A polyhedral cell having a multiple metamorphosis configuration

Abstract

This invention discloses a polyhedral cell with a multivariable cellular configuration, comprising an upper contour surface, a middle contour surface, and a lower contour surface. The upper contour surface includes regular n-sided polygonal face units and n square face units, with the regular n-sided polygonal face units located in the center. The n square face units are connected to the n edges of the regular n-sided polygonal face units via common edges. The lower contour surface is the same as the upper contour surface. The middle contour surface is located between the upper and lower contour surfaces and includes n square face units and 2n rectangular face units. The n square face units of the middle contour surface correspond upwards to the n square face units of the upper contour surface and downwards to the n square face units of the lower contour surface. In the middle contour surface, two rectangular face units are provided between two adjacent square face units, and the two rectangular face units are connected to each other via a common edge. The two rectangular face units are also connected to their adjacent square face units via common edges. Each common edge involves two face units, and all common edges are provided with revolute joints.

Description

Technical Field

[0001] This invention belongs to the field of spatial variable cell mechanisms and foldable structures, specifically relating to a polyhedral cell with multiple variable cell configurations. Background Technology

[0002] With the rapid development of the aerospace field, spacecraft payload space faces severe challenges. Deployable structures, as structures that can be folded and unfolded to adapt to different operational requirements, are widely used in spacecraft equipment such as extendable arms, solar panels, and space deployable antennas. Deployable structures can unfold to a predetermined large-scale form during operation, and fold into a smaller form for transportation and storage, thus simultaneously meeting the needs of large-scale operation and small-volume transportation and storage.

[0003] Existing deployable structures mainly include planar deployable structures, spatial mesh deployable structures, and polyhedral deployable structures. Planar deployable structures are built based on planar units, such as scissor mechanisms and parallelogram mechanisms. Spatial mesh deployable structures are often built based on spatially over-constrained mechanism units, with units primarily in the form of rods. Polyhedral deployable structures are often constructed using a combination of rod-shaped and planar units, with a small number utilizing complex spatial mechanisms and built based on purely planar units.

[0004] In existing technologies, planar deployable structures have limited configurations and cannot meet specific spatial configuration requirements; mesh deployable structures are typically constructed using rod-like units, thus often requiring the fabrication of corresponding covering membranes to achieve specific needs; while polyhedral deployable structures often require combinations of various unit types and the application of specially designed kinematic pairs to meet kinematic compatibility requirements. Existing polyhedra based solely on planar units and connected only by revolute joints also suffer from problems such as an excessive number of revolute joints and complex constraint conditions. Furthermore, existing polyhedral structures constructed based on planar units and revolute joints often struggle to form closed structures, and most possess only one folding path.

[0005] Therefore, providing a simple polyhedral cell with multiple variable cell paths has become a problem that the industry needs to solve. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the main objective of this invention is to provide a single-degree-of-freedom spatially expandable polyhedral cell with a large folding ratio, characterized by a simple structure and multiple variable cell paths.

[0007] To achieve the above-mentioned main objectives, the present invention discloses a polyhedral cell with multiple variable cell configurations, which includes an upper contour surface, a middle contour surface, and a lower contour surface.

[0008] The upper contour surface includes a regular n-sided polygonal surface element and n square surface elements. The regular n-sided polygonal surface element is located in the center, and the n square surface elements are connected to the n sides of the regular n-sided polygonal surface element through a common edge.

[0009] The lower contour surface is the same as the upper contour surface;

[0010] The middle contour surface is located between the upper contour surface and the lower contour surface, and it consists of n square face elements and 2n rectangular face elements. The n square face elements of the middle contour surface correspond to the n square face elements of the upper contour surface upwards and the n square face elements of the lower contour surface downwards. Adjacent and corresponding square face elements are connected by a common edge.

[0011] In the middle contour surface, there are two rectangular surface elements between two adjacent square surface elements. The two rectangular surface elements are connected by a common edge, and the two rectangular surface elements are connected to their adjacent square surface elements by a common edge.

[0012] Each common edge involves two face elements, and all common edges have a revolute joint.

[0013] According to one specific embodiment of the present invention, n≥3.

[0014] According to a specific embodiment of the present invention, n=4, the center of the upper contour surface is a square surface unit, and the center of the lower contour surface is also a square surface unit.

[0015] According to a specific embodiment of the present invention, the side length of the square face unit is l, and the lengths of the long side and the short side of the rectangular face unit are l and m, respectively;

[0016]

[0017] According to a specific embodiment of the present invention, the polyhedral cell has a fully unfolded state, at which time the five square face units of the upper contour surface are in the same plane, the five square face units of the lower contour surface are also in the same plane, and every two directly connected rectangular face units are also in a coplanar state.

[0018] According to a specific embodiment of the present invention, depending on the driving method, the five square face units on the upper contour surface and the five square face units on the lower contour surface simultaneously bulge outward or simultaneously concave inward. In the present invention, when the five square face units on each of the upper and lower contour surfaces bulge outward simultaneously, it is defined as folding path I; when the five square face units on each of the upper and lower contour surfaces concave inward simultaneously, it is defined as folding path II. The polyhedral cell of the present invention forms an octagonal prism structure in the fully unfolded state. When folded along folding path I, it folds and shrinks in the width and length directions, forming a closed tetrahedral prism structure in the fully folded state. When folded along folding path II, it also folds and shrinks inward in the width and length directions, while the height direction remains unchanged.

[0019] According to a specific embodiment of the present invention, depending on the driving method, the five square surface units on the upper contour surface are convex outward or concave inward, and the five square surface units on the lower contour surface are concave inward or convex outward.

[0020] In addition, for the rectangular surface units on the side, a plate-shaped unit of a certain thickness is pasted on the inside using a multi-layer material processing method, and physical interference is used to constrain it to fold in only one direction towards the inside of the polyhedron.

[0021] The foldable polyhedral cell of this invention can be folded along multiple paths, each corresponding to different motion characteristics. This foldable polyhedral structure possesses advantages such as single degree of freedom, simple structure, easy processing and manufacturing, and easy modular expansion, showing great application potential and broad prospects in aerospace, construction engineering, modular robotics, metamaterials, and other fields.

[0022] According to one specific embodiment of the present invention, during the unfolding process, two square face units that are opposite each other always remain parallel.

[0023] According to a specific embodiment of the present invention, during the unfolding process, the two square face units at the center of the upper and lower contour surfaces remain perpendicular to the four square face units of the middle contour surface.

[0024] According to one specific embodiment of the present invention, during the unfolding process, every two square face units connected by rectangular face units always remain perpendicular.

[0025] The present invention has the following beneficial effects:

[0026] 1. The polyhedral cell of the present invention is constructed only by planar units and rotational pair structures, and has the characteristics of simple structure and easy manufacturing;

[0027] 2. The polyhedral cell of the present invention has the characteristic of single degree of freedom, is simple to control, has a large folding ratio, and can be folded into a closed and regular prismatic structure.

[0028] 3. The polyhedral cell of the present invention has multiple folding paths, which can realize different folding processes and size change characteristics;

[0029] 4. The polyhedral cell of the present invention has good structural and kinematic symmetry, is easy to modularize and expand, and can be used as a basic module to construct mechanical metamaterials or large-scale modular structures with adjustable properties.

[0030] To more clearly illustrate the purpose, technical solution, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the arrangement of square face units under a certain instantaneous configuration of the polyhedral cell in Example 1;

[0032] Figure 2 This is a schematic diagram of the arrangement of rectangular face units under the instantaneous configuration of the polyhedral cell in Example 1.

[0033] Figure 3 This is a schematic diagram of the structural design parameters of the polyhedral cell in Example 1;

[0034] Figure 4 This is the fully folded state of folding path I in Example 1;

[0035] Figure 5 This is one of the intermediate states of folding path I in Example 1;

[0036] Figure 6 This is the second intermediate state of folding path I in Example 1;

[0037] Figure 7 This is the third intermediate state of folding path I in Example 1;

[0038] Figure 8 This is the fully unfolded state of Example 1;

[0039] Figure 9 This is the intermediate state of folding path II in Example 1;

[0040] Figure 10 This is the fully folded state of folding path II in Example 1;

[0041] Figures 8-4 This is the folding process of the polyhedral cell in Example 1 along folding path I;

[0042] Figures 8-10 This is the folding process of the polyhedral cell in Example 1 along folding path II;

[0043] Figure 11 This is a schematic diagram of the structure of the polyhedral cell in Example 2 at a certain instant;

[0044] Figure 12 This is a schematic diagram of the structure of the polyhedral cell in Example 3 at a certain instant;

[0045] Figure 13 This is a schematic diagram of the structure of the polyhedral cell in Example 4 at a certain instant. Detailed Implementation

[0046] Many specific details are set forth in the following description in conjunction with embodiments in order to provide a full understanding of the invention. However, it should be understood that the following embodiments and detailed descriptions are for illustrative purposes only and do not limit the scope of protection of the invention.

[0047] Example 1 (n=4)

[0048] This embodiment provides a polyhedral cell (foldable polyhedral unit), which includes an upper contour surface, a middle contour surface, and a lower contour surface. For example... Figure 1 and Figure 8 As shown, the upper contour surface includes 5 square surface units S1-S5, and S2-S5 are connected to the four sides of S1 through revolute joints. Figure 8 In the brackets, the annotation indicates the face element number of the lower contour face corresponding to the face element; for example, S2(S10) means that the face element number is S2 and the face element number of the lower contour face is S10.

[0049] The lower contour surface includes five square surface elements S10-S14; S10-S13 are connected to the four sides of S14 via revolute joints.

[0050] The intermediate contour surface is located between the upper and lower contour surfaces, and it includes 4 square surface elements S6-S9 and 8 rectangular surface elements R1-R8 (e.g., ...). Figure 2 and Figure 8 (As shown); the four square face units of the middle contour surface correspond to the four square face units of the upper contour surface upwards and the four square face units of the lower contour surface downwards respectively; adjacent and corresponding square face units are connected by a common edge.

[0051] In the middle contour surface, there are two rectangular surface elements between two adjacent square surface elements. The two rectangular surface elements are connected by a common edge, and the two rectangular surface elements are connected to their adjacent square surface elements by a common edge.

[0052] Each common edge involves two face elements, and all common edges are equipped with revolute joints. Specifically, R1 is connected to R2, R3 to R4, R5 to R6, and R7 to R8 via revolute joints; S6 is connected to R1 and R8, S7 to R2 and R3, S8 to R4 and R5, and S9 to R6 and R7 via revolute joints; S2 is connected to S6, S3 to S7, S4 to S8, and S5 to S9 via revolute joints; and S6 is connected to S10, S7 to S11, S8 to S12, and S9 to S13 via revolute joints.

[0053] Figure 3 This is a schematic diagram of the design parameters for a polyhedral structure, where the side length of the square face unit is l, and the long and short side lengths of the rectangular face unit are l and m, respectively. To achieve a fully unfolded configuration and avoid physical interference during folding, l and m must satisfy the following conditions:

[0054]

[0055] Right now,

[0056]

[0057] Therefore, the polyhedral cell has only one design parameter. The selection of the design parameter only affects the scale of the structure, not its unfolding or motion characteristics.

[0058] In fully unfolded state ( Figure 8 The first to fifth square face units S1-S5 on the upper contour surface are in the same plane, and the tenth to fourteenth square face units S10-S14 on the lower contour surface are also in the same plane. At this time, every two directly connected side rectangular face units are also coplanar. For the side rectangular face units, a method of adding a patch of a certain thickness on the inner side is used, utilizing physical interference to constrain them to fold only in one direction towards the inside of the polyhedron. For the square face units on the upper and lower contour surfaces, depending on the driving method, simultaneous outward convexity can be achieved (…). Figure 7 ) or simultaneously concave inward ( Figure 9 These two modes are defined as fold path I and fold path II, respectively.

[0059] H, L, and W represent the height, length, and width dimensions of the polyhedral cell, respectively. When along the folding path I ( Figures 8-4 When folding, L and W simultaneously fold inward while maintaining a consistent size, while H gradually increases. Figure 8 Indicates the fully unfolded state. Figure 4 This indicates the fully folded state of fold path I; when along fold path II ( Figures 8-10 When folded, L and W fold inward while maintaining the same dimensions, while H remains unchanged. Figure 10This represents the fully folded state of folding path II. Utilizing the dimensional variation characteristics of the foldable structural unit, mechanical metamaterials with positive Poisson's ratio, negative Poisson's ratio, and alternating positive and negative Poisson's ratio can be designed based on this unit.

[0060] During the movement of the unfoldable polyhedron, the square face units S1 and S14, S2 and S12, S3 and S13, S4 and S10, S5 and S11, S6 and S8, and S7 and S9 that are opposite each other always remain parallel to each other; S1 and S14 always remain perpendicular to S6-S9; S6 is perpendicular to S7 and S9, and S7 is perpendicular to S6 and S8.

[0061] In particular, when two directly connected rectangular face units (such as R1 and R2) move to a mutually perpendicular state, the H, L and W scales of the developable polyhedron structure are the same, and the polyhedron forms a small rhombic half-cube outline.

[0062] Example 2 (n=3)

[0063] like Figure 11 As shown, the difference between this embodiment and Embodiment 1 is that the center of the upper and lower contour surfaces is an equilateral triangular surface unit; the number of rectangular surface units is 6.

[0064] Example 3 (n=5)

[0065] like Figure 12 As shown, the difference between this embodiment and embodiment 1 is that the center of the upper and lower contour surfaces is a regular pentagonal surface unit; the number of rectangular surface units is 10.

[0066] Example 4 (n=6)

[0067] like Figure 13 As shown, the difference between this embodiment and Embodiment 1 is that the center of the upper and lower contour surfaces is a regular hexagonal surface unit; the number of rectangular surface units is 12.

[0068] Although the present invention has been described above by way of embodiments, the above embodiments are only used to exemplify possible implementations of the present invention and are not intended to limit the scope of protection of the present invention. Any equivalent substitutions or changes made by those skilled in the art in accordance with the present invention should also be covered by the scope of protection defined by the claims of the present invention.

Claims

1. A polyhedral cell unit with multiple variable cellular configurations, characterized in that, The polyhedral cell includes an upper contour surface, a middle contour surface, and a lower contour surface; The upper contour surface includes a regular n-sided polygonal surface unit and n square surface units. The regular n-sided polygonal surface unit is located in the center, and the n square surface units are respectively connected to the n sides of the regular n-sided polygonal surface unit through a common edge. The lower contour surface is the same as the upper contour surface; The intermediate contour surface is located between the upper contour surface and the lower contour surface, and includes n square face units and 2n rectangular face units; the n square face units of the intermediate contour surface correspond upward to the n square face units of the upper contour surface and downward to the n square face units of the lower contour surface; adjacent and corresponding square face units are connected by a common edge. In the intermediate contour surface, two rectangular surface units are provided between two adjacent square surface units. The two rectangular surface units are connected by a common edge, and the two rectangular surface units are connected to their adjacent square surface units by a common edge. Each of the common edges involves two face elements, and all of the common edges are provided with a revolute joint; n=4, the center of the upper contour surface is a square face unit, and the center of the lower contour surface is also a square face unit; the polyhedral cell has a fully unfolded state, at which time the five square face units of the upper contour surface are in the same plane, the five square face units of the lower contour surface are also in the same plane, and every two directly connected rectangular face units are also in a coplanar state. Depending on the driving method, the five square face units on the upper contour surface and the five square face units on the lower contour surface bulge outward or inward simultaneously; during the folding process, the two square face units opposite each other always remain parallel; during the folding process, the two square face units in the center of the upper and lower contour surfaces always remain perpendicular to the four square face units on the middle contour surface. Alternatively, depending on the driving method, the five square face units on the upper contour surface are either convex outward or concave inward, while the five square face units on the lower contour surface are either concave inward or convex outward.

2. The polyhedral cell according to claim 1, characterized in that: The side length of the square face unit is The lengths of the long side and the short side of the rectangular surface unit are respectively and ; 。 3. The polyhedral cell unit according to claim 1, characterized in that: During the unfolding process, every two square face units connected by the rectangular face units remain perpendicular.

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