JP6256867B2 - Cylindrical folding structure manufacturing method, cylindrical folding structure manufacturing apparatus, and cylindrical folding structure - Google Patents

Description

  The present invention relates to a method for manufacturing a cylindrical folding structure, a manufacturing apparatus for the cylindrical folding structure, and a cylindrical folding structure.

Conventionally, as a foldable structure that can be folded / expanded so as to be deformed between a folded state in which the outer shape becomes smaller and a deployed state in which the outer shape becomes larger, the parts surrounded by the fold line are folded so as to overlap each other. A tubular structure (cylindrical, rectangular, conical and pyramidal) that can be folded is known (see, for example, Patent Document 1).
Further, as a conventional cylindrical folding structure, there is known a structure having a cylindrical shape (torus shape) whose axis is curved in a deployed state (see, for example, Non-Patent Document 1).

Japanese Patent No. 4253145

Tomohiro Tsuji, “Free-form deformation of (non) disc origami that retains expandability and flat foldability”, Japan Origami Society, Vol. 2, No. 1 (2012), p. 45-58

  However, in the conventional torus-shaped cylindrical folding structure, there is no regularity in the pattern of the folding line, so various products using the cylindrical folding structure that becomes a curved cylindrical body (curved cylindrical body) are used. There is a problem that the design becomes complicated.

  The present invention has been made in view of the above-described circumstances, and a manufacturing method for a cylindrical folding structure and a cylindrical folding structure capable of easily and freely designing a cylindrical folding structure that becomes a curved cylindrical body in an unfolded state. An object of the present invention is to provide a product manufacturing apparatus and a cylindrical folding structure.

In order to solve this problem, in the method for manufacturing a cylindrical folding structure according to one embodiment of the present invention, the planar development portion orthogonally intersects the axial direction with the cylindrical structure virtually represented in a three-dimensional space. A two-dimensional development view including a plurality of cylindrical members divided into a plurality of cylindrical members in a direction in which the divided cylindrical members are developed on a two-dimensional plane, and at least one strip development view corresponding to the developed cylindrical members. And the fold line creation part includes a plurality of symmetrical strips having the same length as the axial width of the cylindrical member divided by the planar development part, and has a symmetry axis at a predetermined angle. A two-dimensional broken line diagram in which a broken line intersecting with each other is provided in the symmetric strip figure is created, and a broken line development drawing creation unit is created by the two-dimensional development drawing created by the planar development unit and the folding line creation unit based on said 2-dimensional polygonal line diagram is, the axis of the tubular member To become symmetrical with respect to the center axis passing through the center in the width of the direction, creating a fold line development view in which a fold line in said strip developed view.

  Further, in the above-described manufacturing method of the cylindrical folded structure, the folding line development drawing creating unit draws a connection line connecting points where the outer edge of the band plate development drawing the cylindrical member and the folding line intersect with each other. Then, the broken line development view is created.

  Moreover, in the manufacturing method of the above-mentioned cylindrical folding structure, the said broken line expanded view preparation part determines the area | region enclosed by the said connection line as a junction part.

  Moreover, in the manufacturing method of the above-mentioned cylindrical folding structure, the folding line development drawing creation unit is a folding line in which the joining part is in a planar state in the cylindrical folding construction created based on the folding line development drawing. Is provided at the joint.

In the manufacturing method of the tubular folding structure described above, before Symbol fold line developed view creation unit, the band in a state of being matched with said central axis of the tubular member and the axis of symmetry of the symmetrical strip shape The connecting line connecting the points where the outer edge of the strip developed by developing the tubular member and the fold line intersect is drawn by overlapping the developed plate and the symmetrical strip graphic.

  Further, in the above-described manufacturing method of the cylindrical folded structure, the folding line development drawing creating unit creates a curved band development drawing curved by converting the outer edge of the band development drawing by conformal mapping, and the symmetry A curved symmetric strip shape is created by performing isometric mapping conversion of the strip shape, and the curved strip development view and the curved symmetry strip shape are overlapped, and the outer edge of the curved strip development view and the curved symmetry The connection line connecting the points where the broken lines of the strips intersect is drawn.

  Further, in the above-described method for manufacturing a cylindrical folding structure, the folding line development drawing creating unit includes a valley fold line connected to a valley fold node provided on the central axis, and the valley fold node on the central axis. And a mountain fold line connected to the mountain fold nodes alternately provided in the fold line development view, and two fold lines smaller than the number of the valley fold lines connected to the valley fold line nodes. A valley fold line is connected to the valley fold node, and two valley fold lines less than the number of the mountain fold lines connected to the mountain fold line node are connected to the mountain fold node.

  Moreover, in the manufacturing method of the above-described cylindrical folding structure, the planar development portion is divided into the plurality of cylindrical members with different lengths in a direction orthogonal to the axial direction, and the divided cylindrical members are A two-dimensional development view is created which is developed on a two-dimensional plane and includes at least one strip development view corresponding to the developed cylindrical member.

  Further, in the above-described method for manufacturing a cylindrical folded structure, the folding line development drawing creation unit is configured to be symmetrical with respect to the central axis when the cylindrical structure is curved with a certain curvature. The fold line development diagram is created by duplicating the strip fold diagram in which the fold line is provided on the strip development diagram and connecting the plurality of strip fold diagram diagrams.

  In order to solve this problem, a cylindrical folding structure according to an embodiment of the present invention is manufactured based on the above-described folded line development created by any one of the above-described cylindrical folding structure manufacturing methods. A curved tubular folding structure characterized by that.

In order to solve this problem, a manufacturing apparatus for a cylindrical folding structure according to an embodiment of the present invention includes a plurality of cylindrical structures virtually represented in a three-dimensional space in a direction perpendicular to the axial direction. Dividing into cylindrical members, developing the divided cylindrical members into a two-dimensional plane, and creating a two-dimensional development view including at least one strip development view corresponding to the developed cylindrical member. And a plurality of symmetrical strips having the same length as the axial width of the cylindrical member divided by the planar development portion, and the fold line intersecting the symmetry axis at a predetermined angle is symmetrical A fold line creation unit for creating a two-dimensional fold diagram provided in a band figure, the two-dimensional development diagram created by the plane development unit, and the two-dimensional fold diagram created by the fold line creation unit based on, it passes through the center in the axial direction of the width of the tubular member That such a symmetrical with respect to the central axis, and a polygonal line developed view creation unit for creating a polyline development view in which a fold line in said strip developed view.

  According to the present invention, it is possible to create a broken line development view having regularity.

It is a schematic block diagram of the manufacturing apparatus of the cylindrical folding structure which concerns on 1st embodiment of this invention. It is a reference figure for explaining an outline of a manufacturing method of a cylindrical folding structure concerning a first embodiment of the present invention. It is a figure which shows an example of the schematic diagram of the torus which is an example of the cylindrical structure which concerns on 1st embodiment of this invention. It is a figure which shows an example of the strip developed view which concerns on 1st embodiment of this invention. It is a figure which shows an example of the two-dimensional expanded view which concerns on 1st embodiment of this invention. It is a figure which shows an example of the two-dimensional broken line figure which concerns on 1st embodiment of this invention. It is a figure which shows the state which accumulated the two-dimensional broken line figure and two-dimensional expansion | deployment figure which concern on 1st embodiment of this invention. An example of the figure which depicted the connection line on the two-dimensional broken line figure concerning a first embodiment of the present invention is shown. It is a flowchart for demonstrating an example of the manufacturing method of the cylindrical folding structure which concerns on 1st embodiment of this invention. It is a figure which shows the other example of the two-dimensional broken line figure which concerns on 1st embodiment of this invention. It is a figure which shows the state which accumulated the two-dimensional broken line figure and two-dimensional expansion | deployment figure which concern on 1st embodiment of this invention. An example of the figure which depicted the connection line on the two-dimensional broken line figure concerning a first embodiment of the present invention is shown. It is a figure which shows one strip | belt (1 node 4 fold line (type 1)) which comprises the cylindrical folding structure by 1st embodiment of this invention. It is a figure which shows one strip | belt (1 node 4 fold line (type 2)) which comprises the cylindrical folding structure by 1st embodiment of this invention. It is a flowchart for demonstrating an example of the manufacturing method of the cylindrical folding structure which concerns on 1st embodiment of this invention. It is a figure which shows one strip | belt board (1 node 6 fold line) which comprises the cylindrical folding structure by 1st embodiment of this invention. It is a fold line expansion | deployment figure of the cylindrical folding structure (1 node 4 fold line (type 1)) by 1st embodiment of this invention. It is a figure which shows the cylindrical body which expand | deployed the cylindrical folding structure (1 node 4 fold line (type 1)) by 1st embodiment of this invention. It is a figure which shows the plate-shaped object which folded the cylindrical folding structure (1 node 4 fold line (type 1)) by 1st embodiment of this invention. It is a fold line expansion | deployment figure of the cylindrical folding structure (1 node 4 fold line (type 2)) by 1st embodiment of this invention. It is a figure which shows the cylindrical body which expand | deployed the cylindrical folding structure (1 node 4 fold line (type 2)) by 1st embodiment of this invention. It is a figure which shows the plate-shaped object which folded the cylindrical folding structure (1 node 4 fold line (type 2)) by 1st embodiment of this invention. It is a fold line expansion | deployment figure of the cylindrical folding structure (1 node 6 fold line) by 1st embodiment of this invention. It is a figure which shows the cylindrical body which expand | deployed the cylindrical folding structure (1 node 6 fold line) by 1st embodiment of this invention. It is a figure which shows the plate-shaped object which folded the cylindrical folding structure (1 node 6 fold line) by 1st embodiment of this invention. It is explanatory drawing which shows the production method of the 1st modification of the cylindrical folding structure by 1st embodiment of this invention. It is explanatory drawing which shows the production method of the 1st modification of the cylindrical folding structure by 1st embodiment of this invention. It is explanatory drawing which shows the production method of the 1st modification of the cylindrical folding structure by 1st embodiment of this invention. It is a fold line expanded view of the 1st modification of the cylindrical folding structure by 1st embodiment of this invention. It is a figure which shows the cylindrical body which expand | deployed the 1st modification of the cylindrical folding structure by 1st embodiment of this invention. It is a figure which shows the middle process in which a cylindrical folding structure is folded from the state of FIG. It is a fold line expanded view of the 2nd modification of the cylindrical folding structure by 1st embodiment of this invention. It is a figure which shows the cylindrical body which expand | deployed the 2nd modification of the cylindrical folding structure by 1st embodiment of this invention. It is a figure which shows the plate-shaped body which folded the 2nd modification of the cylindrical folding structure by 1st embodiment of this invention. It is explanatory drawing which shows the production method of the cylindrical folding structure shown to FIGS. It is explanatory drawing which shows the production method of the cylindrical folding structure shown to FIGS. It is a fold line expanded view of the 3rd modification of the cylindrical folding structure by 1st embodiment of this invention. It is a figure which shows the process in the middle of folding a cylindrical folding structure from the state of FIG. It is a fold line expansion | deployment figure of the cylindrical folding structure (1 node 4 fold line (type 1)) by 2nd embodiment of this invention. It is a figure which shows the cylindrical body which expand | deployed the cylindrical folding structure (1 node 4 fold line (type 1)) which assembled the folding expanded view of FIG. 39, without joining the parts for adjacent joining. It is a figure which shows the cylindrical body which expand | deployed the cylindrical folding structure (1 node 4 fold line (type 1)) by 2nd embodiment of this invention. It is a figure which shows the plate-shaped object which folded the cylindrical folding structure (1 node 4 fold line (type 1)) by 2nd embodiment of this invention. It is a 1st example ((delta) _i > 0) of the fold line expansion drawing of the cylindrical folding structure (1 node 6 fold line) by 2nd embodiment of this invention. It is a 2nd example ((delta) _i <0) of the broken line expanded view of the cylindrical folding structure (1 node 6 fold line) by 2nd embodiment of this invention. It is a 3rd example ((delta) _i = 0) of the broken line expanded view of the cylindrical folding structure (1 node 6 folding line) by 2nd embodiment of this invention. It is a figure which shows the cylindrical body which expand | deployed the cylindrical folding structure (1 node 6 fold line) which assembled the folding expanded view of FIGS. 43-45, without joining the parts for adjacent joining. It is a figure which shows the cylindrical body which expand | deployed the cylindrical folding structure (1 node 6 fold line) by 2nd embodiment of this invention. It is a figure which shows the plate-shaped object which folded the cylindrical folding structure (1 node 6 fold line) by 2nd embodiment of this invention. It is a figure for demonstrating an example of the manufacturing method of the cylindrical folding structure which concerns on 3rd embodiment of this invention. It is a fold line expansion | deployment figure of the cylindrical folding structure (1 node 4 fold line (type 1)) by 3rd embodiment of this invention. It is a figure which shows the cylindrical body which expand | deployed the cylindrical folding structure (1 node 4 fold line (type 1)) by 3rd embodiment of this invention. It is a figure which shows the middle process in which a cylindrical folding structure is folded from the state of FIG.

[First Embodiment]
FIG. 1 is a schematic block diagram of a cylindrical folding structure manufacturing apparatus 100 according to the present embodiment. As shown in FIG. 1, the manufacturing apparatus 100 of the cylindrical folding structure which concerns on this embodiment is provided with the plane expansion | deployment part 101, the fold line production | generation part 102, and the fold line expansion drawing production | generation part 103. As shown in FIG. The cylindrical folding structure manufacturing apparatus 100 is connected to a printing apparatus 200. In the present embodiment, a sheet that can be bent but not elastically deformed, such as paper, metal foil, and plastic sheet, can be used as a medium on which the broken line development diagram is printed.

  Here, before description of each structure, the outline | summary of the manufacturing method of the cylindrical folding structure which the manufacturing apparatus 100 of the cylindrical folding structure which concerns on this embodiment performs is demonstrated previously with reference to FIG. . FIG. 2 is a reference diagram for explaining the outline of the manufacturing method of the cylindrical folding structure according to the present embodiment.

The planar development unit 101 inputs three-dimensional data of model data (hereinafter referred to as a curved cylindrical structure) for creating a cylindrical folded structure. This three-dimensional data is, for example, cylindrical structure data that is virtually represented in a three-dimensional space, as shown in FIG. In the illustrated example, a cylindrical structure that curves with a certain curvature is shown. The axis of this cylindrical structure is AX1, and the center of curvature of the axis AX1 is AX2.
This planar development part 101 divides | segments the cylindrical structure shown to Fig.2 (a) into a some cylindrical member in the direction orthogonal to the axis line AX1 direction, as shown in FIG.2 (b). Thereby, the planar development part 101 obtains a cylindrical member as shown in FIG.2 (c). As shown in the figure, the cylindrical member defines a central axis S ₀ that passes through the center in the width in the direction of the axis AX1.
And the plane expansion | deployment part 101 expand | deploys a cylindrical member on a two-dimensional plane, and produces the strip | belt-plate expansion | deployment figure corresponding to a cylindrical member as shown in FIG.2 (d). In the illustrated example, a part of the outer peripheral surface farthest from the center of curvature AX2 of each cylindrical member is cut in a direction along the axis AX1.
Note that the flat surface development unit 101 may create a strip development view by approximating a cylindrical member to a polyhedron and includes a boundary curve corresponding to the circumference of the circular cross section of the cylindrical member as it is. A development view may be created. The plane development unit 101 creates a two-dimensional development view by connecting the created strip development views, and outputs them to the broken line development view creation unit 103.

Fold lines developed view creation unit 103, so as to be symmetrical with respect to the central axis S ₀ passing through the center in the axial AX1 width of the tubular member, provided with a fold line to strip development view, FIG. 2 (e Create a folded strip diagram as shown in The broken line development drawing creation unit 103 creates a plurality of the strip folding diagrams.
Then, the broken line development drawing creation unit 103 connects a plurality of strip plate folding diagrams to create a broken line development drawing as shown in FIG.

Next, each component will be specifically described.
For example, the plane development unit 101 generates a two-dimensional development view by approximating a curved cylindrical structure to a polyhedron based on the input three-dimensional image data, and outputs the two-dimensional development view to the polygonal line development drawing creation unit 103. In addition, this plane expansion | deployment part 101 is the cylindrical structure (for example, three-dimensional data of the cylindrical structure (for example, torus) which curves with a fixed curvature, or the cylindrical structure (curved with a non-constant curvature) as a curved cylindrical structure (for example). For example, three-dimensional data of Archimedean spiral) can be input, and a plan view in which each cylindrical structure is developed can be created.
Hereinafter, an example using three-dimensional data of a torus-shaped cylindrical structure that is curved with a certain curvature will be described. An example of using a cylindrical folding model that curves with a non-constant curvature will be described later.

FIG. 3 shows an example of a schematic diagram of a torus. The torus shown in FIG. 3 is located in an XYZ virtual three-dimensional space, and points on the surface are defined by XYZ coordinate values of the XYZ space.
When this torus is divided by a plane including the center of curvature AX2, the cross section is a perfect circle. The planar development unit 101 approximates the circular cross section of the torus with a regular u-gon. Note that u can be arbitrarily set and is preferably a large value. In this embodiment, for simplicity, u is an even number, and one of the vertices of the regular u-gon passes through the point where the diameter of the torus is the largest.
The planar development unit 101, first, the circumferential _{d 1} of the circular cross section of the torus by approximating the positive u square acquires XYZ coordinate values of the positive u square vertices _AA 1 _{~AA u.} Then, the planar development unit 101 rotates the angle d ₁ around the center of curvature AX2 from the position of the circumference d ₁ of the torus circular section, and approximates the circumference d ₂ of the torus circular section to a regular u-gon. The XYZ coordinate values of the _u- angle vertices AB _{1 to} AB _u are acquired. That is, the vertices AB _{1 to} AB _u are vertices obtained by approximating a circular cross section obtained by rotating the circular cross section having the vertices AA _{1 to} AA _u by an angle θ with a regular u-gon.
Then, the plane development unit 101 develops u square elements on a two-dimensional plane so that the length of each side does not change, and creates a band plate development view. An example of the development of the band plate is shown in FIG.

Fig.4 (a) is a figure which shows an example of the strip | board expansion drawing which expand | deployed u square elements on the plane. The strip development view shown in FIG. 4A is created on a two-dimensional plane indicated by an xy coordinate system. The band plate development view is developed in the xy coordinate system so that the direction of the axis AX1 of the cylindrical structure and the x axis are parallel to each other. In other words, the cylindrical structure is developed in the xy coordinate system so that the circumferential direction and the y-axis are parallel to each other. In the case of the torus according to the present embodiment, in the xy coordinate system, the positions of the vertices AA _{1 to} AA _{u + 1 and} the positions of the vertices AB _{1 to} AB _{u + 1} are symmetrical with respect to the symmetry axis S ₀ . That is, as shown in FIG. 4, the graphic indicated by the outer edge of the strip developed view are symmetrical shapes with respect to the symmetry axis S _0. In FIG. 4, the line connecting the vertices AA _{1 to} AA _{u + 1} approximates the circumference d ₁ of the circular cross section of the torus, and the line connecting the vertices AB _{1 to} AB _{m + 1} is the circumference of the circular cross section of the torus. It approximates to d _2.
The straight line AA _i AB _i (i = 1,..., U) is a straight line that approximates an arc centered on the curvature center AX2 of the torus. The arc including the point where the torus diameter is maximum corresponds to the line segment AA _i AB _i = (AA _{i + 1} AB _{i + 1} ), and the arc including the point where the torus diameter is minimum is the line segment AA _{u / 2} AB. It corresponds to _{u / 2} .

Further, the planar development unit 101 according to this embodiment, as shown in FIG. 4 (b), may be configured to create a strip developed view and a boundary curve d ₁ and the boundary curve d _2.

The flat surface development unit 101 further rotates the rotation angle θ to create the next strip development view. The plane development unit 101 creates a plurality of strip development views, connects the vertices shown at the same position on the three-dimensional data of the curved cylindrical structure, and completes the two-dimensional development view. The plane development unit 101 outputs the data of the created two-dimensional development diagram to the broken line development diagram creation unit 103.
In the present embodiment, a cylindrical folding model (torus model) that is curved with a constant curvature is used, so that the flat surface development unit 101 duplicates the belt plate development view shown in FIG. A plurality of strip development views can be created. Then, the plane development unit 101 connects the vertices AA ₁ and AB ₁ and the vertices AA _{u + 1} and AB _{u + 1} , respectively, to complete a two-dimensional development view.

Next, an example of a completed two-dimensional development view will be described with reference to FIG. FIG. 5 is a diagram showing an example of a completed two-dimensional development view.
FIG. 5 shows an example in which a plurality of strip development views shown in FIG. 4 are copied and arranged. In addition, adjacent strip development views are connected by adjacent vertices AA ₁ and AB ₁ and vertices AA _{u + 1} and AB _{u + 1} .

The broken line creation unit 102 creates a two-dimensional broken line diagram corresponding to a predetermined broken line model and outputs it to the broken line development view creation unit 103. In the present embodiment, the broken line creation unit 102 includes a plurality of symmetrical strips having the same length as the axial width of the cylindrical member divided by the planar development unit 101, and is symmetric at a predetermined angle. A two-dimensional broken line diagram in which a broken line intersecting with the axis is provided in the symmetric strip figure is created.
If it demonstrates concretely, this broken line creation part 102 can create the two-dimensional broken line figure according to the broken line model which consists of 1 point 4 broken lines. In addition, the broken line model consisting of this one-point four-fold line includes a Miura fold type and a bellows type. it can.
The broken line creation unit 102 draws a broken line having regularity on a plane according to the broken line model. However, when irregular processing is performed in the two-dimensional development view, the regularity of the broken line can be changed according to the two-dimensional development drawing. The details will be described in the modification example in the case where the conformal mapping method is used together.

Here, with reference to FIG. 6, an example of creating a two-dimensional broken line diagram corresponding to a Miura folding type broken line model composed of one point and four broken lines will be described.
FIG. 6 shows an example of a two-dimensional broken line diagram corresponding to a Miura folding type broken line model composed of one point and four broken lines. The two-dimensional broken line diagram shown in FIG. 6 is created on a two-dimensional plane indicated by an xy coordinate system. In the illustrated example, the solid line indicates a mountain fold, and the alternate long and short dash line indicates a mountain fold. Further, in a two-dimensional broken line diagram corresponding to a Miura fold type broken line model composed of one point and four broken lines, a plurality of symmetrical strips including a symmetric axis S ₁ parallel to the y-axis direction are arranged in parallel. Yes. The symmetric strip pattern is a valley fold line that intersects the symmetry axis S _{1 at} an angle α _v , a mountain fold line that intersects the symmetry axis S _{1 at} an angle α _m , and a side line that touches the adjacent symmetric strip pattern Is formed by. Incidentally, on the symmetry axis S _1, a valley-folded nodes three valley fold lines intersect, and mountain fold node intersects three mountain fold lines are alternately positioned. The valley fold nodal axis of symmetry S ₁ and parallel to one mountain fold line and is crossed, the mountain fold nodal point symmetry axis S ₁ and parallel to one valley fold lines intersect.
Further, on the axis of symmetry S _1, the length of the valley-folding line L _1, the length of the mountain fold lines and L _2.

The broken line creation unit 102 (condition 1) is that adjacent nodes on the symmetry axis S ₁ are alternately arranged at different distances L ₁ and L ₂ , and the total is the length L of the initial overall development view. equals _tot, and equal total to 2π since to continue to rotate by (condition 2), respectively valley folding to become an angle alpha _v and edges by folding mountain fold to become angle alpha _m is -2Arufa _v and 2.alpha _m A mountain fold line and a valley fold line are created so as to satisfy these two conditions. The length L _tot is the length in the longitudinal direction (symmetric axis direction) of the band plate development view and is equal to the circumference of the cylindrical structure that is three-dimensional data.

  Condition 1 is expressed by the following equation.

  Condition 2 is expressed by the following equation.

In Expressions 1 and 2, m represents the number of nodes on connection lines BA ₀ , connection lines BB ₀ ... Described later (in other words, the number of nodes on the symmetry axis S ₁ ).
As a result, when assembled into a three-dimensional structure, line segment BA ₁ BB ₁ and line segment BA _{m + 1} BB _{m + 1, which} will be described later, are the same line segment. can do.
Note that the two-dimensional broken line diagram shown in FIG. 6 is an example satisfying the conditions 1 and 2, and a plurality of symmetrical band-like figures satisfying the conditions 1 and 2 are displayed side by side, and the broken line of the cylinder curved with a certain curvature. A development view is shown. As can be seen when multiple sheets are displayed side by side, the expanded view of the bent line of the curved tube with a constant curvature is the same as the expanded view of the uncurved cylinder. It is a thing. Since it is hollowed out symmetrically, there will be no discontinuity of points to be attached when assembled. In addition, making the curvature constant can be paraphrased as making the hollow shape constant.

  The polygonal line development diagram creation unit 103 is a two-dimensional development diagram on the two-dimensional polygonal diagram based on the data of the two-dimensional development diagram input from the plane development unit 101 and the data of the two-dimensional polygonal diagram input from the polygonal line creation unit 102. Create a broken line development drawing depicting the connection line corresponding to. The broken line development drawing creating unit 103 draws a connection line connecting points where the outer edge of the strip development drawing in which the tubular member is developed and the folding line of the strip folding diagram intersects to create a folding development drawing. Further, the broken line development drawing creation unit 103 determines a region surrounded by the connection lines as a joint. In addition, the broken line development drawing creation unit 103 may be provided with a folding line in the joining portion such that the joining portion is in a planar state in the cylindrical folding structure created based on the folding line development drawing.

Specifically, fold line developed view creation unit 103, so as to match the symmetry axis S ₁ of the symmetry axis S ₀ and symmetric strip shape of the strip development view, 2-dimensional development view and a two-dimensional polygonal line diagram And a two-dimensional development drawing is temporarily drawn on the xy coordinate plane of the two-dimensional broken line diagram. This state is shown in FIG.
Then, the broken line development drawing creation unit 103 sets the intersection points of the mountain fold line and the valley fold line on the two-dimensional broken line diagram that intersect the outer edge of the two-dimensional development drawing as the junction points BA _{1 to} BA _{m + 1} and BB _{1 to} BB _{m + 1} . Note that m is a value determined in advance according to the two-dimensional broken line diagram. The broken line development drawing creation unit 103 connects a line connecting the junction points BA _{1 to} BA _{m + 1} (hereinafter referred to as connection line BA ₀ ) and a line connecting the junction points BB _{1 to} BB _{m + 1} (hereinafter referred to as connection line BB ₀ ). ). Then, the broken line development drawing creation unit 103 deletes the two-dimensional development drawing temporarily drawn on the two-dimensional broken line drawing, and displays the drawing in which the connection line BA ₀ and the connection line BB ₀ are drawn on the two-dimensional broken line drawing. Create as a broken line development.

FIG. 8 shows an example of a diagram in which a connection line BA ₀ and a connection line BB ₀ are depicted on a two-dimensional broken line diagram. The broken line development drawing creation unit 103 determines a region surrounded by the connection line BA ₀ and the connection line BB ₀ as a junction. In the present embodiment, the broken line development drawing creation unit 103 creates a broken line development drawing with the joint portion hollowed out as shown in FIG. This fold line development view is a drawing that is a design drawing of the cylindrical folding structure. The broken line development drawing creation unit 103 outputs data of the created broken line development drawing to the printing apparatus 200.
Note that the present invention is not limited to this, and the broken line development drawing creating unit 103 may provide a margin for joining the connection line BA ₀ and the connection line BB ₀ at the joint.

Further, the broken line development drawing creation unit 103 generates a broken line development drawing (hereinafter referred to as a hollow folding line development drawing) in which the joint is hollowed as shown in FIG. At least one of folding line development views (hereinafter referred to as folding line development views) is created.
In the present embodiment, an example in which the broken line development drawing creation unit 103 creates a cut-out broken line development drawing will be described. Note that an example in which the broken line development drawing creation unit 103 creates the folding line development drawing will be described later with reference to the second embodiment.

Next, with reference to FIG. 9, an example of the manufacturing method of the cylindrical folding structure which concerns on this embodiment is demonstrated. FIG. 9 is a flowchart for explaining an example of the manufacturing method of the cylindrical folding structure according to the present embodiment.
(Step ST1)
The plane development unit 101 inputs data of a target structure and three-dimensional data of a curved cylindrical structure. For example, when the target structure is a structure in which a plurality of cylindrical structures having a certain curvature are connected, the plane development unit 101 is based on the input three-dimensional data of the curved cylindrical structure, The input target cylindrical structure is approximated to a combination of a plurality of cylindrical structures having a certain curvature. And the following processes are performed for every cylindrical structure of a fixed curvature. In addition, when the target structure is a structure in which a curved cylindrical structure and a non-curved cylindrical structure are connected, the following processing is performed for each divided structure. Run. Note that the present invention is not limited to this, and the target structure is a tubular structure having a certain curvature, a tubular structure having a non-constant curvature, and a tubular structure that is not curved. Even if it is a structure, it can divide | segment these similarly and the following processes can be performed for every divided | segmented structure.

(Step ST2)
Next, the planar development unit 101 determines a circular cross section for dividing the cylindrical structure into a plurality of cylindrical members in a direction orthogonal to the direction of the axis AX1. For example, the planar development unit 101 determines a circular cross-section including a positive u square vertices _AA 1 _{~AA u} described above, a circular cross section including a positive u square vertices _AB 1 to ab _u. Then, the planar development unit 101 acquires a boundary curve d ₁ corresponding to the circumference d ₁ of the former circular section and a boundary curve d ₂ corresponding to the circumference d ₂ of the latter circular section. The flat surface development unit 101 determines a circular cross section for dividing the next cylindrical member by rotating the angle θ determined from the center of curvature AX2, and divides the plurality of cylindrical members. And the boundary curve between the some cylindrical member divided | segmented is each acquired.

(Step ST3)
The planar development unit 101, a tubular member which is surrounded by a boundary curve d ₁ and the boundary curve d ₂ developed a two-dimensional plane, to create a strip developed view. Further, the plane development unit 101 develops adjacent cylindrical members based on a plurality of circular cross sections divided by the process of step ST2, and creates a plurality of band plate development views.
Next, the flat surface development unit 101 connects a plurality of belt plate development views to complete a two-dimensional development view. The plane development unit 101 outputs the data of the completed two-dimensional development diagram to the broken line development diagram creation unit 103.

(Step ST4)
On the other hand, the broken line creation unit 102 creates a two-dimensional broken line diagram corresponding to a predetermined broken line model and outputs it to the broken line development view creation unit 103. For example, the broken line creation unit 102 creates a two-dimensional broken line diagram as shown in FIG. 6 and outputs the data of the created two-dimensional broken line diagram to the broken line development view creation unit 103.

(Step ST5)
Then, the polygonal line drawing creation unit 103 performs a two-dimensional drawing on the two-dimensional polygonal drawing based on the data of the two-dimensional development drawing input from the plane development unit 101 and the data of the two-dimensional polygonal drawing input from the polygonal line creation unit 102. Create a broken line development view depicting the connection lines corresponding to the development view. The broken line development drawing creation unit 103 outputs data of the created broken line development drawing to the printing apparatus 200.

(Step ST6)
The printing apparatus 200 prints a broken line development diagram on a print medium based on the input data of the broken line development diagram.

Next, an example of creating a two-dimensional broken line diagram corresponding to a bellows type broken line model composed of one point and four broken lines will be described with reference to FIG.
FIG. 10 shows an example of a two-dimensional broken line diagram corresponding to a bellows type broken line model consisting of one point and four broken lines. The two-dimensional broken line diagram shown in FIG. 10 is created on a two-dimensional plane indicated by an xy coordinate system. In the illustrated example, the solid line indicates a mountain fold, and the alternate long and short dash line indicates a mountain fold. Further, in the two-dimensional polygonal line diagram in accordance with the bellows-type fold line model consisting of one point 4 fold line, they are arranged in parallel a plurality of symmetrical strip shape are continuously including symmetry axis parallel S ₂ in the y-axis direction . The symmetric strip shape includes a convex fold which intersect at an angle α to the axis of symmetry S _2. On the axis of symmetry S ₂ are mountain folds node three mountain fold lines intersect, are located in succession. The mountain folding node, the axis of symmetry S ₂ parallel to one valley fold lines intersect.
Further, this symmetric strip graphic shares a line with the adjacent symmetric strip graphic, and this shared line is called a connection line. The mountain fold line intersects this connecting line at an angle α. On this connection line, there is a mountain fold node where three mountain fold lines and one valley fold line parallel to the connection line intersect.

  The broken line creation unit 102 creates a mountain fold line and a valley fold line so as to satisfy the condition 3 that satisfies the following expression 3 in addition to the condition 1 described above.

By making the angle α constant, a line segment CA ₁ CB ₁ to be described later and a line segment CA _{m + 1} CB _{m + 1 to be} described later are the same line segment in both the solid state and the folded state. Can be present at the same position without being separated from each other.

Next, the broken line development drawing creation unit 103 superimposes the two-dimensional development drawing and the two-dimensional broken line drawing so that the symmetry axis S ₀ of the strip development drawing coincides with the symmetry axis S ₂ of the symmetry strip graphic, A two-dimensional development view is provisionally drawn on the xy coordinate plane of the two-dimensional broken line diagram. This state is shown in FIG.
In the example shown in FIG. 11, a two-dimensional development view including a plurality of belt-like development views formed by boundary curves d ₁ , d ₂ .

Fold lines developed view creation unit 103, the junction intersection of mountain fold lines and valley fold lines on the diagram 2D polyline intersects the two-dimensional boundary curve _d 1 of development _{view, d 2 ··· CA 1 ~CA m} + 1, CB 1 ˜CB _{m + 1} . Note that m is a value determined in advance according to the two-dimensional broken line diagram. The broken line development drawing creating unit 103 connects a line connecting junction points CA _{1 to} CA _{m + 1} (hereinafter referred to as connection line CA ₀ ) and a line connecting junction points CB _{1 to} CB _{m + 1} (hereinafter referred to as connection line CB ₀ ). ). Then, the broken line development drawing creation unit 103 deletes the two-dimensional development drawing temporarily drawn on the two-dimensional broken line drawing, and displays the drawing in which the connection line CA ₀ and the connection line CB ₀ are drawn on the two-dimensional broken line drawing. Create as a broken line development.

FIG. 12 shows an example of a diagram in which the connection line CA ₀ and the connection line CB ₀ are depicted on a two-dimensional broken line diagram. Fold lines developed view creation unit 103, a region surrounded by the connecting line CB ₀ this connecting line CA _0, determines a joint. In the present embodiment, the broken line development drawing creation unit 103 creates a broken line development drawing with the joints hollowed out as shown in FIG. This fold line development view is a drawing that is a design drawing of the cylindrical folding structure. The broken line development drawing creation unit 103 outputs data of the created broken line development drawing to the printing apparatus 200.
The present invention is not limited to this, line developed view creation unit 103, a margin for bonding the connecting wire CA ₀ and connecting line CB _0, or may be provided in the joint portion.

Next, the cylindrical folding structure manufactured by the above method will be described. Here, a fold line pattern formed on one band plate (band plate development view) constituting the cylindrical folding structure will be described. Here, with reference to FIGS. 13 and 14, two fold line patterns (the fold line pattern illustrated in FIG. 8 and the fold line pattern illustrated in FIG. 12) will be described separately.
In FIGS. 13 and 14, the folding line pattern (mountain fold line) by mountain fold is represented by a solid line, and the folding line (valley fold line) by valley fold is represented by a broken line. In addition, in the strips 10 and 20 shown in FIGS. 13 and 14, the sides on both ends in the longitudinal direction (the direction of the symmetry axis S ₂ ) are connection lines (circumferential directions) that are connected when the strips 10 and 20 are assembled into a cylindrical portion. Connection line) BD ₀ , BE ₀ , CD ₀ , CE ₀ . The width direction (direction perpendicular to the symmetry axis _{S 2)} of the strip 10, 20 at both ends of the sides, the cylindrical portion adjacent the axial AX1 direction (see FIG. 3) (strip 10, 20) for connecting to each other Connection lines (axial connection lines) BA ₀ , BB ₀ , CA ₀ , CB ₀ .

Next, the cylindrical folding structure manufactured by the above method will be described. Here, a fold line pattern formed on one band plate (band plate development view) constituting the cylindrical folding structure will be described. Here, with reference to FIGS. 13 and 14, two fold line patterns (the fold line pattern illustrated in FIG. 8 and the fold line pattern illustrated in FIG. 12) will be described separately.
In FIGS. 13 and 14, the folding line pattern (mountain fold line) by mountain fold is represented by a solid line, and the folding line (valley fold line) by valley fold is represented by a broken line. In addition, in the strips 10 and 20 shown in FIGS. 13 and 14, the sides on both ends in the longitudinal direction (the direction of the symmetry axis S ₂ ) are connection lines (circumferential directions) that are connected when the strips 10 and 20 are assembled into a cylindrical portion. Connection line) BD ₀ , BE ₀ , CD ₀ , CE ₀ . The width direction (direction perpendicular to the symmetry axis _{S 2)} of the strip 10, 20 at both ends of the sides, the cylindrical portion adjacent the axial AX1 direction (see FIG. 3) (strip 10, 20) for connecting to each other Connection lines (axial connection lines) BA ₀ , BB ₀ , CA ₀ , CB ₀ .

(1) 1-node 4-fold line (Type 1)
FIG. 13 is a fold line in which four fold lines are gathered at one node as a first example of a fold line pattern that enables the tubular structure to be folded on the band plate (band plate development view) illustrated in FIG. It is the figure which applied the Miura folding which is one of the typical examples of a pattern.

In the fold line pattern shown in FIG. 13, the fold line formed on the band plate 10 and the circumferential connection line BD ₀ so that the difference between the number of mountain fold lines and the number of valley fold lines gathered at each node is two. , BE ₀ and the fold line at the axial connection line BA ₀ , BB ₀ are set. In the fold line pattern of FIG. 13, four fold lines are gathered at one node, so three mountain fold lines and one valley fold line are gathered at one node, or one mountain fold line and one crease line at one node. Three valley fold lines are gathered.

In the strip 10 of FIG. 13, a mountain fold line (axial mountain fold line BML1) and a valley fold line (axial valley fold line BVL1) extending from the axial connection lines BA ₀ and BB ₀ to the symmetry axis S ₂ are The strips are alternately arranged in the longitudinal direction at intervals.
A plurality of nodes (connection line first nodes BA _i , BB _i (i) which are intersections of the plurality of axial mountain fold lines BML1 arranged in the longitudinal direction of the strip 10 and the axial connection lines BA ₀ , BB _0. = 1, 3, 5,...)) Are arranged at intervals along the longitudinal direction of the strip 10. Further, the plurality of nodes is the intersection of the plurality of axially convex fold BML1 and the axis of symmetry _{S 2} (symmetry axis first node _{BC i, BC i (i =} 1,3,5 ...)) is band They are arranged at equal intervals along the longitudinal direction of the plate. On top of that, each axial convex fold BML1 is inclined at an angle alpha _m to the axis of symmetry S _2. That is, the plurality of axial mountain fold lines BML1 arranged in the longitudinal direction of the strip 10 are parallel to each other. In the present embodiment, axial mountain fold lines BML1 are also formed on the upper and lower circumferential connection lines BD ₀ and BE ₀ of the strip 10. The axial mountain fold line BML1 in these two circumferential connection lines BD ₀ and BE ₀ is the same line segment in a state where the strip 10 is assembled into a cylindrical portion.

Further, longitudinally arranged a plurality of axially concave fold BVL1 axially connecting line _BA 0, which is the point of intersection between the BB ₀ plurality of nodes (connection line second node BA _i + 1 of the strip 10, BB _{i +} 1 ( i = 1, 3, 5,...)) are arranged at intervals along the longitudinal direction of the strip. The connection line second nodes BA _{i + 1} and BB _{i + 1} are located between the connection line first nodes BA _i and BB _i . Further, the plurality of nodes which are a plurality of intersection of the axial concave fold BVL1 axis of symmetry _{S 2} (symmetry axis second node _{BC i + 1, BC i +} 1 (i = 1,3,5 ...)) are strip 10 are arranged at equal intervals along the longitudinal direction. The symmetry axis second nodes BC _{i + 1} and BC _{i + 1} are located between the symmetry axis first nodes BC _i and BC _i . On top of that, each axial valley fold line BVL1 is inclined at an angle alpha _v to the axis of symmetry S _2. That is, the plurality of axial valley fold lines BVL1 arranged in the longitudinal direction of the strip 10 are parallel to each other.
These axial convex fold BML1 and axial concave fold BVL1 is formed so as to be symmetrical about a symmetry axis S _2.

Furthermore, on the symmetry axis S ₂ of the strip 10 shown in FIG. 13, the circumferential convex fold extending symmetry axis S ₂ direction BML2 and circumferential concave fold BVL2 are alternately arranged. These circumferential convex fold BML2 and circumferential concave fold BVL2 are arranged alternately symmetry axis first node BC _i on the symmetry axis _{S 2,} the BC _i and axis of symmetry second node _{BC i + 1, BC i +} 1 as a boundary Has been. Thus, the difference between the count of the number and concave fold of mountain fold lines gather nodes on the axis of symmetry S ₂ is two.

Further, on each of the axial connection lines BA ₀ and BB _{0 of the} strip 10 shown in FIG. 13, a connection mountain fold line BML3 and a connection valley fold line BVL3 extending along the axial connection lines BA ₀ and BB ₀ are alternately arranged. Is arranged. The connection mountain fold line BML3 and the connection valley fold line BVL3 have the connection line first nodes BA _i and BB _i and the connection line second nodes BA _{i + 1} and BB _{i + 1} on the axial connection lines BA ₀ and BB ₀ as boundaries. They are arranged alternately. As a result, the difference between the number of mountain fold lines and the number of valley fold lines gathered at the nodes on the axial connection lines BA ₀ and BB ₀ is two.

As described above, the band plate 10 on which the folding line pattern is formed is constituted by a plurality of polygonal parts 11 (rectangular parts) which are formed in a plate shape and surrounded by the folding lines. That is, the outer side of each polygonal part 11 is constituted by a folding line pattern of the band plate 10.
When the upper and lower circumferential connection lines BD ₀ and BE _{0 of} the strip 10 on which the broken line pattern is formed are connected to each other and folded in the cylindrical portion assembled as described above, these upper and lower circumferential connection lines. In order for BD ₀ and BE ₀ to exist at the same position without being separated from each other, the above-described equations (1) and (2) may be satisfied.

(2) 1-node 4-fold line (Type 2)
FIG. 14 shows another example of a folding line pattern that enables folding of a cylindrical structure on the band plate (band plate development view) illustrated in FIG. 4, in which four folding lines gather at one node. It is a figure to which a folding line pattern is applied. The folding line pattern in FIG. 14 has a bellows shape in the cylindrical structure.

In the fold line pattern shown in FIG. 14, the fold lines formed on the band plate 20 and the circumferential connection lines are set so that the difference between the number of mountain fold lines gathered at each node and the number of valley fold lines becomes two. Fold lines are set in CD ₀ , CE ₀ and axial connection lines CA ₀ , CB ₀ . In the fold line pattern of FIG. 14, as in the case of FIG. 13, four fold lines gather at one node, so that three mountain fold lines and one valley fold line gather at one node, or 1 One mountain fold line and three valley fold lines are gathered at the node.

In the band plate 20 of FIG. 14, a plurality of mountain fold lines (axial mountain fold lines CML1) extending from the axial connection lines CA ₀ , CB ₀ to the symmetry axis S ₂ are spaced apart in the longitudinal direction of the band plate 20. It is arranged. A plurality of nodes BA _i , BB _i (i = 1, 2,... M) that are intersections of the plurality of axial mountain fold lines CML1 and the axial connection lines CA ₀ , CB ₀ are along the longitudinal direction of the strip 20. Are arranged at intervals.
Axially convex fold CML1 adjacent in the longitudinal direction of the strip 20 is inclined in opposite directions with respect to the symmetry axis S _2. Angle α of the plurality of axially convex fold CML1 respect symmetry axis S ₂ are equal to each other. In the present embodiment, axial mountain fold lines CML1 are also formed on the upper and lower circumferential connection lines CD ₀ and CE ₀ of the band plate 20. The axial mountain fold line CML1 in the two circumferential connection lines CD ₀ and CE ₀ is the same line segment in a state where the band plate 20 is assembled into a cylindrical portion.
The plurality of axially convex fold CML1 is formed so as to be symmetrical about a symmetry axis S _2.

Furthermore, on the symmetry axis S ₂ of the strip 20 shown in FIG. 14, the circumferential convex fold extending symmetry axis S ₂ direction CML2 and circumferential concave fold CVL2 are alternately arranged. These circumferential convex fold CML2 and circumferential concave fold CVL2 are arranged alternately node CC _i the symmetry axis _{S 2} and axially convex fold CML1 the (i = 1,2 ... m) as a boundary . As a result, the difference between the number of mountain fold lines gathered at the node CC _i on the symmetry axis S ₂ and the number of valley fold lines becomes 2.

Further, on each of the axial connection lines CA ₀ and CB _{0 of the} strip 20 shown in FIG. 14, the connection mountain fold line CML3 and the connection valley fold line CVL3 extending along the axial connection lines CA ₀ and CB ₀ are alternately arranged. Is arranged. The connection mountain fold line CML3 and the connection valley fold line CVL3 are alternately arranged with the nodes BA _i and BB _i on the axial connection lines CA ₀ and CB ₀ as boundaries. As a result, the difference between the number of mountain fold lines and the number of valley fold lines gathered at the nodes BA _i and BB _i on the axial connection lines CA ₀ and CB ₀ is two.
The band plate 20 having the fold line pattern formed as described above is formed of a plurality of polygonal parts 21 (rectangular parts) which are formed in a plate shape and surrounded by the fold lines. That is, the outer side of each polygonal part 21 is constituted by a folding line pattern of the band plate 20.

Then, when folded it in cylindrical portion circumferentially connecting line CD 0 of the upper and lower polygonal line pattern formed strip _20, a CE ₀ together assembly connected as described above, the circumferential direction of the upper and lower In order for the connection lines CD ₀ and CE ₀ to exist at the same position without being separated from each other, the above-described formulas (1) and (3) may be satisfied.

Next, with reference to FIG. 15, another example of the manufacturing method of the cylindrical folding structure according to the present embodiment will be described. FIG. 15 is a flowchart for explaining another example of the manufacturing method of the cylindrical folding structure according to the present embodiment.
In addition, since the process of step ST11-13, 15 is the same as the process of step ST1-3, 6, detailed description is abbreviate | omitted.
(Step ST14)
Fold lines developed view creation unit 103 (Condition 4) Sort plurality of nodes on the axis of symmetry S ₂ is at equal intervals, the sum of the distances of the nodes to each other equal to the length L _tot of the developed view of the whole early and (condition 5) the angle alpha _i of the valley fold lines and the mountain fold line intersecting the respective nodes on the axis of symmetry S _2, the angle corresponding to all nodes on the axis of symmetry S ₂ (m pieces) alpha _i A two-dimensional development view that is input from the plane development unit 101 with a mountain fold line and a valley fold line so as to satisfy the two conditions that the sum of (i = 1, 2,..., M) is π. draw. The length L _tot is the length in the longitudinal direction (symmetric axis direction) of the band plate development view and is equal to the circumference of the cylindrical structure that is three-dimensional data.

  Condition 4 is expressed by the following equation.

  Condition 5 is expressed by the following equation.

In Expressions 4 and 5, m represents the number of nodes on the connection line DA ₀ , connection line DB ₀ ... Shown below (in other words, the number of nodes on the symmetry axis S ₂ ). .

That is, the broken line development drawing creation unit 103 determines m + 1 nodes on the symmetry axis S ₀ that satisfy the conditions 4 and 5 for each strip development of the two-dimensional development drawing, and m + 1 pieces. Are determined on the boundary curve d ₁ and the boundary curve d ₂ . Note that the nodes determined on the symmetry axis S ₀ , the boundary curve d ₁ , and the boundary curve d ₂ are mountain fold nodes where four mountain fold lines and two valley fold lines intersect. Then, the broken line development drawing creating unit 103 generates a mountain fold line and a valley fold line each having a regularity in which the fold line intersecting each node is composed of four mountain fold lines and two valley fold lines. Draw on the strip development.
Note that under the condition that points are placed on the boundary curve d ₁ and the boundary curve d ₂ , the size of the angle α _i (i, 2,. The creation unit 103 first determines L so as to satisfy Expression (4), and numerically obtains design variables so as to satisfy Expression (5) while shifting the point on the symmetry axis S ₀ up and down.

Next, the cylindrical folding structure manufactured by the above method will be described. Here, a folding line pattern formed on one band plate (band plate development view) constituting the cylindrical folding structure will be described with reference to FIG. In FIG. 16, as in FIGS. 13 and 14, the folding line pattern (mountain folding line) by the mountain fold is represented by a solid line in the folding line pattern of the strip, and the folding line by valley folding (the valley folding line). ) Is represented by a broken line. Further, the strip 30 shown in FIG. 16, the longitudinal direction (axis of symmetry S ₂ direction) ends of the sides, the connecting lines connected in assembling the strip 30 to the tubular portion (the circumferential direction connecting line) DD _0, DE ₀ . The width direction (direction perpendicular to the symmetry axis S ₂₎ of the strip 30 at both ends of the sides, the cylindrical portion adjacent the axial AX1 direction (see FIG. 3) (strip 30) connecting lines for connecting to each other ( Axial direction connecting lines) DA ₀ and DB ₀ .

(3) 1 Node 6 Folding Line FIG. 16 is a third example of a folding line pattern that allows the tubular structure to be folded on the band plate (band plate development view) illustrated in FIG. It is the figure which applied the fold line pattern in which the fold line of a book gathers.

In the fold line pattern shown in FIG. 16, the fold line formed on the band plate 30 so that the difference between the number of mountain fold lines gathered at each node and the number of valley fold lines becomes 2, and the circumferential connection line DD. Fold lines in ₀ , DE ₀ and axial connection lines DA ₀ , DB ₀ are set. In the fold line pattern of FIG. 16, six fold lines are collected at one node, so that four mountain fold lines and two valley fold lines are collected at one node.

In the band plate 30 of FIG. 16, a mountain fold line (axial mountain fold line DML1) and a valley fold line (axial valley fold line DVL1) extending from the axial connection lines DA ₀ and DB ₀ to the symmetry axis S ₂ are The strips 30 are alternately arranged in the longitudinal direction at intervals.
A plurality of nodes (connection line nodes DA _i , DB _i (i = 1, 1), which are intersections of the plurality of axial mountain fold lines DML1 arranged in the longitudinal direction of the strip 30 and the axial connection lines DA ₀ , DB ₀ 2... M)) are arranged along the longitudinal direction of the strip 30.
Further, the plurality of nodes is the intersection of the plurality of axially convex fold DML1 and the axis of symmetry S ₂ (symmetry axis nodal _{DC i (i = 1,2 ... m} )) is along the longitudinal direction of the strip 30 Are arranged at regular intervals. The plurality of axially convex fold DML1 is inclined in the same direction to the axis of symmetry S _2. However, the inclination angle _{α i (i = 1,2 ... m} ) of a plurality of axially convex fold DML1 respect symmetry axis _{S 2} are different from each other. In the present embodiment, axial mountain fold lines DML1 are also formed on the upper and lower circumferential connection lines DD ₀ and DE ₀ of the strip 30. The axial mountain fold line DML1 in these two circumferential connection lines DD ₀ and DE ₀ is the same line segment in a state where the strip 30 is assembled into a cylindrical portion.

Each axial valley fold line DVL1 is a diagonal line of a rectangular part surrounded by the symmetry axis S ₂ , the axial connection lines DA ₀ , DB ₀ , and two axial mountain fold lines DML1 adjacent in the longitudinal direction of the strip 30. as will be also a plurality of axial valley fold line DVL1 is to be inclined in the same direction as the axial convex fold DML1 to the axis of symmetry S _2, are formed. Thus, the intersection between the axial concave fold DML1 axis of symmetry _{S 2} matches the axis of symmetry node DC _i mentioned above, also, the respective axial concave fold DML1 axially connecting line _DA 0, DB ₀ Are coincident with the connection line nodes DA _i and DB _i .
These axial convex fold DML1 and axial concave fold DVL1 is formed so as to be symmetrical about a symmetry axis S _2.

Furthermore, on the symmetry axis S ₂ of the strip 30 shown in FIG. 16, the circumferential convex fold DML2 extending symmetry axis S ₂ direction are arrayed an axis of symmetry node DC _i as a boundary. Thus, the difference between the count of the number and concave fold of mountain fold lines gather nodes on the axis of symmetry S ₂ is two.
Further, on each axial connection lines _DA 0, DB ₀ of the strip 30 shown in FIG. 16, the axial connection line _DA 0, extending along the DB ₀ connection convex fold DML3 connection line node DA _i, DB _A plurality are arranged with _i as a boundary. As a result, the difference between the number of mountain fold lines and the number of valley fold lines gathered at the nodes on the axial connection lines DA ₀ and DB ₀ is 2.

As described above, the band plate 30 on which the fold line pattern is formed is composed of a plurality of polygonal parts 31 (rectangular parts) which are formed in a plate shape and surrounded by the fold lines. That is, the outer side of each polygonal part 31 is configured by a folding line pattern of the band plate 30.
Then, when the upper and lower circumferential connection lines of the strip having the folded line pattern formed as described above are connected and assembled in the cylindrical portion, the upper and lower circumferential connection lines are not separated from each other. In order to exist at the same position, the above-described formulas (4) and (5) may be satisfied.

In addition, in strips 10, 20, and 30 with reference to FIGS. 13, 14, and 16, axially mountain folds are formed on the upper and lower circumferential connection lines BD ₀ , BE ₀ , DD ₀ , DE ₀ , DD ₀ , DE _0. The lines BML1, CML1, and DML1 are formed. For example, the axial valley fold lines BVL1, CVL1, and DVL1 may be formed, or the fold lines may not be formed.

(1) Cylindrical Folding Structure Constructed by a Folding Line Pattern of One Node 4 Folding Line (Type 1) FIGS. 17 to 19 are views of a cylindrical folding structure manufactured using a plurality of strips 10 of FIG. It is an example. The fold line development view of the cylindrical folding structure shown in FIG. 17 is obtained by arranging a plurality of strips 10 of FIG. 13 in the width direction.

In the broken line development view shown in FIG. 17, two axial connection lines BA ₀ , BB ₀ facing each other in two adjacent strips 10, 10 are connected only in a part in the longitudinal direction of the strip 10. . The two axial connection lines BA ₀ and BB ₀ are connected at the longitudinal position of the strip 10 where the width dimension of the strip 10 is maximum. In FIG. 17, since the circumferential direction connection lines BD ₀ and BE ₀ of the strip 10 are set at positions where the width direction dimension of the strip 10 is maximized, the two axial connection lines BA ₀ and BB ₀ are long. Connected at both ends of the direction. Thereby, a gap region 15 is formed between the two adjacent strips 10 and 10 (between the two axial connection lines BA ₀ and BB ₀ ).
Further, in the broken line development view, the dimension of the gap between the strips 10 and 10 formed by the two axial connection lines BA ₀ and BB ₀ is maximized at the position where the width dimension of the strip 10 is minimized. .

In the broken line development view of FIG. 17, the shapes and sizes of all the strips 10 are set equal. In other words, the length and shape of two axial connection lines BA ₀ , BB ₀ facing each other in the two adjacent strips 10, 10 are the same. Further, the size and shape of the gap region 15 between the two adjacent strips 10, 10 are also the same.

18 and 19, in the folded line development view of FIG. 17, the circumferential connection lines BD ₀ and BE ₀ of the respective band plates 10 are connected to each other to assemble the band plate 10 into a cylindrical portion. It is produced by connecting the axial connection lines BA ₀ and BB ₀ of the adjacent strips 10 and 10 (cylindrical portions).
As shown in FIG. 18, the cylindrical folding structure has a curved axis line AX1 when the adjacent polygonal parts 11 and 11 are opened along the mountain fold line and the valley fold line (see FIG. 17). A cylindrical body is obtained. As described above, in the broken line development view of FIG. 17, since the shape and size of the strip 10 are set equal, the curvature of the axis AX1 of the cylindrical body in FIG. 18 is constant.
Moreover, this cylindrical folding structure can fold adjacent polygon parts 11 and 11 along a mountain fold line and a valley fold line (refer FIG. 17) so that it may shrink | contract in the axis line AX1 direction. In this folded state, as shown in FIG. 19, the cylindrical folded structure becomes a plate-like body having an annular shape in plan view. In FIG. 19, the AR direction corresponds to the thickness direction of the plate-like body.

(2) Cylindrical Folding Structure Constructed by Folding Line Pattern of 1 Node 4 Folding Line (Type 2) FIGS. It is an example. The fold line development view of the cylindrical folding structure shown in FIG. 20 is obtained by arranging a plurality of band plates 20 of FIG. 14 in the width direction.

In the broken line development view shown in FIG. 20, two axial connection lines CA ₀ and CB ₀ facing each other in two adjacent strips 20 and 20 are connected only in a part of the strip 20 in the longitudinal direction. . The two axial connection lines CA ₀ and CB ₀ are connected at the longitudinal position of the strip 20 where the width direction dimension of the strip 20 is maximum. In FIG. 20, the circumferential direction connecting lines CD ₀ and CE ₀ of the band plate 20 are set at positions where the width direction dimension of the band plate 20 is maximized, so that the two axial direction connecting lines CA ₀ and CB ₀ are long. Connected at both ends of the direction. As a result, a gap region 25 is formed between the two adjacent strips 20 and 20 (between the two axial connection lines CA ₀ and CB ₀ ).
Moreover, in the broken line development view, the dimension of the gap between the strips 20 and 20 formed by the two axial connection lines CA ₀ and CB ₀ is maximized at a position where the width direction dimension of the strip 20 is minimum. .

In the broken line development view of FIG. 20, the shape and size of all the strips 20 are set equal. In other words, the lengths and shapes of the two axial connection lines CA ₀ and CB ₀ facing each other in the two adjacent strips 20 and 20 are the same. Further, the size and shape of the gap region 25 between the two adjacent belt plates 20 are the same.

The cylindrical folding structure shown in FIGS. 21 and 22 is constructed by connecting the circumferential connection lines CD ₀ and CE ₀ of the respective band plates 20 to each other in the folded line development view of FIG. It is produced by connecting the axial connection lines CA ₀ and CB ₀ of two strips 20 and 20 (tubular portions) adjacent to each other.
As shown in FIG. 21, in this tubular folded structure, the axis line AX1 is curved in the unfolded state where adjacent polygon parts 21 and 21 are opened along a mountain fold line and a valley fold line (see FIG. 20). A cylindrical body is obtained. As described above, in the broken line development view of FIG. 20, since the shape and size of the band plate 20 are set equal, the curvature of the axis AX1 of the cylindrical body in FIG. 21 is constant.
Moreover, this cylindrical folding structure can fold adjacent polygon parts 21 and 21 along a mountain fold line and a valley fold line (refer FIG. 20) so that it may shrink | contract in the axis line AX1 direction. In this folded state, as shown in FIG. 22, the cylindrical folding structure is a plate-like body having an annular shape in plan view. In FIG. 22, the AR direction corresponds to the thickness direction of the plate-like body.

(3) Cylindrical Folding Structure Constructed by a Folding Line Pattern of 1 Node 6 Folding Lines FIGS. The fold line development view of the cylindrical folding structure shown in FIG. 23 is obtained by arranging a plurality of strips 30 of FIG. 16 in the width direction.

In the broken line development view shown in FIG. 23, two axial connection lines DA ₀ and DB ₀ facing each other in two adjacent strips 30 and 30 are connected only in a part in the longitudinal direction of the strip 30. . The two axial connection lines DA ₀ and DB ₀ are connected at the longitudinal position of the strip 30 where the width direction dimension of the strip 30 is maximum. In FIG. 23, since the circumferential direction connection lines DD ₀ and DE ₀ of the strip 30 are set at positions where the width direction dimension of the strip 30 is maximum, the two axial connection lines DA ₀ and DB ₀ are long. Connected at both ends of the direction. As a result, a gap region 35 is formed between the two adjacent strips 30 and 30 (between the two axial connection lines DA ₀ and DB ₀ ).
Further, in the broken line development view, the dimension of the gap between the strips 30 formed by the two axial connection lines DA ₀ and DB ₀ is maximized at the position where the width dimension of the strip 30 is minimum. .

In the broken line development view of FIG. 23, the shape and size of all the strips 30 are set equal. In other words, the length and shape of the two axial connection lines DA ₀ and DB ₀ facing each other in the two adjacent strips 30 are the same. Moreover, the size and shape of the gap region 35 between the two adjacent strips 30 are also the same.

24 and 25, in the expanded view of the fold line in FIG. 23, the circumferential connection lines DD ₀ and DE ₀ of the respective band plates 30 are connected to each other to assemble the band plate 30 into a cylindrical portion. It is produced by connecting the axial connection lines DA ₀ and DB ₀ of two strips 30 and 30 (cylindrical portions) adjacent to each other.
As shown in FIG. 24, in this tubular folded structure, the axis line AX1 is curved in an unfolded state in which adjacent polygon parts 31 and 31 are opened along a mountain fold line and a valley fold line (see FIG. 23). A cylindrical body is obtained. As described above, in the expanded view of the broken line in FIG. 23, the shape and size of the band plate 30 are set to be equal, so the curvature of the axis AX1 of the cylindrical body in FIG. 13 is constant.
Moreover, this cylindrical folding structure can fold adjacent polygonal parts 31 and 31 along a mountain fold line and a valley fold line (refer FIG. 23) so that it may shrink | contract in the axis line AX1 direction. In this folded state, as shown in FIG. 25, the cylindrical folded structure becomes a plate-like body having an annular shape in plan view. In FIG. 25, the AR direction corresponds to the thickness direction of the plate-like body.

<First modification>
By applying the design method of the present embodiment described above, it is also possible to produce a cylindrical folding structure in which the radius of curvature of the axis AX1 gradually changes as shown in FIGS. Hereinafter, the production method of the cylindrical folding structure in which the radius of curvature gradually changes will be described in detail. Here, the description will be made using the Archimedean spiral shown in FIG.
The Archimedean spiral is a spiral defined by the following equation using polar coordinates where θ is a rotation angle, R is a radius, and a is a constant.

As shown in FIG. 27, the flat surface development unit 101 divides the Archimedean spiral cylindrical structure into intervals of line segments b having the same length to discretize the Archimedean spiral. Then, the plane development unit 101 sets points EA ₁ , EB ₁ , EC ₁ , ED ₁ ,... That connect adjacent line segments b. Note that the set points EA ₁ , EB ₁ , EC ₁ , ED ₁ ,... Are located on the outer periphery of the cylindrical structure and can be represented by XYZ coordinate values. The angle φi (i = 1, 2,...) That bisects the angle formed by two adjacent line segments b is expressed by the following equation.

  The discretized rotation angle θi (i = 1, 2,...) Is a numerical sequence represented by the following expression with respect to the initial value θ1.

Then, as shown in FIG. 28, the plane development unit 101 includes a plurality of planes ES _i that include a straight line that bisects the angle formed by two adjacent line segments b and that are orthogonal to the axis AX1 of the cylindrical structure. To do.
More specifically, the flat surface development unit 101 _first arranges an m-gon on the plane ES ₁ where the point EA ₁ on the cylindrical structure is _one of the vertices, and the vertices of the m-gon are represented by EA _j (j = 1, 2, ... m). Then, the planar development unit 101, to push in parallel along a positive m square was formed on the plane ES ₁ to segment b between the line two points _EA 1, EB _1, the vertex EA _j in the plane ES ₁ By setting the point projected onto the plane ES ₂ as EB _j (j = 1, 2,..., M), a new m-gon having the point EB _j as the vertex is obtained on the plane ES ₂ . The plane developing unit 101 can define a curved cylinder along the Archimedes spiral by repeating this process as i = 1, 2,. In addition, the m-square cross section obtained in this way is not a regular m-square.

The planar development unit 101, a section for dividing the tubular structure into a plurality of tubular members in a direction perpendicular to the axial line AX1 direction, plane ES _1, ES _2, is determined to .... The planar development unit 101, the boundary corresponds to the outer periphery of each plane ES _i of 2 .... etc. boundary curve _d corresponding to the outer periphery of the boundary curve _{d 1,} plane ES ₂ corresponding to the outer periphery of the flat ES ₁ curve To get. And the plane expansion | deployment part 101 expand | deploys the cylindrical member enclosed by the two boundary curves adjacent to the axis line AX1 direction on a two-dimensional plane, and produces a strip development view.
On the other hand, the broken line creation unit 102 can create a two-dimensional broken line diagram as shown in FIG. 6 and output the data of the created two-dimensional broken line diagram to the broken line development diagram creating unit 103 as described above.
The polygonal line development diagram creation unit 103 is a two-dimensional development diagram on the two-dimensional polygonal diagram based on the data of the two-dimensional development diagram input from the plane development unit 101 and the data of the two-dimensional polygonal diagram input from the polygonal line creation unit 102. Create a broken line development drawing depicting the connection line corresponding to. The broken line development drawing creation unit 103 outputs data of the created broken line development drawing to the printing apparatus 200. An example of the polygonal line development obtained by this is shown in FIG.

In the broken line development view shown in FIG. 29, as in the broken line development view shown in FIG. 17, a plurality of strip plates 10 'are arranged in the width direction. In FIG. 29, the first strip 10 ′ # 1 is the strip closest to the center of the spiral, and the other strip 10 ′ arranged adjacent to the first strip 10 ′ # 1 The further away from the first strip 10 ′ # 1, the more the strip 10 ′ is disposed at a position away from the center of the spiral (see FIG. 30).
29, the gap region 15 ′ between the two strips 10 ′ # 1, 10 ′ # 2 having the smallest radius of curvature and the vicinity of the center of the spiral is the largest, and as the spiral moves away from the center. Since the radius of curvature increases, the gap region 15 ′ between the two strips 10 ′ and 10 ′ (for example, 10 ′ # 16 and 10 ′ # 17) positioned away from the center of the spiral is reduced. Further, the gap region 15 'between the two strips 10'# 33 and 10 '# 34 located farthest from the center of the spiral is the smallest. In other words, the radius of curvature of the axis AX1 in the cylindrical folding structure is reduced by setting the gap region 15 ′ (gap size) between the two adjacent strips 10 ′ and 10 ′ large. In the broken line development view, the radius of curvature of the axis AX1 in the cylindrical folding structure is increased by setting the gap region 15 '(gap size) between two adjacent strips to be small.
In this way, since the gap region 15 'is changed, the width direction of the symmetry of the strip 10' around the axis of symmetry S ₂ of the strip 10 'is broken.

As shown in FIG. 30, the cylindrical folded structure created by the broken line development view of FIG. 29 is arranged along the mountain fold line and the valley fold line (see FIG. 29) between the adjacent polygonal parts 11 ′ and 11 ′. In the unfolded open state, the curvature radius of the axis AX1 becomes a cylindrical body that gradually changes along the direction of the axis AX1.
In addition, as shown in FIG. 31, this cylindrical folding structure is formed by placing adjacent polygonal parts 11 ′ and 11 ′ along the mountain fold line and the valley fold line so as to shrink in the direction of the axis AX1 (see FIG. 29). By folding the tubular structure, the tubular folded structure can be formed into a plate-like body having an annular shape in plan view as in the case of FIG.

  As in the fold line pattern shown in FIG. 29, the fold satisfying the conditions described in “(1) 1 node 4 fold line (type 1)” or “(2) 1 node 4 fold line (type 2)” described above. By forming the line pattern on the strip, a cylindrical folding structure in which the radius of curvature gradually changes even if each polygonal part 11 ′ surrounded by the folding line does not have flexibility is produced. Is possible. (For example, when a cylindrical folded structure is produced using a cylindrical member having an m-square cross section shown in FIG. 28 as it is without using these folding line patterns, left and right symmetry in the folded line development diagram as shown in FIG. 30 (symmetry in the width direction in the strip), the rectangular element forming the surface of each cylindrical member cannot maintain a flat surface in the expanded state as shown in Fig. 30. That is, the cylindrical element is made of a flexible material. Folding structure must be made.)

《Second modification》
In addition, by applying the manufacturing method of the present embodiment, the axis AX1 is curved in a developed state as shown in FIG. 33 (cylindrical body), and in the folded state as shown in FIG. It is also possible to produce a cylindrical folding structure that becomes the body. The cone is formed such that the diameter dimension gradually changes along the direction of the axis AX1 that is curved. Hereinafter, a production method of the cylindrical folding structure shown in FIGS. 33 and 34 will be described.

It is known to obtain a development view of a cone from a development view of a non-curved cylinder by using vortex flow transformation, which is one of conformal mapping transformations. However, if this conformal mapping transformation is simply applied to the polygonal line development diagrams illustrated in FIGS. 17, 20, and 23, an error occurs. Here, a different point from the manufacturing method of the cylindrical folding structure demonstrated with reference to FIG. 9 is demonstrated. Note that description of similar processing is omitted.
Planar development unit 101 expands the tubular member surrounded by a boundary curve d ₁ and the boundary curve d ₂ in a two-dimensional plane, to create a strip developed view. Thereafter, the plane development unit 101, as shown in FIGS. 35 and 36, shows the boundary curves d1 and d2 similar to those shown in FIG. The curved boundary curves d1 ′ and d2 ′ are converted.
On the other hand, the broken line creating unit 102 divides each created two-dimensional broken line diagram into symmetrical strip figures. Then, the polygonal line creation unit 102 converts the divided symmetric strip figure into a symmetrical strip board figure that is curved in the same manner as the strip development by conformal mapping conversion, and outputs the data to the polygonal line development drawing unit 103. To do. That is, the broken line creating unit 102 converts a symmetric strip shape 13 similar to that shown in FIG. 6 into a curved strip shape 13 ′ shown in FIG. 36 by conformal mapping conversion.

After that, the broken line development drawing creation unit 103 includes data of the strip development drawing including the curved boundary curve input from the plane development unit 101, and data of the band plate folding drawing including the curved strip drawing figure input from the folding line creation unit 102. On the basis of the above, a strip developed view and a strip folded diagram that are curved with the same curvature are overlapped with each other to create a folded developed view depicting connection lines corresponding to the developed strip on the strip folded diagram. The broken line development drawing creation unit 103 outputs data of the created broken line development drawing to the printing apparatus 200. That is, the polygonal line development diagram creation unit 103 superimposes the curved boundary curves d1 ′ and d2 ′ obtained by the respective conformal mapping transformations and the curved strip shape 13 ′, as shown in FIG. A curved strip 10 ″ having axial connection lines FA ₀ and FB ₀ formed following the curved boundary curves d1 ′ and d2 ′ is obtained. A plurality of curved strips 10 ″ obtained in this way are arranged in the width direction, and adjacent axial connection lines FA ₀ and FB ₀ are connected to each other, so that the cylindrical folding shown in FIGS. A structure can be obtained.

In the above description, the fold line pattern of “(1) 1 node 4 fold line (type 1)” illustrated in FIG. 13 is taken as an example, but for example, “(2) 1 node 4 fold line (type 2)”. ”And“ (3) 1-node 6-fold line ”, a similar cylindrical folded structure can be obtained.
In the second modification, for example, the radius of curvature of the axis AX1 may gradually change along the direction of the axis AX1 as in the first modification.

《Third modification》
By using the manufacturing method of the present embodiment, for example, as shown in FIG. 37, a cylindrical body is formed by connecting a curved cylinder portion 10A in which the axis AX1 is bent in a deployed state and a straight cylinder portion 10B in which the axis AX1 is linear. As shown in FIG. 38, the cylindrical folding that can be formed into an annular plate-like body in plan view by folding the polygonal parts adjacent to each other along the mountain fold line and the valley fold line so as to shrink in the direction of the axis AX1. Can produce structures.

As the curved cylindrical portion 10A, for example, a cylindrical body shown in FIGS. Further, as the straight cylindrical portion 10B, for example, a conventional cylindrical body obtained by assembling a two-dimensional broken line diagram shown in FIGS. It is preferable that the folding line patterns formed in the curved cylinder portion 10A and the straight cylinder portion 10B are the same.
In the curved cylindrical portion 10A of the cylindrical body shown in FIG. 37, the radius of curvature of the axis AX1 is constant. For example, the radius of curvature of the axis AX1 may gradually change as shown in FIG. Further, the curved cylindrical portion 10A shown in FIG. 37 has a constant diameter dimension, but may be a cone whose diameter dimension gradually changes as shown in FIG. 33, for example.

  According to the third modified example, the unfolded cylindrical body can be easily arranged with respect to various portions. For example, even if the wall surface of the room has unevenness, the cylindrical body can be easily arranged along the unevenness of the wall surface.

[Second Embodiment]
Next, a second embodiment of the present invention will be described.
Compared with the cylindrical folding structure of the first embodiment, the cylindrical folding structure produced in the present embodiment has a gap region between the axial connection lines of the adjacent strips in the folded line development view. The only difference is that it is filled with the plate part, and the other points are the same. In the present embodiment, this difference will be described, and other descriptions will be omitted by attaching the same reference numerals.

(1) 1-node 4-fold line (Type 2)
39 to 42 are examples of a cylindrical folding structure manufactured using a plurality of the band plates 20 of FIG. In the fold line development view of the cylindrical folding structure shown in FIG. 39, a plurality of the band plates 20 of FIG. 14 are arranged in the width direction as in the fold line development view shown in FIG. Furthermore, in the developed view shown in FIG. 39, the joining plate portion 27 is provided between the axial connection lines CB ₀ and CA ₀ of the two adjacent strips 20 and 20.

The joining plate portion 27 fills a gap between the axial connection lines CB ₀ and CA _{0 of the} two adjacent strips 20 and 20. Joint plate portion 27 is formed symmetrically to the median line S ₄ which extends parallel to the symmetry axis S ₂ of the strip 20 as an axis in its widthwise center. Further, the joining plate portion 27 includes a plurality of joining parts 28 formed in a plate shape of a polygon in plan view (a quadrangle or a triangle in plan view). Further, the joining plate portion 27 is configured by connecting the outer sides of the adjacent joining parts 28 and 28 and forming a plurality of fold lines that can be folded at the connecting portion.

In the fold line pattern shown in FIG. 39, the fold line formed on the band plate 20 and the junction plate portion 27 are formed so that the difference between the number of mountain fold lines gathered at each node and the number of valley fold lines becomes two. And folding lines in the axial connection lines CA ₀ and CB ₀ and the circumferential connection lines CD ₀ and CE ₀ of the band plate 20 are set. In the fold line pattern of FIG. 39, as in the case of FIG. 14, four fold lines are gathered at one node, so that three mountain fold lines and one valley fold line are gathered at one node, or 1 One mountain fold line and three valley fold lines gather at the node.

The folding lines formed on the band plate 20 and the folding lines in the axial direction connection lines CA ₀ , CB ₀ and the circumferential direction connection lines CD ₀ , CE ₀ of the band plate 20 are the same as those in FIG.
Further, in the joint plate portion 27 of FIG. 39, a mountain fold line (axial mountain fold line CML4) extending from a node on each axial connection line CA ₀ , CB ₀ to the intermediate line S ₄ is provided on the joint plate portion 27. A plurality are arranged at intervals in the longitudinal direction. Axially convex fold CML4 adjacent in the longitudinal direction of the joint plate portion 27 is inclined in opposite directions with respect to the intermediate line S _4. Further, a plurality of axial convex fold CML4 formed on the bonding plate 27 is formed so as to be symmetrical about the median line S _4.

Furthermore, on the middle line S ₄ of the joint plate portion 27 shown in FIG. 39, longitudinally extending circumferentially convex fold CML5 and circumferential concave fold CVL5 intermediate line S ₄ are alternately arranged. These circumferential convex fold CML5 and circumferential concave fold CVL5 are arranged alternately node between the intermediate line S ₄ and axially convex fold CML4 as a boundary. Thus, the difference between the count of the number and concave fold of mountain fold lines gather nodes on the median line S ₄ is 2.

In the sheet member composed of the band plate 20 and the joining plate portion 27 on which the broken line pattern is formed as described above, when assembling by connecting only the upper and lower circumferential connection lines CD ₀ and CE _{0 of} each band plate 20, As shown in FIG. 40, the cylindrical folding structure becomes a linear cylindrical body in the unfolded state where adjacent polygon parts 21 and 21 are opened along the mountain fold line and the valley fold line. As shown in FIG. 41, in order for the tubular folding structure to be a tubular body with the axis AX1 curved in the unfolded state, the joining parts 28 and 28 adjacent to each other at the fold line formed on the joining plate portion 27. folded together, the adhesive overlapping the pair of joining parts 28 and 28 located on either side of the median line S _4, may be joined by welding or the like. When joined in this way, the joining parts 28, 28 located on both sides of the circumferential valley fold line CVL 5 of the joining plate portion 27 protrude inside the cylindrical body, and the circumferential mountain fold line CML 5 of the joining plate portion 27. The joining parts 28, 28 located on both sides of the tube are arranged so as to protrude outside the cylindrical body. Thereby, the axial connection lines CB ₀ and CA _{0 of the} two adjacent strips 20 are connected to each other.
Moreover, this cylindrical folding structure can fold adjacent polygon parts 21 and 21 along a mountain fold line and a valley fold line (refer FIG. 39) so that it may shrink | contract in the axis line AX1 direction. In this folded state, as shown in FIG. 42, the cylindrical folded structure becomes a plate-like body having an annular shape in plan view. In FIG. 42, the AR direction corresponds to the thickness direction of the plate-like body.

In addition, in order to obtain the cylindrical folding structure shown in FIGS. 41 and 42, the formula (1) and formula (3) shown in the first embodiment may be satisfied in the fold line development view shown in FIG. A pair of joining parts 28, 28 that connect two axial connection lines CB ₀ , CA ₀ facing each other in two adjacent strips 20, 20 without gaps and that are located on both sides of the intermediate line S ₄ are connected to each other. In order to overlap and join, the following formula should be satisfied.

In the above equation (9), βi (i = 2,..., M) is an angle between the axial mountain fold line CML1 of the strip 20 and the connection mountain fold line CML3 of the axial connection lines CA ₀ and CB ₀ . Γi (i = 2,... M) is an angle between the axial mountain fold line CML4 of the joining plate portion 27 and the connection line valley fold line CVL3 of the axial connection lines CA ₀ , CB ₀ , and βi and γi Are facing each other. M is the number of nodes in the axial connection lines CA ₀ and CB ₀ .
In the present embodiment, the broken line development drawing creating unit 103 draws a broken line at the joint so as to satisfy Equation 9. In other words, the broken line development drawing creation unit 103 draws a broken line that intersects the node at an angle corresponding to the angle at the node on the connection line at the joint.

(2) 1-node 6 folding line FIGS. 43-48 is an example of the cylindrical folding structure produced using the strip | belt board 30 of FIG. In the fold line development view of the cylindrical folding structure shown in FIGS. 43 to 45, a plurality of the strips 30 of FIG. 16 are arranged in the width direction as in the fold line development view shown in FIG. Furthermore, in the broken line development view shown in FIGS. 43 to 45, the joining plate portion 37 is provided between the axial connection lines DA ₀ and DB ₀ of the two adjacent strips 30.
The joining plate portion 37 fills a gap between the axial connection lines DA ₀ and DB _{0 of the} two adjacent strips 30. Joint plate portion 37 is formed symmetrically to the median line S ₄ as an axis extending parallel to the symmetry axis S ₂ of the strip 30 at its widthwise center. The joining plate portion 37 is composed of a plurality of joining parts 38 formed in a plate shape of a polygon in plan view (a quadrangle or a triangle in plan view), and connects the outer sides of the adjacent joining parts 38. A plurality of folding lines that can be folded are formed at the connection portion.

43 to 45, the folding line formed on the band plate 30 and the joining plate part 37 are set so that the difference between the number of mountain fold lines gathered at each node and the number of valley fold lines becomes two. And folding lines in the axial direction connection lines DA ₀ and DB ₀ and the circumferential direction connection lines DD ₀ and DE ₀ are set. The fold line pattern of FIG. 43 to 45, as in the case of FIG. 16, since the symmetry axis _{S 2} upward or axial connection line _DA 0, 6 pieces of folding lines 1 nodes on DB ₀ gather, one node Four mountain fold lines and two valley fold lines gather, or two mountain fold lines and four valley fold lines gather at one node. Further, since the four fold lines to one node on the intermediate line S ₄ is collected, three convex fold and one valley fold lines 1 node gather, or one convex fold to 1 node And three valley fold lines gather.

The fold lines formed on the strip 30 and the fold lines in the axial direction connection lines DA ₀ and DB ₀ and the circumferential direction connection lines DD ₀ and DE ₀ are the same as those in FIG.
Furthermore, Figure the joint plate portion 37 of 43 to 45, convex fold (axial convex fold DML4) extending from the nodes on each axial connection lines _DA 0, DB ₀ until the middle line _{S 4} and the valley fold lines ( The axial valley fold lines DVL4) are alternately arranged at intervals in the longitudinal direction of the bonding plate portion 37. An axial mountain fold line DML4 and an axial valley fold line DVL4 of the joint plate portion 37 extend one by one from the same node on the axial connection lines DA ₀ and DB ₀ .

A plurality of axially convex fold DML4 is inclined in the same direction relative to the intermediate line S _4. However, the inclination angle of the plurality of axial convex fold DML4 the intermediate line S ₄ are different from each other. A plurality of axially concave fold DVL4 is inclined in the same direction relative to the intermediate line S _4. However, the inclination angles of a plurality of axially concave fold DVL4 the intermediate line S ₄ are different from each other.
More axially convex fold formed in the junction plate 37 as DML4 and axial concave fold DVL4 is formed so as to be symmetrical about the median line S _4.

Further, on the intermediate line _{S 4} of the joint plate portion 37 of FIG. 43 to 45, longitudinally extending circumferentially convex fold CML5 and circumferential concave fold CVL5 intermediate line _{S 4} is folded axially mountain as above are alternately arranged nodes (the middle line node) as a boundary is the intersection of the line CML4 and axial concave fold CVL4 and the intermediate line S _4. Thus, the difference between the count of the number and concave fold of mountain fold lines gather nodes on the median line S ₄ is 2.

In the sheet composed of the band plate 30 and the joining plate portion 37 on which the broken line pattern is formed as described above, when the upper and lower circumferential connection lines DD ₀ and DE _{0 of} each band plate 30 are connected and assembled, As shown in FIG. 46, the fold-like structure becomes a linear cylindrical body in the unfolded state in which the adjacent polygon parts 31, 31 are opened along the mountain fold line and the valley fold line. As shown in FIG. 47, in order for the tubular folded structure to be a tubular body with the axis AX1 curved in the unfolded state, the joining parts 38, 38 adjacent to each other at the fold line formed on the joining plate portion 37 are used. folded together, they may be joined by overlapping a pair of bonding parts 38, 38 located on either side of the median line S _4. When joined in this way, the joining plate portion 37 protrudes inside the cylindrical body and is not exposed outward.
Moreover, this cylindrical folding structure can fold the polygonal parts 31 and 31 which adjoin each other along a mountain fold line and a valley fold line (refer FIGS. 43-45) so that it may shrink | contract in the axis line AX1 direction. In this folded state, as shown in FIG. 48, the cylindrical folded structure becomes a plate-like body having an annular shape in plan view. In FIG. 48, the arrow AR direction corresponds to the thickness direction of the plate-like body.

In addition, in order to obtain the cylindrical folding structure shown in FIGS. 47 and 48, the formulas (4) and (5) of the first embodiment described above should be satisfied in the fold line development views shown in FIGS. . Two adjacent axial connection lines DB ₀ and DA ₀ that are opposed to each other in two adjacent strips 30 and 30 are connected without gaps, and a pair of joining parts 38 and 38 located on both sides of the intermediate line S ₄ are connected to each other. In order to overlap and join, the following formula should be satisfied.

In the formula (10), m is the number of nodes in each axial connection lines _{DA 0,} DB 0, the number of connection lines convex fold DML3 in each axial connection lines _{DA 0,} DB 0. θi (i = 2,... m) is an angle formed by the i-th connecting line mountain fold line DML3 and the (i + 1) th connecting line mountain fold line DML3, and the counterclockwise direction is positive. For example, in the broken line development view shown in FIG. 43, θ ₃ and θ ₄ are negative. βi (i = 2,... m) is an angle between the axial mountain fold line DML1 and the axial valley fold line DVL1 of the strip 30 extending from the same node of the axial connection lines DA ₀ and DB ₀ . γi (i = 2,... m) is an angle between the axial mountain fold line DML4 and the axial valley fold line DVL4 of the joint plate portion 37 extending from the same node of the axial connection lines DA ₀ and DB ₀ .
43 to 45, the inclination angle δi (i = 2,. If it meets, you can set it arbitrarily. That is, the fold line patterns of the axial mountain fold line DML4 and the axial valley fold line DVL4 formed in the joining plate portion 37 are not limited to those illustrated in FIGS. For example, the fold line patterns of the axial mountain fold line DML4 and the axial valley fold line DVL4 formed in the joining plate portion 37 may be appropriately combined with those shown in FIGS.

According to the present embodiment, the cylindrical parts (adjacent to each other) can be obtained simply by joining the adjoining joining parts 28, 28 (38, 38) arranged between the strips 20, 20 (30, 30). Since the axial connection lines CA ₀ , CB ₀ (DA ₀ , DB ₀ ) of the strips 20, 20 (30, 30) can be connected to each other, it is easy to assemble a folded line drawing into a cylindrical body or a plate-like body Is possible.
Moreover, in the state assembled in the cylindrical body, the gap between the axial connection lines CA ₀ , CB ₀ (DA ₀ , DB ₀ ) of the cylindrical portions adjacent to each other is filled with the joining plate portion 27 (37). Further, it is possible to prevent a hole communicating with the inside and outside of the cylindrical body from being formed by a gap between the axial connection lines CA ₀ and CB ₀ (DA ₀ , DB ₀ ). Therefore, when air or liquid is filled in the cylindrical body, it is possible to reliably prevent the air or liquid from leaking to the outside, which is useful.

  In the present embodiment, the broken line development drawing creation unit 103 draws a broken line at the joint so as to satisfy Expression 10. In other words, the broken line development drawing creation unit 103 draws a broken line that intersects the node at an angle corresponding to the angle at the node on the connection line at the joint.

[Third embodiment]
Next, a third embodiment of the present invention will be described.
The cylindrical folding structure produced in the present embodiment is a cylindrical folding structure in which the radius of curvature of the axis AX1 gradually changes, as in the first modification of the first embodiment (see FIGS. 29 to 31). However, there is a difference in the broken line development diagram in the middle of the production.
That is, in the first modified example of the first embodiment, in order to produce a cylindrical folding structure in which the radius of curvature of the axis AX1 gradually changes, two adjacent strips 10 ′ in the folded line development view (FIG. 29). , 10 'are different in size (gap size) (the shape of the connecting line in the axial direction of the strip 10' is different). On the other hand, in this embodiment, in the broken line development view (FIG. 50), the width dimensions of two adjacent strips 10 ′ and 10 ′ are different. Hereinafter, this point will be described with reference to FIGS.

Cylindrical folded structure curvature of the axis R ₁ radius changes gradually as shown in FIG. 51, for example, in a polygonal line developed view shown in FIG. 50, next to the width of a plurality of strips 10 'are arranged in the width direction It is possible to produce by differentiating between the matching strips 10 ', 10'. 50, the folding line pattern formed on each strip 10 ′ is the same as the folding line pattern of “(1) 1 node 4 folding line (type 1)” illustrated in FIG. 13 of the first embodiment. It is.
In Figure 50, the most pairwise strip located on the left side 10 ', width _{R 1} of the 10' is the smallest, pairwise strip 10 ', in units of 10', the strip 10 ' Are gradually increased to R ₂ and R ₃ . In this case, the size and shape of the gap region 15 ′ (gap size) between the two adjacent strips 10 ′ and 10 ′ may be the same among the plurality of gap regions 15 ′.

The cylindrical folding structure shown in FIGS. 51 and 52 is connected to the circumferential connection lines BD ₀ and BE ₀ of the respective band plates 10 ′ in the folded line development view of FIG. It is produced by assembling and connecting the axial connection lines BB ₀ and BA ₀ of two strips 10 ′ and 10 ′ (cylindrical portions) adjacent to each other.
As shown in FIG. 51, in this unfolded state where the adjacent polygonal parts 11 ′ and 11 ′ are opened along the mountain fold line and the valley fold line, the cylindrical folding structure has a radius of curvature of the axis AX1. A cylindrical body that gradually changes along the direction of the axis AX1. In the cylindrical body shown in FIG. 51, the smaller the axial dimension of the cylindrical part (the width dimension of the strip 10 '), the smaller the radius of curvature of the cylindrical body, and the axial dimension of the cylindrical part (the strip 10'). The larger the width dimension is, the larger the radius of curvature of the cylindrical body is.
In addition, as shown in FIG. 52, this cylindrical folding structure is formed by folding adjacent polygonal parts 11 ′ and 11 ′ along a mountain fold line and a valley fold line so as to shrink in the direction of the axis AX1. As in the case of the first embodiment, the cylindrical folded structure can be a plate-like body having an annular shape in plan view.

50 to 52, the fold line pattern of the strip 10 'is a fold line pattern of "(1) 1 node 4 fold line (type 1)" illustrated in FIG. However, for example, the fold line pattern of the band plate 10 ′ may be a fold line pattern of “(2) 1 node 4 fold line (type 2)” illustrated in FIG. 14.

Here, a different point from the manufacturing method of the cylindrical folding structure demonstrated with reference to FIG. 9 is demonstrated. Note that description of similar processing is omitted.
In step ST2, when the planar development unit 101 determines a circular cross section for dividing the cylindrical structure into a plurality of cylindrical members in a direction orthogonal to the axis AX1 direction, the length of the cylindrical member in the axis AX1 direction is determined. Increase the length gradually. That is, as shown in FIG. 49, the flat surface development portion 101 sets the length of the first two cylindrical members in the direction of the axis AX1 to R ₁ , and the length of the next two cylindrical members in the direction of the axis AX1 as R _2. to the axis AX1 direction of length of the next two tubular members with R _{3. However,} it is _{R 1 <R 2 <R 3} .
Moreover, in step ST4, the broken line creation part 102 sets the width | variety of a symmetrical strip board figure according to the length of the axial line AX1 direction of a cylindrical member.
Then, in step ST5, the broken line development diagram creation unit 103 is based on the two-dimensional development diagram data input from the plane development unit 101 and the two-dimensional polygon diagram data input from the folding line creation unit 102. A broken line development diagram is created in which connection lines corresponding to the two-dimensional development diagram are drawn on the top. Thereby, the broken line development drawing creation unit 103 can create a broken line development drawing as shown in FIG.

  As described above, based on the two-dimensional development created by the plane development unit 101, the broken line development drawing creation unit 103 becomes symmetrical with respect to the central axis passing through the center in the axial width of the cylindrical member. Then, a broken line development view in which a broken line is provided on the belt plate development drawing is created. Thereby, the broken line development drawing creation unit 103 can create a broken line development drawing having regularity, and can simplify the manufacturing process of the cylindrical folding structure.

According to the cylindrical folding structure of the present invention, a cylindrical body having a curved axis can be used for various products. For example, it can be used for lifebuoys, liferafts, paragliders, clothes, lighting equipment, and the like.
For example, a donut-shaped life-saving device is known as a general life-saving device, but if the cylindrical folding structure of the present invention is used, a C-shaped life-saving device having a notch in a part in the circumferential direction Can be configured. In this case, the lifebuoy can be easily detached by passing the body (torso) through the notch.
Further, for example, by connecting a large number of U-shaped (half-torus-shaped) cylindrical bodies, it is possible to configure a life raft having a bottom wall and a side wall and a roof portion that covers the top of the life raft. In this case, even if one of the many cylindrical bodies is damaged and flooded, lifesaving rafts can be prevented from undergoing fatal damage.

Furthermore, the above-described structure of the life raft and the roof portion can be applied to, for example, a simple bed in an evacuation center or a roof portion of the simple bed, and a private space can be secured. Comfort in the private space can also be improved because the air layer inside the cylindrical body plays a role as a heat insulating layer.
In addition, the cylindrical body having a curved axis can be used for a canopy (film portion) that constitutes a parachute such as a paraglider.

And when conveying the cylindrical folding structure which can be used for various uses as mentioned above, it is folded very small so that it becomes a plate-like body, and the storage performance is improved, so it is easily transported. It is possible. For example, it is possible to effectively utilize the indoor space of a ship or aircraft by reducing the storage space for a lifebuoy, a liferaft, or an emergency parachute in a ship or aircraft. In addition, for example, even in a distant disaster area, a large number of simple beds can be transported simultaneously. Furthermore, the simple bed can be easily stored in the evacuation bag even at home.
Compared with the case where the axis formed by the elastically deformable material curves the linear tubular body, for example, there is an advantage that the tubular folded structure is not stressed and therefore does not deteriorate.

Moreover, the cylindrical folding structure of the present invention can be applied to clothes suitable for storage and travel, for example, by folding it into a flat surface (plate-like body). In particular, since the cylindrical folding structure of the present invention can form a cylindrical body having a curved axis, the clothes using this have good adaptability to the human body (for example, arms, legs, and trunk). .
Moreover, since the cylindrical folding structure of the present invention can fold a complex shape into a flat surface (plate-like body), it can be applied to, for example, shades of lamps, lamp shades, and the like. By utilizing the present invention, it is possible to obtain a lighting fixture that is easy to store and that has excellent design.

DESCRIPTION OF SYMBOLS 100 Manufacturing apparatus of cylindrical folding structure 101 Plane expansion | deployment part 102 Folding line preparation part 103 Folding line expansion drawing preparation part 200 Printing device 10,10 ', 20,30, strip 10 "Curved strip 10A Curved cylinder 10B Linear cylinder Part 13 Symmetrical strip graphic 13 'Curved strip graphic 11, 11, 1', 21, 31 Polygonal parts 15, 15 ', 25, 35 Gap area 27, 37 Joint plate parts 28, 38 Joint parts BA ₀ , BB ₀ , CA ₀ , CB ₀ , DA ₀ , DB ₀ axial connection line BD ₀ , BE ₀ , DD ₀ , DE ₀ , DD ₀ , DE ₀ circumferential connection line AX 1 axis S ₂ symmetry axis

Claims (11)

The plane expansion part
The cylindrical structure virtually represented in a three-dimensional space is divided into a plurality of cylindrical members in a direction orthogonal to the axial direction, the divided cylindrical members are expanded on a two-dimensional plane, and the expanded Creating a two-dimensional development view including at least one strip development view corresponding to the tubular member;
The polygonal line creation department
A plurality of symmetrical strip figures having the same length as the axial width of the cylindrical member divided by the planar development portion, and the folding line intersecting the symmetry axis at a predetermined angle is the symmetrical strip figure Create a 2D line diagram in the
The polygonal line drawing creation department
Based on the two-dimensional development drawing created by the plane development unit and the two-dimensional folding diagram created by the folding line creation unit, a central axis passing through the center in the axial width of the cylindrical member A manufacturing method of a cylindrical folding structure, comprising creating a folded line development view in which a folding line is provided on the belt plate development view so as to be symmetrical with respect to the left and right sides. The broken line development drawing creation unit
2. The tubular shape according to claim 1, wherein the broken line development view is created by drawing a connecting line connecting points where the outer edges of the strip development view where the tubular member is developed and the folding line intersect. A manufacturing method of a folding structure. The broken line development drawing creation part
3. The method for manufacturing a cylindrical folding structure according to claim 2, wherein a region surrounded by the connection line is determined as a joint portion. The broken line development drawing creation part
The tubular folding structure according to claim 3, wherein a folding line is provided in the joining portion so that the joining portion is in a planar state in the tubular folding structure created based on the folded line development view. Manufacturing method. The broken line development drawing creation unit
The strip plate in which the cylindrical member is developed by overlapping the strip plate development diagram and the symmetrical strip plate figure in a state where the symmetry axis of the symmetrical strip plate figure and the central axis of the tubular member coincide with each other. 5. The method for manufacturing a cylindrical folding structure according to claim 2, wherein the connection line connecting the points where the outer edge of the development view intersects with the folding line is drawn. 6. The broken line development drawing creation part
Create a curved curved strip developed by transforming the outer edge of the strip developed by conformal mapping, create a curved curved strip by transforming the symmetrical strip graphic, and create the curved The connection line connecting the points where the outer edge of the curved strip development and the fold line of the curved strip are crossed is drawn by overlapping the strip development and the curved strip graphic. 5. A method for producing a cylindrical folded structure according to 5. The broken line development drawing creation part
The valley fold line connected to the valley fold node provided on the central axis and the mountain fold line connected to the mountain fold node provided alternately with the valley fold node on the central axis in the fold line development view The number of the mountain fold lines connected to the mountain fold line node by providing a mountain fold line two fewer than the number of the valley fold lines connected to the valley fold line node and connecting the mountain fold line to the valley fold node The manufacturing method of the cylindrical folding structure according to any one of claims 1 to 4, wherein a valley fold line that is two fewer than is connected to the mountain fold node. The planar development part is
Dividing into a plurality of cylindrical members having different lengths in a direction orthogonal to the axial direction, expanding the divided cylindrical members on a two-dimensional plane, and developing a strip corresponding to the expanded cylindrical member The manufacturing method of the cylindrical folding structure according to any one of claims 1 to 7, wherein a two-dimensional development view including at least one figure is created. The broken line development drawing creation part
When the cylindrical structure is curved with a constant curvature, a plurality of the bands are duplicated by duplicating a band plate folding diagram in which a folding line is provided in the band plate development view so as to be bilaterally symmetrical with respect to the central axis. The manufacturing method of the cylindrical folding structure according to any one of claims 1 to 7, wherein the development of the folding line is created by connecting plate folding diagrams.   A curved tubular folded structure manufactured on the basis of the folded line drawing created by the method for producing a tubular folded structure according to any one of claims 1 to 8. The cylindrical structure virtually represented in a three-dimensional space is divided into a plurality of cylindrical members in a direction orthogonal to the axial direction, the divided cylindrical members are expanded on a two-dimensional plane, and the expanded A plane development unit for creating a two-dimensional development view including at least one strip development view corresponding to the tubular member;
A plurality of symmetrical strip figures having the same length as the axial width of the cylindrical member divided by the planar development portion, and the folding line intersecting the symmetry axis at a predetermined angle is the symmetrical strip figure A polygonal line creation section for creating a two-dimensional polygonal line diagram provided in
Based on the two-dimensional development drawing created by the plane development unit and the two-dimensional folding diagram created by the folding line creation unit, a central axis passing through the center in the axial width of the cylindrical member A fold line development drawing creation unit for creating a fold line development view in which a fold line is provided in the band plate development view so as to be symmetrical with respect to the left and right,
The manufacturing apparatus of the cylindrical folding structure characterized by including.