A foldable origami unit and flexible deployable deformable member

Abstract

The application discloses a foldable origami unit and a flexible deployable deformable member, and the deformable member comprises a plurality of layers of bendable tubular structures based on the origami principle in the axial direction, and each layer of the origami structure comprises a plurality of combined origami units connected in the circumferential direction; in each layer of the origami structure, two foldable origami units in each combined origami unit are connected in the following manner: a fold line segment of one foldable origami unit is connected with a fold line segment of another foldable origami unit; two combined origami units are connected in the following manner: two fifth edges of two foldable origami units in one combined origami unit are connected with two fifth edges of two foldable origami units in another combined origami unit. The deployable deformable member has the advantages of flexible planar parallel stacking in a folded state, a small folding envelope and high specific stiffness, and is suitable for special space application scenarios.

Description

TECHNICAL FIELD

[0001] The present application relates to a foldable paper structure, in particular to a foldable paper unit and a flexible deployable deformable member. BACKGROUND

[0002] The existing foldable paper tubular structure configuration is mostly a basic configuration, and the innovation of the foldable paper structure configuration has no theoretical guidance. The existing tubular structure based on the foldable paper principle cannot realize the stable state of the bending shape, and most of them are the stable state of the vertical complete unfolding. For special space application scenarios, the unfolding state of the tube is required, that is, the tube needs to be curved and stable when completely unfolded. SUMMARY

[0003] The present application provides a foldable paper unit and a flexible deployable deformable member to overcome the prior art. The member is curved and in a stable state when completely unfolded.

[0004] A foldable paper unit is a combination of two symmetrical hexagonal structures, the symmetry line is the common long side of the two hexagonal structures, the long side forms a straight crease OO' common to the two hexagonal structures, the common side boundary point O between the triangular apex B of the two hexagonal structures forms a peak crease, the common side boundary point O between the quadrilateral apex C of the two hexagonal structures forms a valley crease, the common side boundary point O' between the quadrilateral apex C of the two hexagonal structures forms a peak crease, and the third side AB and the fourth side BC are boundary creases, which are connecting creases common to the foldable paper unit and the adjacent foldable paper unit. Wherein, in each hexagonal structure, ∠OAB = 90°, ∠O'DC = 90°, α1 represents the angle of ∠AOB in each hexagon, α2 represents the angle of ∠BOC in each hexagon, and m represents the number of combined paper units.

[0005] A flexible deployable deformable member is an axial k-layer bendable tubular structure based on the foldable paper principle. The bendable tubular structure is defined as a foldable paper structure, and each layer of foldable paper structure includes m connected combined paper units in the circumferential direction. Wherein k≥1, m≥2; each combined paper unit includes two foldable paper units; in each combined paper unit, the fold line segment AOG of one foldable paper unit is connected to the fold line segment AOG of the other foldable paper unit; and the fifth edge CD of two combined paper units is connected to the fifth edge CD of two foldable paper units in another combined paper unit.

[0006] Based on the first scheme, further, when k>=2, the connection mode of the adjacent layers of the origami structure is that the four third edges AB of the two combined origami units in the upper layer of the origami structure are connected with the four third edges AB of the two combined origami units in another lower layer of the origami structure, and the four fourth edges BC of the two combined origami units in the upper layer of the origami structure are connected with the four fourth edges BC of the two combined origami units in another lower layer of the origami structure.

[0007] Another foldable origami unit is a combination of two parallelogram structures, the symmetry line is the long edge shared by the two parallelogram structures, the long edge is the boundary crease OD shared by the two parallelogram structures, the boundary crease OD has a foldable vertex O', the boundary point O is connected with two boundary points E of the two parallelogram structures to form diagonal creases, the opposite long edges of the two parallelogram structures are respectively provided with foldable points F, the boundary point O is connected with the two foldable points F to form straight creases OF, and the foldable vertex O' is connected with the boundary point O, the connection point D and the two boundary points E to form straight creases O'D, wherein the straight crease O'D and the two diagonal creases OE are valley lines, the straight creases OO', the two straight creases OF and the two straight creases O'E are peak lines, wherein, α 11 represents the angle of ∠GOF in each hexagon, α 21 represents the angle of ∠FOE in each hexagon, and n represents the number of the foldable origami units.

[0008] Another flexible deployable deformable member is a k-layer bendable tubular structure based on the principle of origami in the axial direction, the bendable tubular structure is defined as an origami structure, each layer of the origami structure comprises n connected origami units in the circumferential direction; wherein k>=1 and n>=3; in each layer of the origami structure, the connection mode of the adjacent two foldable origami units is that the fold line edge EDE of the former foldable origami unit is connected with the fold line edge GOG of the latter foldable origami unit, and the adjacent two foldable origami units are connected in a closed loop.

[0009] Based on the second scheme, further, when k>=2, the connection mode of the adjacent layers of the origami structure is that all the third interlayer boundary creases GF of the adjacent foldable origami units are connected, all the fourth interlayer boundary creases FE of the adjacent foldable origami units are connected, the third interlayer boundary crease GF is a valley line, and the fourth interlayer boundary crease FE is a peak line.

[0010] The beneficial effects of the present application compared with the prior art are:

[0011] Compared with the prior art, the application provides an innovative paper folding configuration, and the flexible deployable and deformable member structure has an axial stretchability and a bendability, in particular, the flexible deployable and deformable member structure constructed by the hexagonal foldable paper folding unit has a bistable characteristic, has the advantages of kresling mode and yoshimura mode, is free of stress in a stable state plane, and has a panel deformation transition function in a bending process.

[0012] The two deployable and deformable members have the advantages of a small folding envelope and high specific stiffness in a folded state, and are suitable for special space application scenarios, such as a space stretching arm, a flexible solar wing deployment and support, a space sunshade, and the like.

[0013] The technical solutions of the application are further described below with reference to the drawings and embodiments: DESCRIPTION OF DRAWINGS

[0014] Figure 1 A schematic view of the foldable paper folding unit of the first solution of the application in an unfolded state;

[0015] Figure 2 A schematic view of the paper folding unit of the first solution of the application in a folded state; Figure 1

[0016] A schematic view of a combined paper folding unit in the bistable deployable and deformable member of the first solution of the application; Figure 3

[0017] A geometric configuration view of the combined paper folding unit; Figure 4

[0018] A top view of a single-layer tubular member obtained by splicing two combined paper folding units in the embodiment of the first solution; Figure 5

[0019] A schematic view of the first solution of the embodiment in which a plurality of foldable paper folding units are spliced and unfolded in a transverse and longitudinal direction; Figure 6

[0020] A folded state view of the tubular member obtained by connecting a plurality of paper folding structures in the embodiment of the first solution; Figure 7

[0021] A schematic view of the half-unfolded state of the tubular member in the embodiment of the first solution; Figure 8

[0022] A schematic view of the fully unfolded state of the tubular member in the embodiment of the first solution; Figure 9

[0023] A bending state view of the double-layer paper structure tubular member in the embodiment; Figure 10

[0024] ​Figure 11 A schematic view of the folded paper unit of the second aspect of the present application after unfolding;

[0025] Figure 12 A schematic view of the folded paper unit of the second aspect of the present application after unfolding; Figure 11

[0026] Figure 13 A schematic view of the folded paper unit of the second aspect of the present application after unfolding;

[0027] Figure 14 A schematic view of the folded paper unit of the second aspect of the present application after unfolding;

[0028] Figure 15 A schematic view of the folded paper unit of the second aspect of the present application after unfolding;

[0029] Figure 16 A schematic view of the folded paper unit of the second aspect of the present application after unfolding;

[0030] Figure 17 A schematic view of the folded paper unit of the second aspect of the present application after unfolding;

[0031] Figure 18 A schematic view of the folded paper unit of the second aspect of the present application after unfolding; DETAILED DESCRIPTION

[0032] The embodiments of the technical solutions of the present application will be described in detail below with reference to the accompanying drawings. Unless otherwise specified, the technical terms or scientific terms used in this application should be understood as the usual meanings understood by the skilled person in the field of the present application.

[0033] As shown in FIGS. 1 and 2, the present embodiment provides a first aspect, a foldable paper unit is a combination of two symmetrical hexagonal structures, the symmetry line is the common long side of the two hexagonal structures, the long side forms a straight crease OO' common to the two hexagonal structures, the peak crease is formed between the common edge point O and the triangular vertex B of the two hexagonal structures, the valley crease is formed between the common edge point O and the quadrilateral vertex C of the two hexagonal structures, the peak crease is formed between the common edge point O' and the quadrilateral vertex C of the two hexagonal structures, the third side AB and the fourth side BC are boundary creases, which are connecting creases common to the foldable paper unit and the adjacent foldable paper unit; Figure 1 Figure 2 In each hexagonal structure, ∠OAB = 90°, ∠O' DC = 90°,

[0034] In each hexagonal structure, ∠OAB = 90°, ∠O' DC = 90°,

[0035] In each hexagonal structure, ∠OAB = 90°, ∠O' DC = 90°,​ α1 represents the angle of ∠AOB in each hexagon, α2 represents the angle of ∠BOC in each hexagon, and m represents the number of combined origami units.

[0036] As can be seen from the figure, the outer edges of the crease lines of the origami units are irregular, and the edge line O'D of the two hexagons needs to be bonded when actually bending and folding.

[0037] Mirror connection of basic origami units: the eight-crease vertices O of two identical foldable origami units are bonded to each other, and the two foldable origami units are mirror-symmetric about the mirror axis OA to form a combined origami unit, as shown in Figure 3 .

[0038] The origami units for constructing a tubular member need to meet the above conditions, which are verified as follows:

[0039] Figure 4 The middle crease OO' intersects with the extension line of the crease CB at point G, and the corresponding point about the symmetry axis OA is H. The intersection O" of the perpendicular bisector of OG and CG is the center of the circumscribed circle of the regular polygon, and the length R of O" G is the radius of the circumscribed circle.

[0040] Since points O, G, and C are all points on the circumference of the circumscribed circle O", O"O = O"C = R, so triangle O"OC is an isosceles triangle. In triangle O"OC, we have

[0041] ∠O"OC = ∠O"CO (1)

[0042] Also

[0043]

[0044] By combining equation (1) and equation (2), we have

[0045] α1 = β2 (3)

[0046] Then we have

[0047] θ = π - 2α1 + 2α2 = π - 2β2 + 2α2 (4)

[0048] Therefore, the condition for the combined unit to form a closed tubular member is:

[0049]

[0050] By combining equation (4) and equation (5), we have

[0051]

[0052] In the formula, m is the number of combined origami units required to form a closed tubular member.

[0053] In particular, when α1+β1=90°, the combined origami unit becomes a standard bistable combined unit configuration; taking m=2, the closed tubular member composed of bistable combined origami units is shown in Figure 5 .

[0054] In particular, a bistable flexible deployable deformable member is an axial k-layered tubular structure based on the principle of origami, the bendable tubular structure is defined as an origami structure, each layer of the origami structure comprises m connected combined origami units in the circumferential direction; wherein k≥1, m≥2; each combined origami unit comprises two foldable origami units based on the foregoing;

[0055] As shown in Figure 5 and Figure 6 , in each layer of the origami structure, the connection mode of the two foldable origami units in each combined origami unit is that the fold line segment AOG of one foldable origami unit is connected to the fold line segment AOG of the other foldable origami unit; the connection mode of the two combined origami units is that the two fifth edges CD of the two foldable origami units in one combined origami unit are connected to the two fifth edges CD of the two foldable origami units in the other combined origami unit.

[0056] The combined origami unit becomes the smallest unit for building a bistable deployable member, and a closed tubular member composed of multiple layers of paper structures requires multiple combined origami units, and the splicing of the combined origami units is shown in Figure 6 .

[0057] The crease pattern of the closed circular tube composed of combined origami units is shown in Figure 6 , in which the solid line represents the peak crease, the dashed line represents the valley crease, and the double line with an arrow indicates that the adjacent edges are bonded together. It is worth noting that when the combined origami unit is used to form a closed tubular member, it cannot be folded into a closed tube like a classic crease pattern, but some edges need to be bonded, which means that this kind of combined origami unit cannot be unfolded into a plane after bonding.

[0058] In particular, as described in Figure 5 , the deployable deformable member is a single-layer tubular structure.

[0059] In particular, as shown in Figures 7-9 , when k≥2, the connection mode of the origami structures of adjacent layers is that the four third edges AB of the two combined origami units in the upper layer origami structure are connected to the four third edges AB of the two combined origami units in the other lower layer origami structure, and the four fourth edges BC of the two combined origami units in the upper layer origami structure are connected to the four fourth edges BC of the two combined origami units in the other lower layer origami structure.

[0060] Figure 7 For the retracted state, the retracted state flexible plane parallel stack, the advantages: retracted envelope small; no stress in the plane;

[0061] Figure 8 For the half-open state, the plane can produce flexible buckling deformation, wrinkle deformation occurs;

[0062] Figure 9 For the fully open state, the specific rigidity is high, and there is no stress in the plane;

[0063] Figure 10 For the bending state, the unilateral angle in the plane is changed from a right angle to an obtuse angle, and the folded paper structure is changed from vertical to curved stable state. The folded paper structure can break the stable state under the action of external force and occur bending deformation.

[0064] The tubular member constructed in this embodiment has a bistable structure.

[0065] Further, the material of the deployable member is silica gel plastic or thermoplastic polyurethane elastomer rubber, etc. It is easy to obtain materials, convenient for processing and use.

[0066] To verify the foldability and bistable characteristics of the proposed paper folding configuration, a foldable folded tubular member is made of PP plastic. The size of the paper folding structure: the cross section radius (outer section circle) R is 0.25m, and the single layer unfolded length is 0.72m; the preliminary folding test verifies that the paper folding structure has the characteristics of unfoldable, bendable and bistable; the axial fully unfolded state is a stable state with certain structural rigidity; after bending, the paper folding structure has good cross section rigidity, and the specific physical diagram is shown in Figures 16-18 .

[0067] Based on the above foldable paper folding unit and bistable deployable deformable member, the size design of the tubular member needs to be designed according to the specific application scene, therefore, the cross section size and the unfolded height of the tubular member need to be analyzed and calculated. Considering the length of the crease in the paper folding configuration, the configuration description of the paper folding unit and the combined paper unit is shown in Figure 4 ;

[0068] As shown in Figure 4 , in triangle OHB, ∠HOB = α3-α2, assuming O'H = BH = m, O'O = L, OB = c

[0069] According to the cosine theory, we have:

[0070] m 2 = (L + m) 2 + c 2 - 2 (L + m) c cos (α3-α2) (7)

[0071] It can be derived that:

[0072]

[0073] Similarly, in isosceles triangle OO"H, we have:

[0074]

[0075] Thus, the radius R of the circumscribed circle of the cross section of the cylindrical origami structure can be calculated.

[0076] The fully unfolded state of the double-layer cylindrical origami structure is shown in FIG. 2B. In the fully unfolded state, the crease OA is in a vertical state, and thus the height of the single-layer tubular member after being fully unfolded is h. Figure 9 h = 2a; where a is the length of side OA (10)

[0077] In another embodiment, another solution is provided, as shown in FIG. 3A. The foldable origami unit provided in this embodiment is a combination of two parallelogram structures that are symmetrical about a common long side of the two parallelogram structures.

[0078] Figures 11-12 The common long side is a boundary crease OD shared by the two parallelogram structures, and the boundary crease OD has a foldable vertex O' thereon. The common boundary point O and two boundary points E of the two parallelogram structures form diagonal creases OE. The opposite long sides of the two parallelogram structures respectively have two foldable points F. The common boundary point O and the two foldable points F form straight creases OF. The foldable vertex O' and the common boundary point O, the common connection point D, and the two boundary points E form straight creases O'D and O'OE. The straight creases O'D and the two diagonal creases OE are valley lines, and the straight creases OO', the two straight creases OF, and the two straight creases O'E are peak lines. In this embodiment, the angle of ∠GOF in each hexagon is represented by a, the angle of ∠FOE in each hexagon is represented by β, and the number of the origami units is represented by n. α 11 The angle of ∠GOF in each hexagon is represented by a. 21 The angle of ∠FOE in each hexagon is represented by β, and the number of the origami units is represented by n.

[0079] The unfolding and crease diagram of the origami unit is shown in FIG. 3B, and the schematic diagram of the folded origami unit is shown in FIG. 3C. α 11 The angle of ∠GOF in each hexagon is represented by a. 21 The angle of ∠FOE in each hexagon is represented by β, and the number of the origami units is represented by n. Figure 11 The unfolding and crease diagram of the origami unit is shown in FIG. 3B, and the schematic diagram of the folded origami unit is shown in FIG. 3C. Figure 12 The unfolding and crease diagram of the origami unit is shown in FIG. 3B, and the schematic diagram of the folded origami unit is shown in FIG. 3C. The unfolding and crease diagram of the origami unit is shown in FIG. 3B, and the schematic diagram of the folded origami unit is shown in FIG. 3C.

[0080] The unfolding and crease diagram of the origami unit is shown in FIG. 3B, and the schematic diagram of the folded origami unit is shown in FIG. 3C. The unfolding and crease diagram of the origami unit is shown in FIG. 3B, and the schematic diagram of the folded origami unit is shown in FIG. 3C.

[0081] The unfolding and crease diagram of the origami unit is shown in FIG. 3B, and the schematic diagram of the folded origami unit is shown in FIG. 3C. Figure 13The figure shows the four-fold and eight-fold combined unit after the folding paper units are spliced, the dotted area in the figure represents the folding paper unit of the above embodiment, the vertex where the "●" is located is the eight-fold vertex, and the vertex where the "○" is located is the four-fold vertex, and the combined unit is composed of two Kresling paper structures and four triangles. The above combined unit can be constructed into a multi-layer tubular member.

[0082] Figure 14 The figure shows the splicing process of two adjacent folding paper units, Figure 15 The figure shows the splicing process based on Figure 14 The figure shows the top view of the splicing of eight folding paper units into a single-layer or multi-layer deployable tubular member.

[0083] Specifically, based on the second folding paper unit scheme, the flexible deployable and deformable member is an axially k-layer bendable tubular structure based on the folding paper principle, and the bendable tubular structure is defined as a folding paper structure, and each layer of the folding paper structure comprises n connected folding paper units in the circumferential direction; wherein k≥1, n≥3; in each layer of the folding paper structure, the connection mode of the adjacent two folding paper units is that the fold line edge EDE of the former folding paper unit is connected with the fold line edge GOG of the latter folding paper unit, and the adjacent two folding paper units are connected end to end.

[0084] Further, the deployable and deformable member is a single-layer tubular structure.

[0085] Further, when k≥2, the connection mode of the adjacent layers of the folding paper structure is that all the third interlayer boundary folds GF of the adjacent folding paper units are connected, all the fourth interlayer boundary folds FE of the adjacent folding paper units are connected, and the third interlayer boundary fold GF is a valley line and the fourth interlayer boundary fold FE is a peak line.

[0086] Optionally, the material of the deployable and deformable member is silica gel, plastic, or thermoplastic polyurethane elastomer rubber, etc.

[0087] The second folding paper unit is constructed into a tubular structure, and the size verification principle of the tubular member meets the conditions as shown in the first scheme, which will not be described here.

[0088] The present application has been disclosed above with reference to the preferred embodiments, but is not intended to limit the present application, and any person skilled in the art can make some changes or modifications to the above disclosed structure and technical content without departing from the scope of the technical solutions of the present application, and equivalent embodiments with equivalent changes are still within the scope of the technical solutions of the present application.

Claims

1. A foldable origami unit; characterized by: The foldable paper-folding unit is a combination of two symmetrical hexagonal structures, the symmetry line is the common long side of the two hexagonal structures, the long side forms a straight crease OO' shared by the two hexagonal structures, the common side boundary point O forms a peak crease between the triangular vertex B of the two hexagonal structures, the common side boundary point O forms a valley crease between the quadrilateral vertex C of the two hexagonal structures, the common side boundary point O' forms a peak crease between the quadrilateral vertex C of the two hexagonal structures, the third side AB and the fourth side BC are boundary creases, which are connecting creases shared by a paper-folding unit and an adjacent paper-folding unit; Wherein, in each hexagonal structure, ∠OAB = 90°, ∠O'DC = 90°, a1 represents an angle of ∠AOB in each hexagon, a2 represents an angle of ∠BOC in each hexagon, and m represents the number of combined origami units.

2. A flexible deployable deformable member characterized by: The unfoldable and deformable member is a k-layer bendable tubular structure based on the paper-folding principle in the axial direction, the bendable tubular structure is defined as a paper-folding structure, each layer of paper-folding structure comprises m connected combination paper-folding units in the circumferential direction; wherein k≥1, m≥2; each combination paper-folding unit comprises two foldable paper-folding units based on claim 1. In each layer of paper-folding structure, the connection mode of the two foldable paper-folding units in each combination paper-folding unit is that the fold line segment AOG of one foldable paper-folding unit is connected with the fold line segment AOG of the other foldable paper-folding unit; the connection mode of the two combination paper-folding units is that the two fifth sides CD of the two foldable paper-folding units in one combination paper-folding unit are connected with the two fifth sides CD of the two foldable paper-folding units in the other combination paper-folding unit.

3. A flexible deployable morphing member according to claim 2, wherein: The unfoldable and deformable member is a single-layer tubular structure.

4. The flexible deployable morphing member of claim 2, wherein: When k≥2, the connection mode of the paper-folding structures of adjacent layers is that the four third sides AB of the two combination paper-folding units in the upper layer of paper-folding structure are connected with the four third sides AB of the two combination paper-folding units in the lower layer of paper-folding structure, and the four fourth sides BC of the two combination paper-folding units in the upper layer of paper-folding structure are connected with the four fourth sides BC of the two combination paper-folding units in the lower layer of paper-folding structure.

5. The flexible deployable morphing member of claim 2, wherein: The material of the unfoldable and deformable member is craft paper, plastic or thermoplastic polyurethane elastomer rubber.

6. A foldable origami unit, characterized by: The foldable paper unit is a combination of two parallelogram structures, the symmetry line is the long side shared by the two parallelogram structures, the long side is the boundary fold OD, the boundary fold OD has a foldable vertex O', the common boundary point O and the two boundary points E of the two parallelogram structures form diagonal fold OE, the opposite long sides of the two parallelogram structures are respectively provided with foldable points F, the common boundary point O and the two foldable points F form straight fold OF, and the foldable vertex O' and the common boundary point O, the common connecting point D and the two boundary points E form straight fold O'D, wherein the straight fold O'D and the two diagonal folds OE are valley lines, and the straight fold OO', the two straight folds OF and the two straight folds O'E are peak lines, wherein, α 11 represents the angle of ∠GOF in each hexagon, α 21 represents the angle of ∠FOE in each hexagon, and n represents the number of foldable paper units.

7. A flexible deployable deformable member characterized by: The foldable paper-folding unit based on claim 6, the unfoldable and deformable member is a k-layer bendable tubular structure based on the paper-folding principle in the axial direction, the bendable tubular structure is defined as a paper-folding structure, each layer of paper-folding structure comprises n connected foldable paper-folding units in the circumferential direction; wherein k≥1, n≥3; In each layer of paper-folding structure, the connection mode of the two foldable paper-folding units in each combination paper-folding unit is that the fold line edge EDE of the front foldable paper-folding unit is connected with the fold line edge GOG of the rear foldable paper-folding unit, and the two foldable paper-folding units are connected at the end.

8. A flexible deployable morphing member according to claim 7, wherein: The unfoldable and deformable member is a single-layer tubular structure.

9. The flexible deployable morphing member of claim 7, wherein: When k≥2, the connection mode of the paper-folding structures of adjacent layers is that all third interlayer boundary creases GF of adjacent foldable paper-folding units are connected, all fourth interlayer boundary creases FE of adjacent foldable paper-folding units are connected, the third interlayer boundary creases GF are valley lines, and the fourth interlayer boundary creases FE are peak lines.

10. The flexible deployable morphing member of claim 7, wherein: The material of the expandable deformable member is craft paper, plastic or plastic polyurethane elastomer rubber.

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