzag spirals (m = 3) are used as folding lines and folded around the center, where n = 8 and an isosceles triangular element N = (2n + 1 ) m = 5

Figure 87 shows an example of folding around a center with one zigzag spiral (m = l) as the folding line, where n = 10 and the number of isosceles triangle elements N = (2n + 1) A diagram showing an example of a folded development view when m = 21 and a = 0 °.

Figure 8 8 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 = (2 n + 1 FIG. 7 is a diagram showing an example of a development view of a disc-shaped folded structure with a fold line when m == 60 and a = 0 °.

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 (rn = 1 2). Fig. 93 is based on Fig. 77 described above, and is composed of two types of conformal spirals. It is a development view. The number of divisions Ν = 1 2, Θ ^ = π / 18 0, 0 ₂ = 2 9 兀 Z 1 8 ははは, and は is approximately 18 兀. When the developed view in Figure 93 is folded, it is wrapped around the center symmetrically up and down. The one shown in 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 development view of a circular thin plate in which mountain fold lines and valley fold lines are alternately provided. Fig. 95 shows 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 the fan-shaped portion between the adjacent mountain fold lines in FIG. 95 is removed. FIG. 97 is an explanatory view of the folding condition of the sheet-like member. FIG. 97Α is an expanded view before folding, and FIG. 97Β is a view showing a state where the sheet-like member is folded along the folding line of FIG. 97Α.

FIG. 98 is an explanatory diagram of DCC (duouble corrugated core), FIG. 98A is a developed view of 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.

Figure 100 is an explanatory diagram of the newly devised model of the core with a joint. Figure 100A is a developed view, and Figure 100B is a plan view of the developed view of Figure 100A in a half-folded state. Figure, Figure 100C is an external view of a three-dimensional view obtained by folding the developed view of Figure OA, and Figure 101 is an explanatory diagram of another model of a newly devised core with a joint, Figure 101A is a development view, Figure 101 is a plan view of the development view of Figure 101A in a half-folded state, and Figure 101C is a view of the development view of Figure 101A folded. It is an external view of a three-dimensional structure.

FIG. 102 shows another core devised by the present inventor that satisfies another folding condition of a core having a joint. FIG. 102A is a development view, and FIG. 102B is an enlarged view of a main part of FIG. 102A.

FIG. 105 is an explanatory view of a method for manufacturing a honeycomb core from one plate, FIG. 105A is a developed view, and FIG. 105B is a manufactured from a plate having the developed view of FIG. It is a figure of the honeycomb core that was done.

FIG. 106 is a view showing a folding mold for producing the core material shown in FIG. 103A.

Fig. 109 is an explanatory view of an application example of a spiral-shaped cylindrical folding line structure, Fig. 109A is a development view, and Fig. 109B is configured based on Fig. 109A. It is a figure which shows a stretchable inflatable structure.

FIG. 110 is a plan view of a folding line forming die according to Embodiment 1 of the present invention.

FIG. 11 is a perspective view of a sheet-like member on which a fold line is formed using the fold line forming die of FIG. FIG. 11 is an explanatory view of a folding line forming die according to a second embodiment of the present invention. One of a pair of flexible molds for sandwiching both sides of a sheet-like member forming a folding line is provided. It is a perspective view of a type | mold.

FIG. 13 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. FIG. 11B is a view showing a state in which the folding line forming mold is folded in two, and FIG. 11B is a view showing a state in which the folding line forming mold shown in FIG. 11A is folded.

FIG. 115 is an explanatory view of a sheet-like member in which a folding line is formed using the folding line forming mold shown in FIGS. 113 and 114, and FIG. 115A is a sheet in a half-folded state. FIG. 115B is a plan view of the state member in a completely folded state.

FIG. 116 is an explanatory view of the folded sheet-like member shown in FIG. 115B, FIG. 116A is a perspective view, and FIG. 116B is the folded sheet-like member shown in FIG. FIG. 3 is a perspective view of a flat sheet-shaped member adhered to one surface (lower surface) of the member.

FIG. 117 is a side view of a socket as a structure with a folding line according to Example 4 of the present invention.

FIG. 118 is a side sectional view of the pot pot of the fourth embodiment.

FIG. 119 is an explanatory view of the state in which the bottle of FIG. 117 is compressed in the axial direction (semi-folded state), FIG. 119A is a view showing the half-folded state, and FIG. FIG. 4 is a side view of a state in which the opening is covered with the opening almost completely folded.

FIG. 120 is an explanatory view of the method of manufacturing the pot potting A, showing a state in which a mold (a mold having a folding line forming surface) is opened.

FIG. 12 1 is an explanatory view of a method for manufacturing the 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 view showing a state where compressed air is blown into the inside of the raw tube of FIG.

FIG. 123 is an explanatory view of a pet bottle as a fifth embodiment of the folded line structure of the present invention, showing a folded line structure (pet bottle) formed along a spiral. FIG. 124 is an explanatory view of a pet bottle as a sixth embodiment of the folded line structure according to the present invention, showing a folded line structure (pet bottle) having a cylindrical wall formed along a spiral. It is.

FIG. 125 is a side view of a coffee can as a structure with a folding line according to a seventh embodiment of the present invention.

FIG. 126 is a side sectional view of the coffee can of the seventh embodiment.

Fig. 127 shows the coffee can of Fig. 126 compressed axially (semi-folded shape). FIG. 127A is a side view of the half-folded state, and FIG. 127B is a side view of the almost 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) arranged on the inner surface of a cylindrical member. FIG. FIG. 128B is a cross-sectional view in which a pair of inner first dies arranged as shown in FIG. 128B are inserted inside the cylindrical member. FIG. 128C is a cross-sectional plan view in which the inner second mold is inserted, and FIG. 128C is a plan view in which a force rod is inserted into the center of the inner first and second molds in FIG. 128B. Sectional view, Fig. 128D shows a state in which the inner mold is pushed outward by rotating the force rod of Fig. 128C and pushing the inner second mold outward. FIG.

Fig. 129 is an explanatory view of the method for manufacturing the coffee can A. Fig. 129A shows an outer mold with an inner mold (a mold having a folding line forming surface) set on the inner surface of the cylindrical member. FIG. 12B shows a state before K 2 is clamped, and FIG. 12B shows a state where the mold is clamped from the state of FIG. 12A.

FIG. 130 is an explanatory view of a coffee can as a foldable structure according to the eighth embodiment of the present invention, showing a foldable structure (coffee can) having a cylindrical wall formed along a spiral. is there.

FIG. 13 1 is an explanatory view of another embodiment of the method for producing the coffee can A. FIG. 13 is an explanatory view of a small container as a structure with a folding line according to the ninth embodiment of the present invention. FIG. 13A is a perspective view of a lid of the small container, and FIG. It is a perspective view of the state which carried out.

FIG. 13 is an explanatory view of the small container of the ninth embodiment, FIG. 13A is a perspective view of the folded small container, and FIG. FIG. 9B—10 9B line sectional view, FIG. 13C is a sectional view in a state where the small container of FIG. 13B is covered. FIG. 134 is an explanatory view of the manufacturing method of 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 view 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 FIG. 135 to FIG.

FIG. 13 is an explanatory view of a paper pack as a structure with a fold line according to Example 11 of the present invention.

FIG. 4 is a perspective view of a used state in which the paper pack is extended.

FIG. 140 is a view showing a state in which the paper pack of FIG. FIG. 141 shows the paper pack of FIG. 140 folded further. FIG. 142 is an exploded view of the paper pack shown in FIGS.

FIG. 144 is an explanatory view of a paper pack as a structure with a folding line according to Embodiment 12 of the present invention.

FIG. 144 shows a state in which the paper pack of FIG. 144 is being folded. FIG. 144 is a view showing a state in which the paper pack of FIG. 144 is further folded. FIG. 146 is an exploded view of the paper pack shown in FIG. 144 to FIG.

FIG. 147 is an explanatory diagram of a paper pack as a structure with a folding line according to Example 13 of the present invention.

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 the paper pack of FIG. 148 further folded. FIG. 150 is a developed view of the paper pack shown in FIGS.

FIG. 151 is an explanatory view 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. 15A is a side view, and FIG. FIG. 153 is an explanatory view of a pencil stand as a structure with a fold 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 view of a gusset (partition member inside a box) as a structure with a folding line according to Embodiment 17 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.

FIG. 157 is an explanatory view of a gusset (partitioning member inside the box) as a structure with a folding line according to Example 18 of the present invention, and is a perspective view of the gusset taken out of the paper box.

FIG. 158 is a developed view of the gusset of FIG.

FIG. 159 is an explanatory view of a gusset (box inner partition member) as a structure with a fold line according to Embodiment 19 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 of FIG.

FIG. 161 is a development view of the gusset of FIG. 159.

FIG. 162 is an explanatory view of a gusset (a box inner partition member) as a structure with a folding line according to Embodiment 20 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.

FIG. 165 is an explanatory view of the gusset (partition member inside the box) as a structure with a folding line according to Embodiment 21 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.

FIG. 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 folding passage force par having the developed view of FIG. 171, FIG. 170A is a perspective view of a half-folded state, and FIG. 170B is a state of a completely folded state. It is a perspective view.

FIG. 171 is a developed 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 the embodiment 24 of the present invention. FIG. 172 is a development view of a sheet-like member which is a material for manufacturing the lamp shade. FIG. 17B is a perspective view of a lamp shade formed by manufacturing a pseudo cone by joining the left and right sides of the sheet-like member of FIG. FIG. 173 is an explanatory diagram of a Christmas card as a structure with a fold line of Example 25 of the present invention, FIG. 173A is a plan view of a folded state of the Christmas card, and FIG. FIG. 173A is a plan view in a state where it is opened, and 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 fold line according to the embodiment 26 of the present invention. FIG. 174A is a perspective view of the hat, and FIG. FIG. 17C is a cross-sectional view taken along the line 1111B—1111B of FIG.

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 an arrow 1 1 2 of FIG. It is the figure seen from B. FIG. 176 is an explanatory view of a hat as a structure with a fold line according to Example 27 of the present invention. FIG. 176A is a perspective view of the hat, and FIG. 176B is a view of FIG. 1 13 B—1 13 B line sectional view, FIG. 176 C is a view as seen from the arrow 1 13 C of FIG.

FIG. 177 is an explanatory view of the hat of Example 27, FIG. 177A is a plan view of the hat in a folded state, and FIG. 177B is an arrow 1 1 4 of FIG. 177A. It is the figure seen from B. FIG. 178 is a perspective view of a wound cap 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 cap in a state further folded from the state of FIG. 179. FIG. 181 is an explanatory view of a method of manufacturing the roll-up type hat shown in FIGS. 178 to 180, and FIG. 18A is a development view of FIG. 1B is a developed view of the temporal region B, and FIG. FIG. 182 is an explanatory view of another manufacturing method of the wind hat shown in FIG. 178 to FIG. ' FIG. 183 is a perspective view of a winding tent as a structure with a folding line according to Example 29 of the present invention.

FIG. 184 is a perspective view of the winding tent of FIG. 183 in a state in which the tent is being folded. FIG. 185 is a perspective view of the tent further folded from the state of FIG.

FIG. 186 is an explanatory view of the method of manufacturing the coil-type tent shown in FIGS. 183 to 185. FIG. 186A shows a parabolic curved dome shape in an extended state. Fig. 186B is an expanded view of one of the parts formed when the tent is divided in the circumferential direction.Fig. 186B shows the connection between the end AB and the CD of Fig. 186A. FIG. 3 is a view showing a conical wall formed in FIG.

FIG. 187 is an explanatory view of a method of manufacturing the coil-type tent shown in FIGS. 183 to 185, and FIG. 187 shows a dome-shaped coil having a radius r1 in an extended state. Assuming that the coordinates of the center of the dome are r = 0 and j = 1, 2, ..., 10, the coordinates of the tent are radially divided into 10 equal parts, rj (rj = r IX (1 1 It is a figure which shows the shape of the part (conical wall) (j) formed at the time of dividing into 10 by the circle which has -j) / 10) as a radius. FIG. 188 is a diagram showing the part number (j) of FIG. 187, the shape and length Lj of the bus, and the inclination 0j.

Fig. 189 shows the parts (1), (2), ..., (10) shown in Figs. 187 and 188 divided into 16 parts in the circumferential direction. J: Explanation of the shape of J = 1, 2, ···, 10). Figure 189A shows each part (j) composed of 16 divided packets (J). Fig. 189B is a diagram showing the divided parts (J) connected in the radial direction.

FIG. 190 is a perspective view of a take-up type tent as a structure with a folding line according to Example 30 of the present invention.

FIG. 191 is a perspective view of the winding tent of FIG. 190 in a state in which the tent is being folded.

FIG. 192 is a perspective view of the tent in a state where the tent is further folded from the state of FIG. BEST MODE FOR CARRYING OUT THE INVENTION Next, specific examples (examples) of embodiments of the present invention will be described with reference to the drawings. However, the present invention is not limited to the following examples. Absent.

(Example 1)

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. I have. The flexible mold 2 has a plurality of rhombic parts P and a craft film 3 bonded to both surfaces of each part P in a state where the outer sides of the plurality of parts P are adjacent to each other. Adjacent outer sides of each of the parts P are connected by the craft film 3, and a foldable linear fold line is formed by the craft film 3 at the connection part (part connection part).

Nodes, which are intersections of the plurality of fold lines, are arranged at a predetermined interval, and a total of four fold lines intersect at one node. The fold line has a mountain fold line that forms a mountain fold and a valley fold line that forms a valley fold on the one surface side when viewed from one surface side of a 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 fold lines and one valley fold line intersect, or three fold lines The line intersects one valley fold line.

In the state of being folded and stacked along the opening / closing axis L: the flexible mold 2, 2, the mountain fold line and the valley fold line are formed to overlap.

The flexible mold, which is constructed by bonding a craft film to both sides of each part (each part, that is, each thin metal plate) P, will make the fold line once on the mountain fold line and the valley fold line. Can be easily folded in a mountain and a valley. Therefore, with a paper or resin sheet placed on the surface of the flexible mold on one side of the opening / closing axis L, When the folding mold is folded along the opening / closing axis L, the paper or the resin sheet or the like is sandwiched by a pair of exible molds. 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 resin sheet.

FIG. 11 is a perspective view of a paper or resin sheet on which a folding line is formed.

As can be seen from FIG. 11, the use of the folding line forming mold 1 shown in FIG. 110 makes it possible to easily form a folding line on a sheet-like member S such as paper or a resin sheet.

(Example 2)

FIG. 112 is an explanatory view of a folding line forming die according to a second embodiment of the present invention. One of a pair of flexible molds for sandwiching both sides of a sheet-like member forming a folding line is shown. It is a perspective view of a flexible mold.

In FIG. 12, a flexible mold 2 forming a folding line forming mold 1 according to a second embodiment of the present invention is formed by a plurality of diamond-shaped parts P, and each part P is located on the side of each part. They are rotatably connected by hinges Pa formed on the edges.

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. 114 is an explanatory view of the use state of the folding line forming die of FIG. 113, and FIG. 114A is a diagram showing a state in which the folding line forming mold is folded in two. FIG. 4 is a view showing a state in which the two-folded folding line forming mold shown in FIG.

In FIG. 13, 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. I have. The flexible mold 2 has a plurality of square parts P 1 and a parallelogram part P 2 and both sides of each of the parts P 1 and P 2 with the outer sides of the plurality of parts PI and P 2 adjacent to each other. And a craft film 3 adhered to the substrate. The smaller one of the interior angles of the parallelogram is 60 °.

When a sheet-like member such as a paper or a resin sheet is placed on the surface of the flexible mold 2 on one side of the opening / closing axis L and the folding line forming mold 1 is folded along the opening / closing axis L, the paper or resin is obtained. The sheets etc. are sandwiched by a pair of: flexible molds 2,2. In that state — a pair of overlapping flexible molds 2 and 2 are folded along the fold line to the state shown in Fig. 11A, and then to the state shown in Fig. 11B, a paper or resin sheet. The folding line can be easily formed on the sheet-like member S such as.

FIG. 115 is an explanatory view of a sheet-like member in which a fold line is formed by using the fold line forming mold shown in FIGS. 113 and 114, and FIG. 115A is a half-folded state. FIG. 11B is a plan view of the sheet-like member, showing a completely folded state.

The areas S1 and S2, and S3 of the sheet-like member S in the half-folded state shown in

54 joins in the fully folded state shown in FIG. 11B or FIG. Therefore

By applying an adhesive to any one of the joints S1 and S2 and any one of S3 and S4 at the time of folding, a strong core member can be formed. Fig. 1 1

6 Adhering the sheet S '(see Fig. 11-16) to one side (lower surface) or both sides of the folded sheet member S shown in A can produce a plate member with large compressive stress resistance. .

Although 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, the folding line forming mold has one sheet. It is possible to form a fold line in a sheet-like member using a 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 attracted to the other side, and the fold line forming member ( It is possible to form a fold line on the sheet member by folding the flexible mold.

In addition, the pair of folding line forming members are supported by separate support members, and the other folding line forming member is mechanically moved to the close contact position with respect to one folding line forming member. It is also possible to adopt a configuration in which it is detached. (Example 4)

FIG. 117 is a side view of a pet 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 pet bottle of the fourth embodiment.

FIG. 119 is an explanatory view of the state in which the pet pot of FIG. 117 is compressed in the axial direction (semi-folded state). FIG. 119A shows a half-folded state, and FIG. FIG. 4 is a side view of a state in which the opening is covered with a completely folded state.

In FIGS. 117 and 118, the pet pottor 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 A 1 has a number of mountain fold lines M (see solid line in FIG. 117) having convex outer surfaces and a number of valley folds having concave valleys. A line V (see the dotted line in FIG. 117) is formed. In FIG. 117 and FIG. 118, in the pet bottle A of the fourth embodiment, the part P, which is a part (enclosed) formed 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 mountain fold lines M intersecting at the nodes = 3 and the number of valley fold lines V = 1 and the difference is 2 (= 3-1).

When the cylindrical wall A1 of the PET bottle A of the fourth embodiment is compressed in the axial direction, it is folded along the folding lines M and V, and passes through the state of FIG. 119A and the state of FIG. 119B. Will be folded. The folded pet bottle attempts to return to its original shape (extended shape) due to the nature, but when folded in the state shown in Fig. 119B, the opening A 3 is closed with a cap C. However, when air is prevented from flowing into the inside of the bottle A, the bottle A is held in a folded state (the state shown in FIG. 12B). In this folded state, the space required to accommodate the cylindrical wall A 1 can be reduced to less than 1/3 of the state shown in FIGS. 117 and 118.

Therefore, it is necessary to recycle the used cylindrical wall A 1 of the pot pot A. The space required for storage of the product can be reduced.

FIG. 120 is an explanatory diagram of the method for manufacturing the pet bottle A, and shows a state in which a mold (a mold having a folding line forming surface) is opened.

FIG. 21 is an explanatory view of a method for manufacturing the pet bottle A, and shows a state in which the mold is closed and a tubular or bag-shaped raw tube (parison) is stretched in the mold.

In FIG. 120, the mold K includes a circular bottom mold K1, a middle mold K2a, K2a obtained by dividing a cylinder into two, and the intermediate molds K2a, K2a. It has an upper first mold K3a for clamping the upper end of the upper mold, 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 pipe B, and the die is clamped and the raw tube C is stretched 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 pet 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, a mountain fold line M or a valley fold line V can be formed on the outer wall of the pet bottle A.

(Example 5)

FIG. 123 is an explanatory view of a pet bottle as a fifth embodiment of the folded line structure of the present invention, showing a folded line structure (pet bottle) formed along a spiral. In the description of the fifth embodiment, components corresponding to the components of the fourth embodiment are denoted by the same reference numerals, and detailed description thereof will be omitted.

The fifth embodiment is different from the fourth embodiment in the following points, but is configured similarly to the fourth embodiment in other points.

In FIG. 123, the shape of a part P, which is a portion formed (enclosed) by the folding lines M and V, of the pet bottle A of the fifth embodiment is different from that of the fourth embodiment. That is, the shape of the part P of the fifth embodiment is trapezoidal as in the fourth embodiment, but the height of the trapezoid is smaller than that of the fourth embodiment. Further, the folding lines M and V of the fifth embodiment Has a fold line formed along the helix.

As in Example 5, a cylindrical wall having a fold line along a spiral (a structure with a cylindrical fold line) A 1 is folded down when compressed in the axial direction while being twisted, and the outer shape is reduced, and the torsion is reduced. While pulling in the axial direction, it expands and the outer shape expands.

(Example 6)

FIG. 124 is an explanatory view of a pet bottle as a sixth embodiment of the folded line structure of the present invention, showing a folded line structure (pet bottle) having a cylindrical wall formed along a spiral. It is.

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 is different from the fifth embodiment in the following points, but is configured similarly to the fifth embodiment in other points.

In FIG. 124, in the pet bottle A of the sixth embodiment, the shape of a part P which is a portion (enclosed) formed by the folding lines M and V is different from that of the fourth embodiment. That is, the shape of the part P of the sixth embodiment is trapezoidal as in the fifth embodiment, but the height of the trapezoid is higher than that of the fourth embodiment. The fold lines M and V of 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 of the embodiment. The tilt angle is about 45 °.

As in Example 6, a cylindrical wall (a structure with a cylindrical folding line) A1 having a folding line along a spiral with a large inclination angle is folded when it is compressed in the axial direction while being twisted, and its outer shape is changed. The size is smaller than that of the fifth embodiment, but requires a slightly larger force than the fifth embodiment when folded. Then, once folded, the cylindrical wall A 1 of the PET bottle is plastically deformed, so that the cylindrical wall A 1 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 the need to hook the opening A 3.

(Example 7)

FIG. 125 is a side view of a coffee can as a structure with a fold line according to Embodiment 7 of the present invention. is there.

FIG. 126 is a side sectional view of the coffee can of the seventh embodiment.

FIG. 127 is an explanatory view of the 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 semi-folded state, and FIG. It is a side view in the state where it was almost completely folded.

In FIGS. 125 and 126, the coffee can A has an aluminum or steel bottom wall A0, a cylindrical wall A1, and an upper wall A2. 7. It has the same shape as the cylindrical part of the pet bottle in Fig. 118. 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 concave valleys having concave outer surfaces. A fold line V (see a dotted line in FIG. 125) is formed.

In the coffee can A of the seventh embodiment, the part P, which is a portion (enclosed) formed 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 mountain fold lines M intersecting at the nodes = 3 and the number of valley fold lines V = 1 and the difference is 2 (= 3-1).

When the cylindrical wall A1 of the coffee can A of Example 7 is compressed in the axial direction, it is folded along the folding lines M and V, and is folded through the state shown in FIG. Plastically deformed.

For thin-walled cans such as coffee cans, if a pattern as shown in Fig. 33 is provided on the outer periphery of the central part in the axial direction, if the coffee can is twisted at the time of disposal, the folding line will extend from the pattern as a starting point. And 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) arranged on the inner surface of a cylindrical member. FIG. FIG. 128B is a cross-sectional view in which a pair of inner first dies arranged as shown is inserted inside the cylindrical member, and FIG. 128B is a pair of inner first dies of FIG. 128A. Fig. 128C is a plan sectional view with the inner second mold inserted, and the force is applied to the center of the inner first and second molds in Fig. 128B. Fig. 128D is a plan cross-sectional view with the mrod inserted.The cam rod shown in Fig. 128C is rotated and the inner second mold is pushed outward, and the inner first and second molds are shown. FIG. 5 is a diagram showing a state in which is pushed outward.

The inner mold K 1 shown in FIGS. 128 and 129 has a pair of inner first molds K la, K la arranged to face each other, and a pair of inner second molds It has a mold K lb, K lb and a cam rod K lc inserted between the inner first and second molds K la, K la, K 1b, K lb. On the outer surface of the inner first and second molds K 1 a, K la, lb, K lb, a mountain fold line of the can A shown in FIGS. An uneven surface (not shown) forming M and valley fold line V is formed. Further, 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 has The uneven surface (not shown) that forms the mountain fold line M and the valley fold line V of the coffee can A shown in FIG. 125 and FIG. 126 is formed.

When the inner mold K1 is set inside the aluminum cylindrical member that is the material for manufacturing the coffee can A, as shown in Fig. 128C, and the cam rod Klc is rotated 90 ° in that state. The inner first and second molds K1a, Kla, Klb, and Klb are pushed outward to the state shown in FIG. 128D.

In this state, the outer mold K2 of Fig. 12A is clamped to form the state of Fig. 12B, so that the folding lines M and V shown in Fig. 12 and Fig. 12 are formed. Coffee can A can be manufactured.

The inner first and second molds Kla, Kla, Klb, and Klb of the inner mold K1 have air vents for discharging air in recesses formed on the outer surfaces thereof. By forming a hole (not shown) between the concave portion on the outer surface and the inner surface, molding of the coffee can A can be easily performed. (Example 8)

In the description of the eighth embodiment, components corresponding to the components of the seventh embodiment are denoted by the same reference numerals, and 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, the coffee can A of Example 8 has a part P, which is a portion (enclosed) formed by the folding lines M and V, formed along a spiral having an inclination angle of 45 °. I have.

As in Example 8, a cylindrical wall (structure with a cylindrical folding line) A1 having a fold line along a spiral having an inclination angle of 20 ° to 30 ° or more is twisted in the axial direction while twisting. When compressed, it is folded and its outer shape becomes smaller, and once it is folded, the cylindrical wall A 1 of the coffee can A plastically deforms, so that the cylindrical wall A 1 does not automatically return to its original shape. For this reason, when coffee can A is used, it is compressed and folded in the axial direction while being twisted, thereby maintaining a small folded state.

FIG. 13 1 is an explanatory view of another embodiment of the method for producing the coffee can A. In Fig. 13 1, a state in which an inner mold K 1 is set inside a cylindrical wall A 1 having a bottom wall AO is fixed to the upper end of the liquid container V, and the cylindrical wall A 1 is accommodated in the liquid container V. Fill the liquid container V with the liquid. The tube T is connected to the upper end of the liquid container V, and the liquid is also filled inside the tube T.

In this state, when an impact pressure is applied to the liquid in the tube T by the piston P, a fold line is formed on the cylindrical wall A 1 according to the unevenness of the surface of the inner mold K 1.

(Example 9)

FIG. 13 is an explanatory view of a small container as a structure with a folding line according to the ninth embodiment of the present invention. FIG. 13A is a perspective view of a lid of the small container, and FIG. It is a perspective view of the state which carried out. FIG. 13 is an explanatory view of the small container of the ninth embodiment, FIG. 13A is a perspective view of the folded small container, and FIG. FIG. 9B—10 9B line sectional view, FIG. 13C is a sectional view in a state where the small container of FIG. 13B is covered. In FIGS. 13 and 13, the small container B (see FIG. 13B) has a circular bottom plate 6, an upper end plate 7, and a foldable pseudo-cylindrical wall 8. The upper plate 7 has a circular outer shape, and a hexagonal opening 7a is formed at the center.

As shown in FIG. 13B, 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.

In FIGS. 13B and 13B, the pseudo-cylindrical wall 8 of the small container B of the ninth embodiment includes a plurality of parts P 1 and P 1, which are portions (enclosed) formed by the folding lines M and V.ぴ Has P2. Part P 1 is triangular and one side is foldably connected to bottom plate 6, and part P 2 is triangular and one side is foldably connected to 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 P 1, and the mountain fold line M, M,… forms a hexagon. Connected to the address.

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 to the endless.

The endlessly connected mountain fold lines M, M,... Form 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 obtain the state shown in FIGS. 13A and 13B. Become. A lid 9 (see FIGS. 13A and 13C) for opening and closing the hexagonal opening 7a at the upper end of the small container B is provided on the circular upper plate 9a and the outer periphery of the upper plate 9a. A short cylindrical wall 9b provided, a pair of protruding portions 9c, 9c extending downward from a lower end of the cylindrical wall 9b, and a lower end locking portion which is provided at a lower end of the protruding portions 9c, 9c and protrudes inward. It has a portion 9d and an upper locking portion 9e that projects slightly on the inner surface of the cylindrical wall 9b above the projections 9c, 9c.

When not using the small container B, fold the small container B as shown in Figure 13B. When the cylindrical wall 9b of the lid 9 is fitted to the upper end plate 7 of the small container B in the folded state, the locking portions 9d, 9d lock the lower surface of the bottom plate 6, and the locking portion 9 e and 9 e lock the lower surface of the upper plate 7. In this state, since the volumes 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 small container B is extended (see FIG. 13B) and the cylindrical wall 9 b of the lid 9 is fitted to the upper end plate 7 of the small container B, the locking portion 9 e and 9 e are 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 objects contained in the small container B can be shielded from the outside air to protect the contents contained therein.

FIG. 134 is an explanatory view of the manufacturing method of 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 an upper mold 11a, lib and a lower mold 11c. The upper molds 11a and 11b are formed along the dividing lines L1 and L2 formed along the mountain fold lines M and M arranged at positions facing each other in Fig. 13B. Divided type.

A resin is injected into the captivity 12 formed in the mold 11 and cured to form a small container B, and then the upper molds 11a and 11b are opened. Thereafter, when the small container B formed on the lower mold 11 c is pulled upward while being twisted, the formed small container B can be easily taken out from the lower mold 11 C.

(Example 10)

FIG. 135 is an explanatory view of a paper pack as a structure with a folding line according to Example 10 of the present invention.

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 in which the paper pack of FIG. FIG. 138 is a developed view of the paper pack shown in FIG. 135 to FIG.

FIG. 138 is an expanded view of a paper pack that is folded in two steps by a folding line that satisfies the folding conditions, and the dashed line in the vertical direction is the mountain fold line in the state of FIG. Fig. 1 3 8 The left and right side edges are glued together to form a cylinder, and then folded along the vertical mountain fold line M and the valley fold line V to obtain the paper pack shown in Fig. 135. Packs).

By folding the paper pack of FIG. 135 along the oblique mountain fold line M and the valley fold line V, the state of FIG. 135 can be folded to the state of FIG.

(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 in which the paper pack is extended.

FIG. 140 is a view showing a state in which the paper pack of FIG. FIG. 141 shows a state in which the paper pack of FIG. 140 is further folded. FIG. 142 is an exploded view of the paper pack shown in FIGS.

Fig. 142 is an expanded view of a paper pack that is folded in four steps along a folding line that satisfies the folding conditions, which is different from the expanded view of Fig. 138 that is folded in two steps. The one-dot chain line in the vertical direction in FIG. 142 is the mountain fold line in the state of H139. The left and right side edges of Fig. 14 2 are glued together to form a cylinder, and then folded along the horizontal mountain fold line M and valley fold line V to obtain the paper shown in Fig. 13 9 Packs (paper packs in use) can be configured. Other configurations and operations are the same as those in the tenth embodiment.

(Example 12)

FIG. 144 is an explanatory view of a paper pack as a structure with a folding line according to Embodiment 12 of the present invention, and is a perspective view of a used state in which the paper pack is extended.

FIG. 146 is an exploded view of a paper pack that is folded in four steps by a folding line that satisfies the folding condition, in which vertical mountain fold lines M are formed alternately inclined. The left and right side edges of Fig. 144 are glued together to form a tube, and then folded along the mountain fold line M and the valley fold line V to obtain the paper pack shown in Fig. 144 (the paper pack in use). ) Can be. Other configurations and operations are the same as those of the above-described embodiment 11. (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.

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. A vertical mountain fold line M is formed to be inclined in the same direction. The left and right side edges of Fig. 150 are glued to form a cylinder, and then folded along the mountain fold line M and the valley fold line V to obtain the paper pack (Fig. Paper pack). As can be seen from Fig. 147, the paper pack is twisted in a certain direction from the upper end to the lower end.By changing the direction in which the paper pack is twisted, it can be easily extended or folded into the use state. it can. Other configurations and operations are the same as those of the embodiment 12.

(Example 14)

FIG. 151 is an explanatory view 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 pet bottle A of the fifth embodiment, and the opening at the upper end is opened and closed by a 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 T 1 is provided with a suction valve V 1, and the discharge tube T 2 is provided with a discharge valve V 2. When the pump chamber A is contracted with the cap C closed, V 1 is closed and V 2 is opened, and the fluid in the pump chamber A is discharged from the discharge tube T 2. When the pump chamber A is expanded, VI opens and V2 closes, and fluid flows into the pump chamber A from the suction tube T1. The pump of the fourth embodiment can be used for refueling 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. 15A is a side view, and FIG.

In FIG. 152, the trash can A is formed of a cylinder 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. are doing. An opening A2a for introducing refuse is formed in the upper wall A2. The cylindrical wall A1 of the trash can A is formed of a plurality of trapezoidal traps P which are inclined by a mountain fold line M and a valley fold line V. Since the part P is formed along an inclined spiral of about 45 °, the extended trash can A can maintain its state (shape).

(Example 16)

FIG. 153 is an explanatory view 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. 15 3, the brush stand A is composed of a cylindrical body with a folding line made of the paper or resin, and the bottom wall A 0, the cylindrical wall A 1, and the upper wall A 2 Yes. An opening A2a for inserting a writing implement such as a pencil is formed in the upper wall A2. The cylindrical wall A 1 of the brush stand A is formed by a plurality of oblique trapezoidal parts P formed by a mountain fold line M and a valley fold line V. The part? Is formed along the spiral of about 45 °, so that the brush stand A in the extended state can maintain its shape.

(Example 17)

In FIG. 154, the paper box C contains the guesses G. Guess G is produced by folding along the mountain fold line M and the valley fold line V in the developed view shown in Figure 156. The gusset G of Example 17 has two rows of rising walls G 1 formed therein, and the rising walls G 1 are formed as partition walls. The storage item support surface G2 formed between the rising walls G1 is a surface for supporting storage items such as buns and crockies, and is inclined in the seventeenth embodiment.

Since Guess G is made of one piece of paper, the time required for setting work is shortened as compared to the case where a Guess composed of multiple sheets of paper is set in paper box C. be able to.

(Example 18)

FIG. 158 is a developed view of the gusset of FIG.

The gusset G in FIG. 157 and FIG. 158 has a wall G1 that rises up on both sides of the gusset G in Example 17 described above. Since the rising walls G 1 on both sides of the gusset G are supported by the side walls of the paper box C when housed in the paper box C (not shown), the position of the guess G in the paper box C is stabilized, and Reinforce the rigidity of the Guess's containment support surface G2.

(Example 19)

FIG. 161 is a developed view of the guess of FIG. 159.

In FIG. 159, the paper box C contains the guesses G. The storage material support surface G2 formed between the rising wall G1 of the guess G is a surface for supporting storage items such as buns and cookies. (Parallel to the bottom surface). This embodiment 19 has a configuration in which the rising portion extends in a direction perpendicular to the rising wall G 1. A gall wall G 3 is provided. The storage item support surface G2 is formed so as to be surrounded by the rising walls Gl and G2.

Since the guesses G in Example 19 are made of one sheet of paper, the guesses G composed of a plurality of papers are required for setting work in comparison with the case of setting the gussets in a paper box C. Time can be shortened.

(Example 20)

FIG. 164 is a developed view of the gusset of FIG.

In FIG. 16 3, the 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 embodiment 20 is formed horizontally (parallel to the bottom surface of the paper box C).

Since the guesses G of Example 20 are also made of one sheet of paper, it is necessary for the work of setting a guess composed of a plurality of sheets of paper in comparison with the case of setting the gusset composed of a plurality of papers in the paper box C. Time can be shortened.

(Example 21)

FIG. 167 is a developed view of the gusset of FIG.

In FIG. 165, a paper box C contains a guess G. The rising walls G 1 and G 3 of the gusset G are formed so as to extend in directions perpendicular to each other, and a stored article support surface G 2 is formed between the rising walls G 1 and G 3. . The storage object support surface G2 is a surface for supporting storage items such as buns and woodpeckers. (Parallel to the bottom of paper box C).

The gusset G of the embodiment 21 is formed by bending a single square sheet of paper along a diagonal fold line M and a valley fold line V. Since this embodiment 21 is also made of one sheet of paper, the time required for the setting work is shortened as compared with the case where a guess made of a plurality of sheets is set in the paper box C. can do.

(Example 22)

FIG. 168 is an explanatory view of the folding passage force par, FIG. 168A is a perspective view in a half-folded state, and FIG. 168B is a perspective view in a completely folded state.

The folding passage force par 16 shown in Fig. 168 is a member that is used to cover the upper and lower sides of the passage through which people pass, and is especially used between railway cars. Suitable for use in places where there is no fixed distance between the structures at both ends of the passage, such as the passage at the connecting part of the building or the passage between the terminal pledge at the airport and the entrance to the aircraft. Is done.

The foldable passage cover 16 is a member formed by attaching a fold line to an elastic and flexible sheet-like member, and is foldable at the fold line portion. In the half-folded state, the foldable passage cover 16 has the shape shown in Fig. 168, and is arranged along the passage so as to cover the upper part of the passage and the left and right sides. Fixed to In the exploded view of the foldable passage cover 16 shown in FIG. 169, the foldable passage cover 16 has many mountain fold lines M and多数 A number of concave valley fold lines V are formed.

At the 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 and the number of valley fold lines V = 1 and the difference is 2 (= 3-1). That is, the folding line pattern of the foldable passage cover 16 of the embodiment 22 is one section. Point 4 is the folding line.

In FIG. 169, the foldable passage cover 16 of the embodiment 22 has a plurality of parts P 1, P 2, and P 3 that are parts (enclosed) formed by the fold lines M and V. ing. Part P1 is triangular, part P2 is equilateral trapezoid, and part P3 is trapezoidal.

The foldable passage force par 16 is folded into a state in which the outer shape is reduced as shown in FIG. 168 during storage or transportation.

(Example 23)

In the description of the embodiment 23, the same reference numerals are given to the components corresponding to the components of the embodiment 22 and the detailed description is omitted.

Example 23 differs from Example 22 in the following points, but has the same configuration as Example 22 in other points.

The foldable passage force par 16 shown in FIG. 170 is similar to the embodiment 22 in that the passage portion at the connection between the railway vehicles, the passage between the end of the terminal bridge at the airport and the entrance to the aircraft, etc. It is suitable for use in places where the distance between structures at both ends of the passage is not fixed.

The foldable aisle cover 16 shown in FIG. 17 1 has the outer shape excluding the center of the fan shape in the developed view. The foldable 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 shape when used in a half-folded state. It is a folding line. Each node satisfies the folding condition.

In FIG. 171, the foldable passage cover 16 of the embodiment 23 includes a plurality of parts PI, P 2, P 3, which are parts (enclosed) formed by the fold lines M, V. Has P4. The part PI is a triangle, and the parts P2 to P4 are all quadrilaterals.

The foldable passage force par 16 of the embodiment 23 is folded in a state where the outer shape is reduced as shown in FIG. It is.

(Example 24)

FIG. 172 is an explanatory view of a lampshade 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 a lampshade. FIG. 17B is a perspective view of a half-folded lamp shade formed by joining the left and right sides of the sheet-like member of FIG. 17A to form a pseudo cone. A lamp seed 17 shown in a half-folded state shown in 2B 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. 17A, the transparent resin sheet for manufacturing the lamp shade 17 of Fig. 17B has a shape excluding the center of the sector. I have. An adhesive margin 17a for bonding is provided on one of both sides of the resin sheet to be joined to each other. A fold line is formed on the resin sheet in the unfolded state using the same member as the fold line forming die shown in the first or third embodiment, and then the elasticity at the time of curing is applied to the adhesive margin 17a. An adhesive having a property is applied and adhered 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 number of concave valley fold lines V having a concave shape in a half-folded state.

At a node which is an intersection of the mountain fold line M and the valley fold line V, a total of six fold lines including four mountain fold lines M and two valley fold lines V intersect. Then, the number of the mountain fold lines M intersecting at each node = 4, the number of the 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 Example 24 is one section. Point 6 is the folding line.

In FIG. 17 2, the foldable pseudo-conical wall of the embodiment 24 includes a plurality of parts P la, P 1b, P 2a, which are (enclosed) portions formed by the fold lines M and V. P 2 b,. The shapes of the parts PIa, P2a, ... are similar triangles having different sizes, and the shapes of the parts パーツ 2a, P2b, ... are similar triangles having different sizes.

Attached to the parts P 1 a, P 1 b, P 2 a, etc. is a transparent cellulosic paper or a normal colored paper with a favorite color such as red, blue, yellow, etc. It is configured. The lampshade 17 is folded into a small external shape when it is stored or transported, and is expanded into a pseudo cone having a large external shape when used.

(Example 25)

FIG. 173 is an explanatory view of a Christmas card as a structure with a fold line of Example 25 of the present invention, FIG. 173A is a plan view of a folded Christmas card, and FIG. FIG. 173A is a plan view of the opened state, and FIG. 173C is a diagram of the arrow 173C of FIG. 173B viewed obliquely from above.

In FIG. 173, the christ mask C has a bridging portion C 1 to which the Christmas tree T is bonded and a tree pressing portion C 2 for pressing down the Christmas tree. The Christmas tree T is formed by a conical wall with a folding line made of a colored sheet that satisfies the folding conditions. In the state where the Christmas card C is folded as shown in FIG. 17A, the Christmas card T is held in a folded state. When the above-mentioned Christmas card C is opened as shown in FIG. T expands due to elasticity, resulting in the three-dimensional shape shown in Fig. 17C when viewed from diagonally above. Therefore, the person who receives the Christmas card C can feel unusual and enjoyable.

(Example 26)

FIG. 174 is an explanatory view of a hat as a structure with a folding line according to Example 26 of the present invention. 17 A is a perspective view of the hat, FIG. 17 B is a cross-sectional view of the above-described FIG. 17 A taken along a line 17 4 B— 17 4 B, and FIG. 17 C is an arrow of the above FIG. It is the figure seen from 1 7 4 C.

FIG. 175 is an explanatory view of the hat of Example 26. FIG. 175A is a plan view of the hat in a folded state, and FIG. 175B is an arrow 175 of FIG. It is the figure seen from B. In Figs. 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 center of the collar 13. are doing. The crown 14 has a hexagonal upper surface portion 14a and a side portion (pseudo-conical wall) 14b formed by twisting a hexagonal pyramid.

On the side (pseudo-conical wall) 14b, as shown in Fig. 174B, a number of mountain fold lines M having a convex outer surface and a number of valley fold lines V having a concave surface are formed. I have.

At a node which is an 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 and the number of valley fold lines V = 1 and the difference is 2 (= 3-1). That is, the fold line pattern of the side surface portion (pseudo-cone wall) 14b of the ninth embodiment is a one-node four-fold line.

In FIGS. 174 and 175, the temporal portion 14b of the hat C of the embodiment 26 has a plurality of parts P 1 which are (enclosed) portions formed by the polygonal lines M and V. And P 2. The part P 1 is triangular and one side thereof is foldably connected to the brim 13, and the part P 2 is triangular and one side thereof is foldably connected to the upper surface 14 a. 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 P 1, and the mountain fold line M, M,… forms a hexagon. So endlessly connected.

A mountain fold line M, M,… is formed at a connection portion between the upper surface member 14 a and one side of each of the six parts P 2, and the mountain fold line M, M,… has a hexagonal shape. Connected to the address to form.

Each of the mountain fold lines M, M,... Connected endlessly has the side part (pseudo-conical wall) 14 b in the state where the side part (pseudo-conical wall) 14 b is extended and folded. Form a closed polygon in a plane perpendicular to the axis of.

The side part 14 b of the cap C of the embodiment 26 is compressed in the axial direction while being twisted. Then, it is folded along the folding lines M and V, resulting in the state of FIG. 175A and FIG. 175B. The angle formed by the mountain fold line M and the valley fold line V formed at the connection 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 temporal part 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, the space required for accommodating the hat C can be reduced by folding the hat C as shown in Fig. 175B.

(Example 27)

FIG. 176 is an explanatory view of a hat as a structure with a fold line according to Example 27 of the present invention. FIG. 176A is a perspective view of the hat, and FIG. 176B is a view of FIG. 1 13 B—1 13 B line sectional view, FIG. 176 C is a view as seen from the arrow 1 13 C of FIG.

FIG. 177 is an explanatory view of the hat of Example 27, FIG. 177A is a plan view of the hat in a folded state, and FIG. 177B is an arrow 1 1 4 of FIG. 177A. It is the figure seen from B. In the description of the embodiment 27, the same reference numerals are given to the components corresponding to the components of the embodiment 26, and the detailed description thereof will be omitted.

This embodiment 27 is different from the above-mentioned embodiment 26 in the following points, but is configured similarly to the above-mentioned embodiment 26 in other points.

In Fig. 176A, a plurality of equiped trapezoidal parts P1 to P5 are formed on the temporal part (pseudoconical wall) 14b 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, and when the end protrudes inward, the valley fold line is formed. Form V. The parts P1 to P5 of the equilateral trapezoid have smaller sizes in order from the part P1 arranged at the bottom to the part P5 arranged at the top.

Each of the equi-legged parts P1 has one bottom side foldably connected to the collar 13 and the part P5 has one bottom side foldably connected to the upper surface part 14a. At the connection portion between the brim 13 and one side of each of the six parts P 1, a mountain fold line M and a valley fold line V are formed so as to be connected alternately, and are connected alternately. The three mountain fold lines M and the three valley fold lines V are connected endlessly 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 M are provided. The fold lines are connected endlessly to form a hexagon.

Similarly to the above-mentioned isosceles trapezoidal parts P 1 and P 2, six parts P 2 to P 4 are also arranged in the circumferential direction, and the bases of the isosceles trapezoids alternately form a mountain fold line. And valley fold lines are connected to the endless in the circumferential direction.

That is, the three mountain fold lines M and the three valley fold lines V connected alternately and to the endless are in a state in which the temporal portion (pseudoconical wall) 14 b is extended and in a folded state. , A closed polygon is formed in a plane perpendicular to the axis of the temporal region (pseudoconical wall) 14 b.

When the side part 14 b of the cap 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, if the hat C is folded, the space required for accommodating the hat C can be reduced.

(Example 28)

FIG. 178 is a perspective view of a wound cap 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 the process of being folded. FIG. 180 is a retractable hat of the retractable hat further folded from the state of FIG. 179. It is a perspective view.

In Fig. 178, the rewindable cap H is composed of a flange A, a temporal part B, and a top part C. As shown in Fig. 179 and Fig. 180, a mountain fold line is shown. It can be wound while folding along M and valley fold line V.

FIG. 181 is an explanatory view of the method of manufacturing the winding cap shown in FIG. 178 to FIG. 180. FIG. 18A is a development view of FIG. 1 B is a development of the temporal region B, Fig. 1 8 1 C is a developed view of the crown C.

As shown in Fig. 18 1A, an inner radius RAi (“i” means in) is drawn on a sector with a central angle of Θ1 (outer radius RAo: “oj” means “out”), and the outer circumference is divided into N (even numbers). Te point Al, A

Define 2, A3,… and draw N equiangular spirals (angles with the radial direction = 5 to 10 °) from these points toward the center in the counterclockwise direction, and intersect with the circle of radius RAi To Bl, B2, B

Assuming 3,…, the line segments B1B2, B2B3, B3B4,… have equal length. Cut the fan shape with these line segments and use this as the flange A. When winding and storing, this spiral is alternately formed into a mountain fold and a valley fold line. Note that FIG. 18A is drawn as Θ1 = 300 ° and N = l 2. When both ends of this curved strip-shaped element are joined, a truncated cone is formed, and since <1 <360 °, a tapered flange is formed.

Similarly, the temporal part B is made of a curved strip-shaped element cut out from a fan shape. However, as shown in Fig. 18B, the vertex angle Θ2, which is extremely smaller than the central angle 11, of the flange is used. 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 R Bo. From these points, draw 螺 spirals or inclined straight lines at an angle φ = 5 to 10 ° in the same manner as above, and define the radius Dl, D2, D3, D4,… on the concentric circle of RBi, Determine the inner circumference of the temporal element. When both ends of a curved strip-shaped element are joined, a frustoconical shell close to a cylinder is obtained because the Θ2 value is small. The arc length B1B2 = B2B3 = B3B4,… and the arc length C1C2 = C2C3 = C3C4,… of the inner periphery of the flange element are equally selected. Head B is joined or sutured.

Next, the crown C is also made of a sector shape with a vertex angle Θ3 close to 360 ° or a circular film with © 3 = 360 °. Fig. 18 1C is for Θ3 = 360 °, and the center angle © 3 is equally divided by Ν (= 1 2) to determine points E1, Ε2, Ε3, Ε4,…. The length of the arc of the outer circumference of the crown C Ε 1 Ε2 = Ε2Ε3 = Ε3Ε4,… is equal to that of the inner circumference of the temporal 頭部 (D1D2 = D2D 3 = D3D4 = D4D5,-) Join with the inner periphery of part B. That is, when these three elements are joined, the hat shown in Fig. 178 is obtained. When the two fold lines are wound alternately around the central axis as mountain folds and valley folds, the result is as shown in Figure 180. FIG. 182 is an explanatory view of another manufacturing method of the wind hat shown in FIG. 178 to FIG. In Fig. 18 2, three elements are divided into an even number of small elements (Figure 18 1A, Fig. 18 1 B, and Fig. 18 2 1 and 2 of these elements are created, and the points A1 and Al, B1 and Bl, C1 and Cl, D1 and Dl, E1 and El match, and the sides A1B1C1D1E1 and A1B1C1D1E1 By joining or suturing the hats and performing this joining on 12 fan-shaped elements, the rewindable hat shown in FIGS. 178 to 180 can be manufactured.

(Example 29)

FIG. 183 is a perspective view of a retractable tent as a structure with a folding line according to Example 29 of the present invention.

FIG. 184 is a perspective view of the winding tent of FIG. 183 in a state in which the tent is being folded.

FIG. 185 is a perspective view of the tent further folded from the state of FIG.

In FIG. 183, the winding-type tent H has a mountain fold line M and a valley fold line V formed along an equiangular spiral (Bernilly spiral). The shaped fan-shaped parts can be wound up while folding along the folding lines M and V. The tent H has a dome shape in the extended state, and ring-shaped flexible tubes H 1 and H 2 extending in the circumferential direction are fixed to the outer peripheral portion of the outer surface and a radially central portion thereof, respectively. . The tent H is maintained in the extended state shown in FIG. 183 by inflating the flexible tubes HI and H2 by supplying air thereto.

Fig. 186 is an explanatory view of the method of manufacturing the winding type tension shown in Figs. 183 to 185, and Fig. 186A shows a parabolic curved dome-shaped winding in an extended state. Fig. 186B is an expanded view of one of the parts formed when the tent is divided in the circumferential direction.Fig. 186B shows the connection between the end AB and the CD of Fig. 186A. FIG. 3 is a view showing a conical wall formed in FIG.

FIG. 187 is an explanatory view of the method of manufacturing the roll-up tent shown in FIGS. 183 to 185, and FIG. 187 is a roll-up tent having a dome shape with a radius r1 in an extended state. The dome shape Let r = 0, j = 1, 2, ..., 10 be the coordinates of the center position of r and be the coordinates rj (rj = rl X (1 1-j) / 10 FIG. 6 is a diagram showing the shape of a part (conical wall) (j) formed when divided into 10 parts by a circle having a radius of). FIG. 188 is a diagram showing the part number (j) of FIG. 187, the shape and length Lj of the bus, and the inclination 0j.

Fig. 189 shows the parts (1), (2), ..., (10) shown in Fig. 187 and Fig. 188 divided by 16 in the circumferential direction. J: Explanation of the shape of J = 1, 2,..., 10). Fig. 189A shows that each part (j) is composed of 16 divided parts (J). Fig. 189B is a diagram showing the divided parts (J) connected in the radial direction. '

As shown in Fig. 186A, consider a curved strip A BCD with a curvature of width L at the outer periphery on a sector (outer radius R *) with a central angle of Θ. When the left and right ends AB and CD of this strip are joined, a truncated cone as shown in Fig. 186B is obtained. Assuming that the radius of the bottom of this truncated cone is' and the apex angle of the conical shell obtained by extending this truncated cone is 20, the outer circumference of the bottom of the truncated cone is equal to the outer circumference of the strip, and

2 pit R '= ϋ * Θ (5 9) From Fig. 186B, since sinei R'ZR *, ® is given by the following equation (60).

Θ = 2 C sin θ (6 0) A curve that passes through a gentle origin like a parabola as shown in Fig. 1 87 is expressed as Ζ = f (r) on the X plane, and this is rotated around the Z axis. Consider a thin film-like rotating shell obtained by the above method. The radius of the upper end of the container-shaped rotating shell obtained by this rotation is r 1. This rotating shell is divided into n parts on a plane perpendicular to the Z axis, and the rotating shell is approximated by n frustum-shaped frustum-shaped elements using the relationship shown in Fig. 186. The line of intersection of the dividing plane and the shell forms a circle. Let the radius of this circle be r 2, r 3,…-, r n-1 from the top. The n frustoconical elements are named sequentially (1), (2), (3),…, and when these are cut open and expanded, the angles corresponding to the ® values in Figure 1886 A are sequentially determined. 1, © 2, Θ3, ...

Since the inner diameter of element (1) is equal to the outer diameter of element (2), and the inner diameter of element (2) is equal to the outer diameter of element (3), the following equation (6 1) is obtained for the i-th and j + 1 elements Be established. 2 C rj © j = 2 π r j + ΙΘ j +1 (6 1) Now, let the previous shell of revolution be a paraboloid, give Z = C (r / rO) ² , and let n = l 0 Consider the simple case given by s _r 2 = 0.9 rl, r 3 = 0.8 r 1, r4 = 0.7 rl,…. Assuming that C 0.8, and cutting along the Z-X plane, and approximating each element with a truncated cone shape as described above, the sectional shape after division is as shown in FIG. The length Lj (corresponding to L in Fig. 186) of each element when n frustum elements (1), (2), (3), ... are cut open and expanded is easily calculated. In addition, since the angle Θ j (θ in FIG. 1886B) formed by these elements with the Z axis is also obtained, the value j of each element can be calculated by using the equation (60). The width of the element (1) is W1 and its outer circumference is 2πr1. The ratio between the width and the length is set as κ1 as the aspect ratio (Kl = WlZ27crl). If this strip element is drawn on a circle with a radius Ro, the apex angle Θ1 and the width Wl = l'®l'Ro = (W1 / 2 π r 1)-© 1Ro = Wl {01 / (2 π r 1) It becomes} Ro. That is, the dimensionless width Wl / R0 when represented on the radius Ro circle is given by W1®1 / (2πι · 0). The other elements are generally given by the following equation (6 2), with aj = Wj / (2πrj).

L j / R 0 = a j Θ j (6 2) If the outer radius of sector element j is R jo and the inner radius is Rji,

L j = (R j) o — (R j) i (6 3), where (Rj) i® j = (Rj + 1) o® j + l. That is, in FIG. 189A, (Rl) i Θ1 = (R2) ο 2. Using this relationship and equations (59) to (63), the values of j, Lj, Wj, and (Rj) i, (Rj) o are calculated in the order of elements (1), (2), ... it can. Figure 189A shows the development of each element (j) obtained using these values. The figures in Figure 188 are as follows. r j / r l ®j ° Lj / r l a j Wj / Ro (R j) i / Ro (R j) o / Ro

(1) 1.0 197.90.1819 0.02895 0.09997 0.9000 1.0000

(2) 0.99 213.3 30.1 6688 0.02985 0.009277 0.7422 00.8350

(3) 0.8 8 230. 5 0. 1562 0. 03108 0. 08570 0.5.998 0. 6855

(4) 0.7 249.5 0.1443 0.03281 0.07917 0.4749 0.55541 (5) 0.6 270. 3 0. 1332 0. 03533 0. 07306 0. 3653 0.4.384

(6) 0.5 292.2 0.1232 0.03922 0.06760 0.22704 0.3380

(7) 0.4 4 314. 1 0. 1146 0. 04560 0. 06287 0. 1886 0. 2515

(8) 0.333 330.3 0.1077 0.05714 0.05909 0.1181 0.1772

(9) 0.2 350. 0 0. 1028 0. 08184 0. 00564 0. 0564 0. 1128

(10) 0.1 358. 9 0. 1003 0. 15966 0. 00550 0 0. 0550 Next, the development view of each element in FIG. 18A is divided into 2N equal parts (N: integer). At this time, draw a dividing line on the developed view at an angle that forms an angle Φ with the radial direction as shown in the figure so that it becomes a spiral folding line. Figure 189A is a 16-section view of each development. The divided small elements are stacked in the radial direction to create a new sector element. The stacked sector is shown in Figure 189B, which represents a curved sector. If 16 curved sector-shaped elements are joined, and the joining line is alternately formed as a crest or valley fold line, a parabolic shell with a spiral fold line (see Fig. 18-3) is obtained. The ones wound around the central axis passing through the vertex of the parabolic shell in Fig. 183 are shown in Fig. 184 and Fig. 185.

(Example 30)

FIG. 190 is a perspective view of a winding 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 tension in FIG. 190 in a state of being folded.

FIG. 192 is a perspective view of the tent in a state further folded from the state of FIG.

In FIG. 190, 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 is formed by the fold lines M and V. The resulting fan-shaped parts can be wound up while folding along the folding lines M and V. The tent H has a dome shape in the extended state, and ring-shaped flexible tubes H 1 and H 2 extending in the circumferential direction are fixed to the outer peripheral portion and the radially central portion of the outer surface thereof, respectively. The tent H is the flexible tube By supplying air to H 1 and H 2 and inflating it, the stretched 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 center portion. To avoid this, when dividing the FIG. Then, divide it appropriately into unequal parts.

That is, after dividing into eight equal parts, this is further divided into two with a central angle ratio of 0.475: 0.525, and eight sets of curved sector-shaped elements (16 elements) are alternately formed. The curved surface formed by joining is shown in FIG. Here, if the left side of the element with the small central angle is valley-folded and the right side is mountain-folded, it is wound down while shifting downward about the central axis. This is shown in Fig. 191, Fig. 192. This winding method has an advantage of alleviating the above-mentioned degree of cramp.

These models can be used to form the parabolic surface of parabolic antennas, as well as large retractable and deployable tents. Industrial Applicability As described above, the embodiments of the present invention have been described in detail. However, the present invention is not limited to the above-described embodiments, and may fall within the scope of the present invention described in the appended claims. Various changes can be made. Modified embodiments of the present invention will be exemplified below.

(1) In Example 1 and FIG. 2, the folding line forming mold has a pair of foldable folding line forming members (flexible dies), and the pair of folding line forming members forms a sheet-like member. The folding line forming member (fl exi ble mold) that can be folded is not a pair by folding the pair of folding line forming members at the same time, and forming a fold line on the sheet-like member. , Only one may be used. When the number of the folding line forming members is one, the folding may be performed in a state where the sheet-like member is attracted to one surface side. As a method of adsorbing the sheet-like member, for example, it is possible to adsorb the sheet-like member on one side by opening a ventilation hole in the part of the folding line forming member and reducing the pressure on the other side. Becomes

In addition, a folding line forming member using parts made of magnetized material and a flexible magnetic rubber The fold line can be formed by folding the fold line forming member in a state where the sheet-like member is sandwiched between the fold lines.

(2) As can be seen from the results of the research by the 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 foldable structures with various fold lines. Therefore, according to the present invention, it is possible to configure a space structure capable of expanding and contracting in various shapes.

Claims

The scope of the claims

1 A structure with a folding line, characterized by having 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 Wherein the fold line ′ is a plurality of mountain fold lines in which 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 structure with a fold line. A structure with a folding line having a folding line;

(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 2. The plurality of fold lines formed as

(A03) a first mountain fold line, a second mountain fold line, and a third mountain fold line extending radially from one node; and the third mountain fold line and the third mountain fold line being arranged 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 O is the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line, and 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 a == r,

(A05) The foldable structure having the quadrangular part other than the parallelogram.

2. The folding lined structure according to claim 1, wherein the structure has the following configuration 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.

3. The structure with a folding line according to claim 1, wherein the structure has the following constituent requirements (A07):

(A07) The structure with a fold line constituted by an integrally molded product with a fold line. 4 A structure with a folding line, characterized by having the following constituent requirements (A01) to (A04), (Α08)

(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 A fold line, wherein the fold line is a plurality of mountain fold lines and a valley fold where the one surface side forms a mountain fold when viewed from one surface side of the structure with a fold line. A structure with a fold line, comprising:

(Α02) 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 2. The plurality of fold lines formed as

(03) The first fold line extending radially from one node, the second fold line, the third fold line, and the first fold line are disposed between the second fold line. A plurality of fold lines having one node and four fold lines formed by a first valley fold line disposed on the opposite side to the third mountain fold line;

(Α04) The node is the origin Ο, the X axis is taken in the direction of the extension of the third mountain fold line, and one of the first mountain fold line and the second mountain fold line is the X axis Is the angle formed by α, and the angle formed by the other mountain fold line with the first valley fold line? , The plurality of fold lines formed so that α = α,

(Α08) The folding line-shaped structure having the quadrangular part.

5 A structure with a folding line, characterized by having the following components (A01) to (Α05), (Α09)

(Α02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals. The plurality of fold lines formed so that the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is 2.

(A 03) A first mountain fold line, a second mountain fold line, and a third mountain fold line extending radially from one node, and are disposed between the first mountain fold line and the second mountain fold line; The 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 third mountain fold line;

(A 04) The node is the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line, and one of the first mountain fold line and the second mountain fold line is the X axis fold line. The angle formed by the axis is α, and the angle formed by the other mountain fold line with the first valley fold line is α. In this case, the plurality of fold lines formed so that α = τ,

(Α05) The foldable structure having the quadrangular part other than the parallelogram. (Α09) 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 the plate shape becomes uneven with a surface. The above-mentioned structure with a folding line, which can be folded and extended in a plate shape so that the outer shape becomes a three-dimensional structure in which the outer shape is further reduced in a state of being completely folded along the mountain fold line and the valley fold line.

6 A folded line structure characterized by having the following constitutional requirements (A01) to (Α04), (A010), (A011).

(A01) A linear fold having a plurality of polygonal parts and a linear part connecting part connecting outer sides of the parts to each other, and being foldable along the linear part connecting part. A fold line structure provided with a line, wherein the fold line is a plurality of mountain fold lines in which 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 line structure. A structure with a folding line having a folding line.

(Α02) 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 2 The plurality of fold lines formed to be

(Α03) a first mountain fold line, a second mountain fold line, and a third mountain fold line extending radially from one node, and are disposed between the first mountain fold line and the second mountain fold line; The third 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;

(A 04) The node is the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line, and one of the first mountain fold line and the second mountain fold line is the X axis fold line. When the angle formed by the axis is α, and the angle formed by the other mountain fold line with the first valley fold is τ, the plurality of fold lines formed to be << = a,

(A010) A cylindrical wall or a conical wall is formed in a state where the folding line is extended, and a cylindrical wall or a cylindrical wall having a reduced outer shape in a state where the folding line is bent according to a mountain fold line and a valley fold line of the fold line. The structure with a fold line, which forms a conical wall and forms a thick cylindrical wall or a conical wall 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,

(A 011) The structure with a fold line having a plurality of fold lines that are continuous in a plane perpendicular to the axis of the cylindrical wall or the conical wall.

7 A structure with a folding line, characterized by having the following constituent requirements (A01) to (A04), (A012) and (A013).

(A01) A linear fold having a plurality of polygonal parts and a linear part connecting part connecting outer sides of the parts to each other, and being foldable along the linear part connecting part. A fold line structure provided with a line, wherein the fold line is a plurality of mountain fold lines in which 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 line structure. A structure with a folding line having a folding line;

(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 2 The plurality of fold lines formed to be

(A03) Arranged between the first mountain fold line, the second mountain fold line, the third mountain fold line, and the second mountain fold line extending radially from one node A plurality of fold lines having one node and four fold lines formed by a first valley fold line disposed on the opposite side to the third mountain fold line;

(A 04) The node is the origin O, and the X axis is taken in the direction of the extension of the third mountain fold line, When the angle between one of the first mountain fold line and the second mountain fold line and the X axis is α, and the angle between the other mountain fold line and the first valley fold line is τ. The plurality of fold lines formed so that α = Τ,

(A 012) A cylinder 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 and the valley fold line. A wall or cone wall is formed, and in a state of being completely folded along the mountain fold line and the valley fold line, the outer shape is further reduced. Structure,

(A013) The folding line structure in which the part has a polygonal shape of a quadrangle or more

8 A folded line structure characterized by having the following constituent requirements (B 01) to (Β 04):

(B01) A linear fold having a plurality of polygonal parts and a linear part connecting part connecting the outer sides of the parts to each other, and being foldable along the linear part connecting part. A fold line structure provided with a line, wherein the fold line is a plurality of mountain fold lines in which 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 line structure. A structure with a folding line having a folding line;

(Β02) 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 The plurality of fold lines formed to be 2;

(Β03) 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 on the opposite side to the third fold fold line and the fourth fold fold line, and disposed between the third fold fold line and the fourth fold fold line; A first valley fold line, a second valley fold line opposite to the second fold fold line, wherein the first fold fold line and the fourth fold fold line are adjacent to each other, and The plurality of fold lines having one node and six fold lines in which a mountain fold line and a third mountain fold line are arranged adjacent to each other;

(Β 04) The origin is defined as the origin Ο, and the X axis is taken in the direction of the extension of the first valley fold line, The angles formed by the first mountain fold line and the second mountain fold line with the first valley fold line are α and) 3, respectively, and the third mountain fold line and the fourth mountain fold line are the second valley fold line. When the angle between the line and the second valley fold line is set to 0 and the angle between the X-axis and the second valley fold line is set to 0 and 5, respectively, Fold line.

9. The structure with a folding line according to claim 8, wherein the following structural requirements (構成 05) are provided.

(Β05) 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 above-mentioned structure with folding lines, which can be folded and extended in a flat plate shape so that the outer shape becomes a three-dimensional structure further reduced in a state of being completely folded along the folding lines and the valley folding lines.

10. The structure with a fold line according to claim 8, wherein the following structural requirements (要件 06) are provided:

(Β06) A cylindrical wall or 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. In the state of being completely folded along the mountain fold line and the valley fold line, the outer shape is further foldable and extendable to form a thick cylindrical wall or a conical wall having irregularities with further reduced irregularities. Folded structure.

1 1 A folded line structure characterized by having the following constituent requirements (C01) to (C04):

(C01) A linear fold 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. A fold line structure provided with a line, wherein the fold line is a plurality of mountain fold lines in which 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 line structure. A structure with a folding line having a folding line;

(C02) A plurality of nodes, which are intersections of the mountain fold line and the valley fold line, are arranged at predetermined intervals. The plurality of fold lines formed so that the difference between the number of mountain fold lines and the number of valley fold lines intersecting at one node is 2.

(C04) The structure with a folding line having a folding line that forms a closed polygon that is continuous along a plane perpendicular to the axis of the cylinder wall.

1 2 Folded line structure characterized by having the following components (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 is foldable along the linear part connection part. A fold line, wherein the fold line is a plurality of mountain fold lines and a valley fold where the one surface side forms a mountain fold when viewed from one surface side of the structure with a fold line. A structure with a fold line, comprising:

(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 2. The plurality of fold lines formed as

(C05) The structure with a folding line, wherein the part has a polygonal shape of a quadrangle or more. 1 3 A folded line structure characterized by having 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 is foldable along the linear part connection part. Is provided with a fold line, wherein the fold line has a fold line structure. A folding line-shaped structure having a plurality of mountain fold lines that form a mountain fold and one or more valley fold lines that form a valley fold when viewed from one surface side of the object;

(C 02) 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 2 The plurality of fold lines formed to be

(C03) forming a cylindrical wall in a state where the fold line is extended, and forming a cylindrical wall having an unevenness whose outer shape is reduced in a state where the fold line is bent according to a mountain fold line and a valley fold line of the fold line; The structure with a fold line, which forms a thick cylindrical wall having irregularities whose outer shape is further reduced in a state where the fold line is completely folded along the mountain fold line and the valley fold line,

(C06) the folding line-shaped structure, wherein the folding lines are all formed along a spiral, and the parts are only obtuse triangles formed by dividing a parallelogram into two by diagonal lines,

(C07) A structure with a folding line having the above-mentioned configuration, having the obtuse angled triangular part with one of the base angles being 35 ° or more.

1 4 A structure with a folding line, characterized by having the following constituent requirements (D 01) to (D 03):

(D01) A linear fold 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. A fold line structure provided with a line, wherein the fold line is a plurality of mountain fold lines in which 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 line structure. A structure with a folding line having a folding line;

(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 determined. The plurality of fold lines formed to be 2;

(D03) forming a conical wall in a state where the fold line is extended, and forming a conical wall having irregularities with a reduced outer shape in a state where the fold line is bent according to a mountain fold line and a valley fold line of the fold line; The above-mentioned structure with a folding line, which forms a thick conical wall having irregularities whose outer shape is further reduced when completely folded along the mountain fold line and the valley fold line. 15. The structure with a folding line according to claim 14, wherein the following structural requirements (D04) and (D05) are provided.

(D04) a first mountain fold line, a second mountain fold line, a third mountain fold line, and the first mountain fold line and the second mountain fold line which are arranged 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;

(D05) The origin is defined as the node Ο, the X axis is taken in the direction of the extension of the third mountain fold line, and one of the first mountain fold line and the second mountain fold line is the X axis The plurality of fold lines formed to satisfy <¾ = α, where α is an angle formed by the angle α, and τ is an angle formed by the other mountain fold line with the first valley fold line.

15. The structure with a folding line according to claim 14, wherein the following structural requirements (D06) and (D07) are provided.

(D06) a first mountain fold line, a second mountain fold line, a third mountain fold line, a fourth mountain fold line, and a line formed between the first mountain fold line and the second mountain fold line and A first valley fold line disposed on the opposite side of the third fold line and the fourth fold line; and a first fold line disposed between the third fold line and the fourth fold line. And a second valley fold line disposed on the opposite side to the second fold line, wherein the first fold line and the fourth fold line are adjacent and the second fold line and the third fold line The plurality of fold lines having one node and six fold lines in which the lines are arranged adjacent to each other;

(D07) The node is the origin Ο, 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 α and) 3, the angles formed by the third mountain fold line and the fourth mountain fold line with the second valley fold line are a and δ, respectively, and the angle formed between the X axis and the second valley fold line is 0 The plurality of folding lines formed so that 8−α = <5−α + 0.

17. The structure with a folding line according to claim 14, wherein the following structural requirements (D08) and (D09) are provided.

(D08) The first mountain fold line, the second mountain fold line, the third mountain fold line, the fourth mountain fold line, and the first mountain fold line 1 valley fold line and the second A second valley fold line located between the mountain fold line and the third mountain fold line, and the fourth mountain fold line is between the first mountain fold line and the third mountain fold line. The plurality of fold lines having one node and six fold lines arranged on the opposite side to the second mountain fold line;

(D09) The node is the origin O, the X axis is taken in the direction of the extension of the fourth mountain fold line, and the angle formed by the first mountain fold line and the second mountain fold line with the first valley fold line Are 01 and 02, respectively, and the angles between the second mountain fold line and the second valley fold line are 03 and 04, respectively, and the X axis and the first mountain fold line are And the angle formed by the axis and the third mountain fold line) is 3 *, where α * = 02 + 04, β == 01 + 03. Multiple fold lines.

1 8 A structure with a folding line, characterized by having the following components (E01) to (Ε04):

(E01) 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. A fold line, wherein the fold line is a plurality of mountain fold lines and a valley fold where the one surface side forms a mountain fold when viewed from one surface side of the structure with a fold line. A structure with a fold line, comprising:

(Ε02) 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 2. The plurality of fold lines formed as

(Ε 03) The above structure with a folding line constituted by a sheet-like member having a folding line formed along a spiral

(Ε04) When the fold line is extended, the fold line has a circular sheet shape, and when the fold line is bent according to the mountain fold line and the valley fold line, the outer shape is a disc shape having reduced irregularities, The structure with a fold line, which has a shape having a thickness with irregularities whose outer shape is further reduced when completely folded along the mountain fold line and the valley fold line.

1 9 A mold for forming a fold line, characterized by having the following components (F01) and (F02): (F01) A linear fold having a plurality of polygonal parts and a linear part connecting part connecting the outer sides of the parts to each other, and being foldable along the linear part connecting part. A pair of fold line forming members provided with a line, wherein the fold line is a plurality of mountain fold lines and one or more valley folds in which the one surface side forms a mountain fold when viewed from one surface side of the fold line forming die 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 A pair of folding linear forming members having the plurality of folding lines formed so that

20 A folding line forming method characterized by having the following constitutional requirements (G 01) and (G 02),

(G01) A linear fold that has a plurality of polygonal parts and a linear part connecting part that connects outer sides of the parts to each other, and is foldable along the linear part connecting part. A fold line structure provided with a line, wherein the fold line is a plurality of mountain fold lines in which 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 line structure. 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 2. A sheet-like member sandwiching step of sandwiching a foldable sheet-like member having an integral structure between a pair of fold line forming members having the plurality of fold lines formed to be 2.

(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.