Rigid foldable spiral structure with single degree of freedom

By combining the rigid foldable spiral structure designed with planar triangles and quadrilateral basic units, the problem that the existing spiral origami structure cannot be folded and expanded based on a given plane is solved, and the folding and expansion functions are achieved in a single degree of freedom and adapted to different application needs.

CN119508708APending Publication Date: 2025-02-25HEFEI UNIV OF TECH
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Patent Information

Application Number
CN202411915755.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-24
Publication Date
2025-02-25

AI Technical Summary

Technical Problem

The existing spiral origami structures cannot be folded and unfolded based on a given plane, and lack of closed tips, limiting their application areas.

Method used

By combining planar triangle basic units and planar quadrilateral basic units, a rigid foldable helical structure with a single degree of freedom is designed to achieve folding and unfolding based on a given plane, and to adapt to different application needs by designing the shape and size of the tip.

Benefits of technology

It realizes the function of folding and expanding in a single degree of freedom, adapts to different application environments, and can design different appearance contours according to needs.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention provides a rigid foldable spiral structure with a single degree of freedom, which comprises a planar quadrilateral basic unit and a planar triangular basic unit, common edges with the same length and single rotational degree of freedom are shared between the adjacent planar triangular basic units, between the planar quadrilateral basic units and between the planar triangular basic units and the planar quadrilateral basic units, so that the planar triangular basic units and / or the planar quadrilateral basic units are mutually folded or unfolded. The plane triangular basic units and the plane quadrilateral basic units are combined, folding and unfolding based on the given plane single freedom degree are achieved, the shapes and sizes of the basic units can be designed according to actual requirements, and therefore different applicable appearance contours can be formed; the problems that a spiral folding mechanism with a bent axis cannot be folded and unfolded based on a given plane, and the application field expansion is limited are solved.
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Description

Technical Field

[0001] The invention relates to the technical field of folding mechanisms, and in particular to a rigid foldable spiral structure with a single degree of freedom. Background Art

[0002] Foldable structures inspired by origami have received extensive attention and development in recent decades. They can be prepared by cutting planar materials to form the overall framework of the structure. This type of foldable structure can be unfolded to a working state or folded for storage and transportation. It has broad application prospects in aerospace, composite materials, metamaterials, robotics, and building structures. The prior art has proposed design methods for cylindrical and axisymmetric origami structures, whose axes are all straight lines; spiral structures with curved axes have also appeared, but the vertices of the upper and lower layers of the structure are not in the same plane, and it is not convenient to fold and unfold based on a given plane. And the foldable structures currently proposed basically do not have closed tips.

[0003] Therefore, for a spiral origami structure that can be folded, there is a need for the ends of the structure to be closed as needed without affecting its foldability. In addition, in a spiral structure with a curved axis, there is also a need for folding and unfolding based on a given plane to expand the applicable field.

[0004] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present invention and does not constitute any limitation to the present invention. Summary of the invention

[0005] In view of the shortcomings of the prior art mentioned above, the present invention provides a rigid foldable spiral structure with a single degree of freedom. By combining a plane triangular basic unit and a plane quadrilateral basic unit, folding and unfolding based on a single degree of freedom on a given plane can be achieved. The shapes and sizes of the plane triangular basic units and the plane quadrilateral basic units can be designed according to actual needs to form different applicable appearance contours, so as to solve the problem that the spiral folding mechanism with a curved axis cannot be folded and unfolded based on a given plane and the application field is limited.

[0006] The present invention provides a rigid foldable spiral structure with a single degree of freedom, comprising a planar quadrilateral basic unit and a planar triangular basic unit, wherein a first number of the planar quadrilateral basic units are arranged along a first direction and a second direction, and a second number of the planar triangular basic units are arranged along the first direction, and the tips of the second number of the planar triangular basic units converge at a point, and the edges of the planar quadrilateral basic units are connected through the opposite sides of the tips of the planar triangular basic units; wherein the first number is an integer multiple of the second number, and common edges of equal length are shared between adjacent planar triangular basic units, between planar quadrilateral basic units, and between planar triangular basic units and planar quadrilateral basic units, and there is a single degree of rotational freedom between the common edges, so that the planar triangular basic units and / or the planar quadrilateral basic units can be folded or unfolded with each other.

[0007] In one embodiment of the present invention, the plane triangle basic unit includes a first type of triangle and a second type of triangle. The three internal angles of the first type of triangle are α 0 ,π-α 1 and α 2 ; The three interior angles of the second type of triangle are α 0 ,π-α 3 and α 1 .

[0008] In one embodiment of the present invention, the plane quadrilateral basic unit includes a first type quadrilateral and a second type quadrilateral, and the four internal angles of the first type quadrilateral are π-α 1 ,π-α 1 , α 2 and α 3 ; The four interior angles of the second type quadrilateral are π-α 2 ,π-α 3 , α 1 and α 1 .

[0009] In one embodiment of the present invention, in the plane triangle basic unit and the plane quadrilateral basic unit, α 0 The plane angle at the tip of the plane triangle basic unit is formed, and the plane angles satisfy the relationship α 1 =α 2 +α 0 and α 3 =α 1 +α 0 .

[0010] In one embodiment of the present invention, on the common edges formed between adjacent planar quadrilateral basic units or between adjacent planar triangle basic units and planar quadrilateral basic units, every four common edges intersect to form four crease vertices, and the four crease vertices include a first type of vertices whose creases are colinear and a second type of vertices whose creases are not colinear.

[0011] In one embodiment of the present invention, the first type of vertices are located in the same plane during the folding process of the corresponding adjacent planar quadrilateral basic units or planar triangle basic units.

[0012] In one embodiment of the present invention, an axis formed by the first number of planar quadrilateral basic units and the second number of planar triangular basic units in the first direction and the second direction is a planar bending axis.

[0013] In one embodiment of the present invention, in the foldable spiral structure, the planar triangular basic unit is detachably connected to the planar quadrilateral basic unit.

[0014] In one embodiment of the present invention, in the foldable spiral structure, any plane quadrilateral basic unit or plane triangle basic unit corresponding to the four fold vertices is used as a reference plane for folding and unfolding.

[0015] In one embodiment of the present invention, the foldable spiral structure is transformed between a planar state and a folded state through a dihedral mechanism between adjacent planar triangular basic units or planar quadrilateral basic units, and the dihedral mechanism includes a hinge, a hinge or a bearing.

[0016] Beneficial effects of the present invention: The present invention provides a rigid foldable spiral structure with a single degree of freedom, which can realize the folding and unfolding of the entire structure under a single degree of freedom by driving a single position point. In the folding process, the folding and unfolding based on a given plane can be realized to adapt to the corresponding application environment space. The multiple beak-shaped tips formed by the plane triangular basic units converging at one point can be retained or removed according to actual needs, and the shapes and sizes of the plane triangular basic units and the plane quadrilateral basic units can be designed according to actual needs to form different applicable appearance contours.

[0017] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the present invention, and together with the specification, are used to explain the principles of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0019] Figure 1 is a schematic diagram of the rigid foldable spiral structure of the present invention;

[0020] Figure 2 is a schematic diagram of the rigid foldable spiral structure of the present invention with the tip removed;

[0021] Figure 3 is a schematic diagram of a vertex structure in which folds are not collinear in one embodiment of the present invention;

[0022] Figure 4 is a schematic diagram of a Miura-ori vertex structure with collinear folds in one embodiment of the present invention;

[0023] Figure 5 is a schematic plan view of a basic unit extending along a first direction and a second direction in one embodiment of the present invention;

[0024] Figure 6 is a schematic plan view of a basic unit including two internal vertex combinations in one embodiment of the present invention;

[0025] Figures 7 to 9 for Figure 2 Schematic diagram of the process of the overall structure folding from a planar state to a spatial folded state. DETAILED DESCRIPTION

[0026] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied by other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the features in the following embodiments and embodiments can be combined with each other without conflict. It should also be understood that the terms used in the embodiments of the present invention are to describe specific specific embodiments, rather than to limit the scope of protection of the present invention.

[0027] See also Figures 1 to 9. It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings in this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the limiting conditions for the implementation of the present invention, so they have no substantial technical significance. Any structural modification, change in proportional relationship, or adjustment of size, without affecting the effects and purposes that can be achieved by the present invention, should still fall within the scope of the technical content disclosed by the present invention. At the same time, the terms such as position and quantitative relationship cited in this specification are only for the convenience of description, and are not used to limit the scope of the implementation of the present invention. Changes or adjustments in their relative relationships should also be regarded as the scope of the implementation of the present invention without substantially changing the technical content.

[0028] See also Figure 1 and Figure 2 The present invention provides a rigid foldable spiral structure with a single degree of freedom, comprising a planar quadrilateral basic unit 100 and a planar triangular basic unit 200, wherein a first number of planar quadrilateral basic units 100 are arranged along a first direction and a second direction, and a second number of planar triangular basic units 200 are arranged along the first direction, and the tips of the second number of planar triangular basic units 200 converge at a point, and the edges of the planar quadrilateral basic units 100 are connected through the opposite sides of the tips of the planar triangular basic units 200; wherein the first number is an integer multiple of the second number, and adjacent planar triangular basic units 200, planar quadrilateral basic units 100, and planar triangular basic units 200 and planar quadrilateral basic units 100 share common sides of equal length, and there is a single rotational degree of freedom between the common sides, so that the planar triangular basic units 200 and / or the planar quadrilateral basic units 100 can be folded or unfolded with each other.

[0029] Specifically, in an embodiment of the present invention, the foldable spiral structure is formed by combining a plane triangle basic unit 200 and a plane quadrilateral basic unit 100 (the plane triangle basic unit 200 and the plane quadrilateral basic unit 100 correspond to the triangle block and the quadrilateral block in the attached drawings, respectively), so that the two basic units (the plane triangle basic unit 200 and the plane quadrilateral basic unit 100) are connected to each other to achieve folding and unfolding actions under a single degree of freedom, and by setting the side lengths of the two basic units, the foldable overall structure is formed in a spiral shape. The plane triangle basic units 200 can be the basis for forming the spiral structure, which are arranged along the second direction (usually in the length direction), and one end of each plane triangle basic unit 200 converges at the same common point to form a tip. In other words, the plane triangle basic units 200 are in the same posture, and are arranged with their vertices as the center to form a shape similar to a fan, and this shape structure is used as the starting point of the foldable spiral structure. The planar quadrilateral basic unit 100 cooperates with the planar triangular basic unit 200 to be arranged in a first direction and a second direction (usually perpendicular to the first direction), that is, the planar quadrilateral basic unit 100 is connected to the opposite side of the tip of the planar triangular basic unit 200, and continues to extend and unfold along the fan shape of the planar triangular basic unit 200 to form a final foldable spiral structure. At this time, the first number of the planar quadrilateral basic units 100 is an integer multiple of the second number of the planar triangular basic units 200, so that the integrity and continuity of the foldable spiral structure can be maintained.

[0030] More specifically, adjacent planar triangular basic units 200 and planar quadrilateral basic units 100 share common sides of equal length, providing integrity of the foldable spiral structure, so that folding and unfolding can be performed between the basic units of the two shapes. A single degree of rotational freedom can be set between the common sides through a hinge or other mechanism, that is, each basic unit can rotate independently relative to other basic units, that is, the overall structure can achieve partial folding and unfolding while maintaining its shape. In this way, the end can be closed without sacrificing its folding ability, that is, its closed tip can be used as a protective cover.

[0031] That is to say, by controlling the rotation of a single degree of freedom between each basic unit, the entire structure can be converted between an unfolded state and a folded state. And the conversion process can be carried out in a limited space, making the overall structure suitable for use in a space-constrained environment. Taking advantage of its foldable characteristics, it can be folded up when not in use, reducing the space required for storage and transportation. The independent single degree of freedom settings in the overall structure can accurately control the folding and unfolding of the overall structure.

[0032] In this way, this rigid foldable spiral structure with a single degree of freedom can achieve complex spatial folding and unfolding while maintaining the stability and functionality of the structure. The shape and size of the basic unit and different appearance contours can also be set according to actual needs.

[0033] See also Figures 3 to 6 In one embodiment, the plane triangle basic unit 200 includes a first type of triangle and a second type of triangle. The three internal angles of the first type of triangle are α and 0 ,π-α 1 and α 2 ; The three interior angles of the second type of triangle are α 0 ,π-α 3 and α 1 The plane quadrilateral basic unit 100 includes a first type quadrilateral and a second type quadrilateral. The four internal angles of the first type quadrilateral are π-α 1 ,π-α 1 , α 2 and α 3 ; The four interior angles of the second type quadrilateral are π-α 2 ,π-α 3 , α 1 and α 1 In the plane triangle basic unit 200 and the plane quadrilateral basic unit 100, α 0 The plane angle at the tip of the plane triangle basic unit 200 is formed, and the plane angles satisfy the relationship α 1 =α 2 +α 0 and α 3 =α 1 +α 0 .

[0034] Specifically, in the embodiment of the present invention, the shapes of the plane triangle basic unit 200 and the plane quadrilateral basic unit 100 are limited by limiting the internal angle relationship between the plane triangle basic unit 200 and the plane quadrilateral basic unit 100. Figure 5 , which is a schematic diagram of the basic unit extending in two directions (i.e., the first direction and the second direction) during the design process of the foldable spiral structure. Figure 5 The front end of the plane triangle basic unit 200 and the four plane quadrilateral basic units 100 connected thereto are composed of. The plane triangle basic unit 200 can be divided into two categories. The three internal angles of the first type of triangle are α 0 ,π-α 1 and α 2 , the three interior angles of the second type triangle are α 0 ,π-α 3 and α 1 , where α 0is the plane angle at the tip of the triangle, and the plane angles satisfy the relationship α 1 =α 2 +α 0 and α 3 =α 1 +α 0 In the first direction, the four planar triangular basic units 200 at the front end and the four planar quadrilateral basic units 100 connected thereto can be divided into two categories, wherein the four internal angles of the first type of quadrilateral are π-α 1 ,π-α 1 , α 2 and α 3 , the four interior angles of the second-type plane quadrilateral are π-α 2 ,π-α 3 , α 1 and α 1 The first number can be understood as M×N, and the second number is N. The two pairs of sides of the M×N plane quadrilateral extend in the first direction and intersect at one point, forming N triangles. By analogy, the rigid foldable spiral structure can be extended in the first direction. In the second direction, the reference Figure 4 The Miura-ori vertex with symmetry shown ( Figure 5 The plane angles of the rigid foldable spiral structure in the second direction are regular, the plane angles of the basic units in the N1 and N3 columns are consistent, and the plane angles of the basic units in the N2 and N4 columns are consistent. By analogy, the rigid foldable spiral structure can be extended in the second direction.

[0035] More specifically, Figure 6 for Figure 1 and Figure 2 Schematic diagram of the basic building block of the rigid foldable spiral structure shown in Figure 3 and Figure 4 The vertex type shown. Basic units 1, 2, 5, and 6 meet at point G ( Figure 3 The basic units 2, 3, 4, and 5 converge at point H ( Figure 4 vertices shown). α 1 , α 2 , α 3 They are the first inner angle, the second inner angle and the third inner angle of the plane quadrilateral basic unit 100. The plane quadrilateral basic unit 100 can be divided into two categories, where the four inner angles of the first category of quadrilaterals are π-α 1 ,π-α 1 , α 2 and α 3 , the four interior angles of the second-type plane quadrilateral are π-α 2 ,π-α 3 , α 1and α 1 L12, L23, L34, L45, L56, L61, and L25 are two adjacent quadrilateral basic units that share a common edge of equal length, i.e., a fold. The panel of each basic unit acts as a connecting rod, and each fold acts as a hinge, together forming a complex structure similar to the combined assembly of a spherical 4R mechanism.

[0036] See also Figures 1 to 4 In one embodiment, on the common edges formed between adjacent planar quadrilateral basic units 100 or between adjacent planar triangular basic units 200 and planar quadrilateral basic units 100, every four common edges intersect to form four crease vertices, and the four crease vertices include first-type vertices whose creases are colinear and second-type vertices whose creases are not colinear. The first-type vertices are located in the same plane during the folding process of the corresponding adjacent planar quadrilateral basic units 100 or planar triangular basic units 200. The axis formed by the first number of planar quadrilateral basic units 100 and the second number of planar triangular basic units 200 in the first direction and the second direction is a planar bending axis.

[0037] Specifically, in the embodiment of the present invention, Figure 1 and Figure 2 As shown, Figure 1 The planar triangular basic units 200 may converge at one point to form multiple beak-shaped tips, and the triangular parts may be retained or removed according to actual needs. Figure 2 The rigid foldable spiral structure is obtained by removing the planar triangular basic unit 200. The rigid foldable spiral structure provided in this embodiment can be folded and unfolded based on a given plane (the plane of any basic unit), and the first type of fixed points (Miura-ori vertices) with collinear folds are always coplanar during folding and unfolding. Figure 3 and Figure 4 There are two types of vertices that make up the rigid foldable spiral structure, which are distributed throughout the structure. Figure 3 The vertex angles shown are complementary but neither set of opposing creases is colinear. Figure 4 The vertex angles shown are complementary but two of the four creases are collinear, such as creases S21 and S23.

[0038] More specifically, based on the shapes of the plane triangular basic unit 200 and the plane quadrilateral basic unit 100. Every four common edges intersect to form four crease vertices. According to the collinearity of the creases, the vertices are divided into two categories: the creases of the first category of vertices are collinear, and these vertices are located in the same plane during the folding process of adjacent plane quadrilateral basic units 100 or plane triangular basic units 200, ensuring the consistency of folding. The creases of the second category of vertices are not collinear, which provides additional flexibility and diversity for the structure. In the first direction and the second direction, the overall structure formed by the plane triangular basic unit 200 and the plane quadrilateral basic unit 100 jointly forms a plane bending axis, which enables the overall structure to present a spiral shape, that is, the overall structure can flexibly adjust its shape and size in different application scenarios to adapt to different space requirements.

[0039] It should be noted that, by designing the bending axis of the overall structure in the first direction and the second direction, the overall structure can solve the problems of low space utilization and incomplete connecting rod function while meeting the functions of folding and unfolding, and also provide a reference for the installation design of the actual connecting rod device. Its foldable characteristics have broad application prospects in the fields of civil, military, aerospace, etc. For example, in the field of construction, this structure can be used for temporary structures such as construction sheds, market sheds, temporary warehouses, as well as military applications such as battlefield command, battlefield rescue, assembly repair and field tents. In the field of aerospace, this structure can be used as a solar sail, a deployable antenna, etc., playing an irreplaceable role. By designing and optimizing the fold (the edge length of the basic unit), the overall structure can be folded and deformed as required under a given input force. For example, its design variables can be described by the folding stiffness coefficient. By determining a fold design method, the overall structure can achieve high efficiency of folding and unfolding while meeting the use requirements.

[0040] In this way, by configuring the plane triangular basic unit 200 and the plane quadrilateral basic unit 100 in the overall structure with a unique geometric design and folding mechanism, the rigid foldable spiral structure not only improves the space utilization, but also enhances the applicability of the overall structure.

[0041] See also Figures 7 to 9 In one embodiment, in the foldable spiral structure, the plane triangle basic unit 200 is detachably connected to the plane quadrilateral basic unit 100. In the foldable spiral structure, any plane quadrilateral basic unit 100 or plane triangle basic unit 200 corresponding to the four fold vertices is used as a reference plane for folding and unfolding. The foldable spiral structure is transformed between the plane state and the folded state through the dihedral mechanism between adjacent plane triangle basic units 200 or plane quadrilateral basic units 100, and the dihedral mechanism includes a hinge, a hinge or a bearing.

[0042] Specifically, in the embodiment of the present invention, the connection between the plane triangle basic unit 200 and the plane quadrilateral basic unit 100 is detachable, which improves the flexibility and convenience. At the same time, the overall structure can be composed of only the plane quadrilateral basic unit 100. The detachable connection method also allows the structure to be quickly assembled or disassembled when necessary, which is convenient for transportation, storage and maintenance. The detachable connection may be achieved through a special interface, buckle or quick release mechanism to ensure the stability and reliability of the connection.

[0043] More specifically, any plane quadrilateral basic unit 100 or plane triangular basic unit 200 corresponding to the four crease vertices can be used as a reference plane to guide the folding and unfolding process of the overall structure. The selection of the reference plane is used to control the folding direction and ensure the unfolding direction of the structure. During the folding process, all other basic units will be folded relative to this reference plane to ensure that the overall structure can be folded into a compact shape evenly and orderly.

[0044] like Figures 7 to 9 As shown, the rigid foldable spiral structure can be folded from a plane state to a space state through a dihedral mechanism between adjacent plane triangle basic units 200 or plane quadrilateral basic units 100. The dihedral mechanism may include hinges, hinges or bearings, which allow the units to rotate in a single degree of freedom to achieve the transformation from a plane state to a folded state. For example, the hinge provides a basic rotation function, allowing the units to rotate on a fixed axis, which is the basis for folding and unfolding. The hinge allows the units to fold around a fixed point as the center, providing greater flexibility and stability. Similarly, the bearing provides a more complex rotation and support function, which can support the rotation of the unit in multiple directions, increasing the stability and durability of the structure. When the overall structure needs to be folded, the angle between adjacent units can be changed through the dihedral mechanism, thereby achieving the folding and unfolding of the structure. The design of the dihedral mechanism allows folding and unfolding without sacrificing strength and stability, and is suitable for application scenarios that require frequent assembly and disassembly.

[0045] In summary, the present invention provides a rigid foldable spiral structure with a single degree of freedom. The overall structure is formed by connecting the plane triangular basic unit and the plane quadrilateral basic unit with a dihedral mechanism. The overall structure can be folded and unfolded in a single degree of freedom by driving a single position point. In the folding process, folding and unfolding based on a given plane can be achieved. The multiple beak-shaped tips formed by the plane triangular basic units converging at one point can be retained or removed according to actual needs, and the shapes and sizes of the plane triangular basic units and the plane quadrilateral basic units can be designed according to actual needs to form different applicable appearance contours.

[0046] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A rigid foldable spiral structure with a single degree of freedom, characterized in that include: Planar quadrilateral basic units, a first number of planar quadrilateral basic units are arranged along a first direction and a second direction; Planar triangular basic units, the second number of planar triangular basic units are arranged along the first direction, the tips of the second number of planar triangular basic units converge at one point, and the edges of the planar quadrilateral basic units are connected through the opposite sides of the tips of the planar triangular basic units; Among them, the first number is an integer multiple of the second number, adjacent planar triangular basic units, planar quadrilateral basic units, and planar triangular basic units and planar quadrilateral basic units share common sides of equal length, and there is a single degree of rotational freedom between the common sides, so that the planar triangular basic units and / or planar quadrilateral basic units can be folded or unfolded with each other.

2. The foldable spiral structure according to claim 1, characterized in that: The plane triangle basic unit includes a first type of triangle and a second type of triangle. The three internal angles of the first type of triangle are α0, π-α1 and α2 respectively; the three internal angles of the second type of triangle are α0, π-α3 and α1 respectively.

3. The foldable spiral structure according to claim 1, characterized in that: The planar quadrilateral basic unit includes a first type quadrilateral and a second type quadrilateral, the four internal angles of the first type quadrilateral are π-α1, π-α1, α2 and α3; the four internal angles of the second type quadrilateral are π-α2, π-α3, α1 and α1.

4. The foldable spiral structure according to claim 2 or 3, characterized in that: In the planar triangle basic unit and the planar quadrilateral basic unit, α0 is the plane angle at the tip of the planar triangle basic unit, and the plane angles satisfy the relationship α1=α2+α0 and α3=α1+α0.

5. The foldable spiral structure according to claim 1, characterized in that: On the common edges formed between adjacent planar quadrilateral basic units or between adjacent planar triangle basic units and planar quadrilateral basic units, every four common edges intersect to form four crease vertices, and the four crease vertices include first-type vertices whose creases are collinear and second-type vertices whose creases are not collinear.

6. The foldable spiral structure according to claim 5, characterized in that: The first type of vertices are located in the same plane during the folding process of the corresponding adjacent planar quadrilateral basic units or the planar triangular basic units.

7. The foldable spiral structure according to claim 1, characterized in that: The axis formed by the first number of planar quadrilateral basic units and the second number of planar triangular basic units in the first direction and the second direction is a planar bending axis.

8. The foldable spiral structure according to claim 1, characterized in that: In the foldable spiral structure, the planar triangular basic unit is detachably connected to the planar quadrilateral basic unit.

9. The foldable spiral structure according to claim 5, characterized in that: In the foldable spiral structure, any one of the planar quadrilateral basic units or the planar triangular basic units corresponding to the four fold vertices is used as a reference plane for folding and unfolding.

10. The foldable spiral structure according to claim 1, characterized in that: The foldable spiral structure is transformed between a planar state and a folded state through a dihedral mechanism between adjacent planar triangular basic units or planar quadrilateral basic units, and the dihedral mechanism includes a hinge, a hinge or a bearing.

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