Extension method for constructing rigid foldable multiple tubular structure and tubular structure

Abstract

The invention provides an extension method for constructing a rigid foldable multi-tubular structure and a tubular structure. The extension method comprises the following steps: constructing a three-dimensional tetrahedron by setting the side length, the interior angle and the dihedral angle of a planar triangle; extending the bottom edges of the tetrahedrons, and determining new vertexes through geometric constraints to generate adjacent transverse extension tetrahedrons; then determining a heterogeneous tetrahedron of the basic tetrahedron through geometric constraint of a BOIII mechanism, and determining an axially extending tetrahedron based on the heterogeneous tetrahedron; the multiple foldable tubular structures are generated by repeating the steps of transverse extension and axial extension and modifying initial side length angle parameters in a matched mode. According to the method, through the steps of basic tetrahedron construction, transverse extension, axial extension and iterative expansion, a set tetrahedron relational expression is met in the process of executing the extension step, so that the problem that the shape complexity of a bent section of the foldable tubular structure needs to be simplified is solved, and the foldable tubular structure which is more flexible and reliable is provided; and the requirements of different engineering fields are met.

Description

Technical Field

[0001] The present invention relates to the technical field of folding structures, and in particular to a method for extending a rigid foldable multi-tubular structure and a tubular structure. Background Art

[0002] Foldable tubular structures have important application values in modern engineering fields. They can be folded into a plane when not in use, facilitating storage and transportation, and can be unfolded to form a tubular channel space when needed. Such structures have broad application prospects in fields such as aerospace, robotics, and architecture.

[0003] However, the foldable tubular structures in the prior art have some limitations. For example, most foldable tubular structures are cylindrical with a straight central axis and usually open ends, which brings inconvenience in certain specific application scenarios. In addition, although there are also foldable tubular structures with curved axes, due to the often complex shape of their curved segments, such as serrated shapes, the folding process becomes cumbersome, thereby limiting their application scope in practical engineering. Therefore, there is an urgent need in the prior art for a foldable tubular structure that can close the ends according to requirements without affecting the folding characteristics. At the same time, in the foldable tubular structure with a curved axis, there is also an urgent need to simplify the shape complexity of the curved segment in order to better expand its application fields.

[0004] It should be noted that the information disclosed in the above background art 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 above-mentioned disadvantages of the prior art, the present invention provides a method for extending a rigid foldable multi-tubular structure and a tubular structure. By setting the parameters of a basic tetrahedron and the steps of lateral extension and axial extension, and satisfying the set tetrahedron relation during the execution of the extension steps, the problem of simplifying the shape complexity of the curved segment of the foldable tubular structure is solved, and a more flexible and reliable foldable tubular structure is provided to meet the requirements of different engineering fields.

[0006] The present invention provides a method for extending a rigid foldable multi-tubular structure, including:

[0007] S1. Based on a given initial plane triangle, determine its origin, first side, and second side. By setting the length of the third side, the first rotation angle, and the included angle β between the second side and the third side O , rotate around the second side to determine the position of the third vertex; by setting the length of the fourth side, the second rotation angle, and the included angle β between the first side and the fourth side O, rotate around the first side to determine the position of the fourth vertex, and determine the constructed basic tetrahedron according to the first side, the second side, the third side and the fourth side; then, according to the parameter relationship of the third type of Bricard octahedron BOIII mechanism, construct an isomeric tetrahedron based on the basic tetrahedron;

[0008] S2. Taking the second base side and the third base side of the bottom surface of the basic tetrahedron as the extension reference, extend along the direction of the third base side to form a third extended side and obtain the fifth side, extend along the direction of the second base side to form a second extended side and obtain the sixth side, and determine the relationship between the third side and the seventh side in the laterally extended tetrahedron based on the relationship between the first side and the third side in the basic tetrahedron. Determine the constructed laterally extended tetrahedron according to the third side, the fifth side, the sixth side and the seventh side;

[0009] S3. Based on the extension of four edge edges of the isomeric tetrahedron, determine the axially extended isomeric tetrahedron, and by setting the length of the extended edge edge and the included angle α between the extended edge edge and the connected base edge A , remove the isomeric tetrahedron in the axially extended isomeric tetrahedron to obtain the axially extended tetrahedron;

[0010] S4. Repeat the generation process of the laterally extended tetrahedron and the axially extended tetrahedron in S2 - S3, and generate a variety of different rigidly foldable multi - tubular structures by changing the initial plane triangle, the first rotation angle, the included angle α between the first side and the second side O and the included angle β between the second side and the third side O set parameter values.

[0011] In an embodiment of the present invention, step S1 further includes:

[0012] S11. Obtain the included angle α between the first side and the second side, the included angle β between the second side and the third side, the included angle α between the first side and the first base side, and the supplementary angle β between the first isomeric side and the first base side in the basic tetrahedron and the first rotation angle and the second rotation angle based on the first side and the second side in the initial plane triangle; O and the included angle β between the second side and the third side O and the included angle α between the first side and the first base side A and the supplementary angle β between the first isomeric side and the first base side A and the first rotation angle and the second rotation angle based on the first side and the second side in the initial plane triangle;

[0013] S12. According to the sum of the opposite angles at the second vertex of the second side and the fourth vertex of the fourth side in the basic tetrahedron being π, determine the angles of each vertex in the basic tetrahedron, and calculate and determine the lengths of each side length in the basic tetrahedron by giving the first side with a basic length.

[0014] In an embodiment of the present invention, step S2 further includes:

[0015] S21. Taking the second base edge and the third base edge of the base tetrahedron as the extension reference, extend along the direction of the third base edge to form a third extended edge and obtain a fifth edge, such that the angle between the third edge and the fifth edge is equal to the angle between the third edge and the fourth edge; extend along the direction of the second base edge to form a second extended edge and obtain a sixth edge, such that the angle between the third edge and the sixth edge is equal to the angle between the third edge and the second edge; and based on the relationship between the first edge and the third edge in the base tetrahedron, determine the relationship between the third edge and the seventh edge in the laterally extended tetrahedron. Determine the constructed laterally extended tetrahedron according to the third edge, the fifth edge, the sixth edge, and the seventh edge.

[0016] S22. According to the lengths of the edges and the formed plane angles in the laterally extended tetrahedron, calculate the side lengths and angles of the next BOIII mechanism in the laterally extended direction through trigonometric functions, and determine the vertex positions of the newly constructed BOIII mechanism.

[0017] S23. During the lateral extension process, based on the previous BOIII mechanism, determine the vertex positions of the next BOIII mechanism in the laterally extended direction by repeating the calculation process of step S21.

[0018] In an embodiment of the present invention, in the base tetrahedron and the heterogeneous tetrahedron of the BOIII mechanism, there are two types of planar triangles. The three interior angles of the first type of planar triangle are α O , α A and α B , and the three interior angles of the second type of planar triangle are α O , π - β B and π - α A , where α O is the planar angle at the tip. The planar angles satisfy the relational expressions α B = π - α O - α A and where

[0019] In an embodiment of the present invention, the contours of the tubular structures formed by multiple axially extended tetrahedrons include spiral and zigzag shapes. By judging according to the α + β - π angle signs of the corresponding vertices A i in the multiple axially extended tetrahedrons, if the signs of the α + β - π angles at adjacent A points are the same, the tubular structure formed by the multiple axially extended tetrahedrons is spiral; if the signs of the α + β - π angles at adjacent A points are opposite, the tubular structure formed by the multiple axially extended tetrahedrons is zigzag.

[0020] In an embodiment of the present invention, the vertices of the axially extended tetrahedron are developable vertices, and the relational expression between the folding angle at the developable vertex and the planar angle of the axially extended tetrahedron satisfies:

[0021]

[0022] In an embodiment of the present invention, step S4 further includes:

[0023] S41. Based on the generation process of S2 - S3, by adjusting the included angle α between the first side and the second side in the initial planar triangle O , the included angle β between the second side and the third side O , the dimension of the first side, and the set values of the first rotation angle and the second rotation angle, generate basic unit variants of laterally extended tetrahedrons and axially extended tetrahedrons in different forms;

[0024] S42. Combine the basic unit variants generated in S41 into a multi - tubular structure through symmetry operations, and obtain a helical tubular structure or a Z - shaped tubular structure by optimizing the set values;

[0025] S43. Through dynamic folding simulation of the tubular structure model generated in S42, verify the rigidity and motion compatibility of the tubular structure under different set values.

[0026] The present invention also provides a method for constructing a rigid foldable multi - tubular structure. According to the set third - type Bricard octahedron BOIII mechanism, laterally extend the given basic tetrahedron in the BOIII mechanism, determine the position coordinates of each point of its lateral extension through the mathematical relationship of the BOIII mechanism, extend a heterogeneous tetrahedron of the BOIII mechanism laterally on the basis of the basic tetrahedron of the BOIII mechanism, and combine it with the basic tetrahedron of the BOIII mechanism to form a composite mechanism of the BOIII mechanism.

[0027] In an embodiment of the present invention, by axially extending the composite mechanism of the BOIII mechanism, a number of frustum units connected axially and laterally are obtained. The adjacent side lengths of the frustum units in the axial direction are not equal, so that the tubular structure formed by connecting a number of frustum units in the axial direction is helical or Z - shaped. The side lengths of the side edges of the frustum units in the lateral direction are not equal, so that the tubular structure of the frustum units is continuous and foldable in the lateral direction.

[0028] In an embodiment of the present invention, the BOIII mechanism includes two frustum units. Each frustum unit includes four side faces. The BOIII mechanism is connected pairwise in the lateral and axial directions. The lengths of the sides of the laterally extended frustum units are restricted by the side lengths of the previous frustum unit; the axially extended frustum units are rotationally connected between the side edges of the side faces to form the side wall of the foldable tubular structure.

[0029] Advantages of the present invention: By designing the methods of lateral extension and axial extension, the tip of the tubular structure can be closed or opened according to requirements. When the tubular structure is folded, its volume is relatively small, which is convenient for storage and transportation; when it is unfolded, it provides a single or multiple pipe spaces with a zigzag or spiral shape. In the whole tubular structure, the planar quadrilateral side of the frustum unit has a single rigid degree of freedom, which has the advantages of simple motion control and high reliability. This makes the tubular structure have important application value and broad prospects in many fields such as aerospace, robotics, and architecture.

[0030] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present invention. Brief Description of the Drawings

[0031] The accompanying drawings herein are incorporated into the specification and form a part of the specification, showing embodiments consistent with the present invention, and are used together with the specification to explain the principles of the present invention. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts. In the drawings:

[0032] Figure 1 is a flowchart of the method for extending the tubular structure in the present invention;

[0033] Figure 2 is a model diagram of the tubular structure in the process of lateral extension in the present invention;

[0034] Figure 3 is a model diagram of obtaining the laterally adjacent frustum O-CEFG by laterally extending the frustum O-ABCD in the present invention;

[0035] Figure 4 is a schematic diagram of the planar angle and folding angle of the vertex of the rigid unfoldable four-fold crease (the arc length of the unit circle is equal to the radian of the planar angle, the left figure is the unfolded diagram, and the right figure is the folded diagram);

[0036] Figure 5 is Figure 2 a model diagram of the frustum unit and a schematic diagram of the angles of each point in the circumferential extension during the lateral extension construction process;

[0037] Figure 6 is a schematic model diagram of the tubular structure with a 2×2 unit quantity in the present invention;

[0038] Figure 7 are model diagrams of two rigidly foldable multi-layer tubular structures with a contour line in a zigzag and spiral shape constructed by the method for extending the tubular structure in the present invention. Detailed Embodiments

[0039] The following specific examples illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other. It should also be understood that the terms used in the embodiments of the present invention are for describing specific implementation manners and are not intended to limit the protection scope of the present invention.

[0040] Please refer to Figures 1 to 7 . It should be noted that the structures, ratios, sizes, etc. shown in the drawings of this specification are only used to cooperate with the content disclosed in the specification for those skilled in this technology to understand and read, and are not intended to limit the limiting conditions under which the present invention can be implemented. Therefore, they do not have technical essential significance. Any modification of the structure, change of the proportional relationship, or adjustment of the size, without affecting the effects that the present invention can produce and the purposes that can be achieved, should still fall within the scope covered by the technical content disclosed in the present invention. At the same time, the terms such as the positions and quantitative relationships cited in this specification are only for the convenience of clear narration and are not intended to limit the scope under which the present invention can be implemented. The change or adjustment of their relative relationships, without substantial change in the technical content, should also be regarded as the scope under which the present invention can be implemented.

[0041] Please refer to Figures 1 to 3 . The present invention provides an extension method for constructing a rigid foldable multi-tubular structure, including:

[0042] S1. Based on a given initial planar triangle OAB, determine its origin O, the first side OA and the second side OB. By setting the length of the third side OC, the included angle β between the second side OB and the third side OC O and the first rotation angle (the included angle between △OBA and △OBC), rotate around the second side OB to determine the position of the third vertex C; by setting the length of the fourth side OD, the included angle β between the first side OA and the fourth side OD O and the second rotation angle (the included angle between △OAD and △OAB), rotate around the first side OA to determine the position of the fourth vertex D. Determine the constructed basic tetrahedron O - ABCD according to the first side OA, the second side OB, the third side OC and the fourth side OD; then, based on the parameter relationship of the third type of Bricard octahedron (BOIII mechanism), construct an isomeric tetrahedron O1 - ABCD based on the basic tetrahedron O - ABCD;

[0043] S2. Taking the second base BC and the third base CD of the bottom surface of the basic tetrahedron O-ABCD as the extension benchmarks, extend along the direction of the third base DC to form the third extended side CE and obtain the fifth side OE (so that the included angles between the third base CD and the third extended side CE corresponding to the origin O are equal), extend along the direction of the second base BC to form the second extended side CG and obtain the sixth side OG (so that the included angles between the second base BC and the second extended side CG corresponding to the origin are equal); according to the included angle θ between the first side OA and the third side OC, rotate the third side OC around the normal vector of the plane formed by the first side OA and the third side OC with the origin O by θ to obtain the direction of the seventh side OF, and based on the relationship between the first side OA and the third side OC in the basic tetrahedron O-ABCD, determine the relationship between the third side OC and the seventh side OF in the laterally extended tetrahedron O-CEFG, and determine the constructed laterally extended tetrahedron O-CEFG according to the third side OC, the fifth side OE, the sixth side OG and the seventh side OF;

[0044] S3. Based on the extension of the four edges of the heterogeneous tetrahedron O1-ABCD, determine the axially extended heterogeneous tetrahedron O1-A1B1C1D1, and by setting the length of the extended edge O1A1 and the included angle α between the extended edge O1A1 and the connected base A1B1 A1 , remove the heterogeneous tetrahedron O1-ABCD in the axially extended heterogeneous tetrahedron O1-A1B1C1D1 to obtain the axially extended tetrahedron ABCD-A1B1C1D1;

[0045] S4. Repeat the generation process of the laterally extended tetrahedron O-CEFG and the axially extended tetrahedron ABCD-A1B1C1D1 in S2-S3, and generate a variety of different rigid foldable multi-tubular structures by changing the initial plane triangle OAB, the first rotation angle, the included angle α between the first side OA and the second side OB O and the included angle β between the second side OB and the third side OC O set parameter values.

[0046] Specifically, in the embodiment of the present invention, starting from a plane triangle, a target tetrahedron can be gradually generated through a conventional design method, and the specific process is as follows: First, design a triangle (such as Figure 2 ΔOAB in) on the two-dimensional 2D plane, and this triangle is determined by a side length and two adjacent interior angles (such as Figure 2 the OA side of △OAB and ∠OAB and ∠OBA in). Using the side length of the triangle and the rotation angle between two adjacent faces in the tetrahedron (that is, the dihedral angle between the four faces), the remaining two vertices of the tetrahedron can be obtained (such as Figure 2Points C and D in it). Take OA as the x-axis, and place the opposite vertices C and D and O in the x-y plane. These two new vertices and the three points of the triangle will form five points of the tetrahedron. Connect the newly obtained vertices with the vertices of the plane triangle, and then connect the remaining four vertices in sequence to form four triangular faces, thus completing the construction of a basic tetrahedron O-ABCD. Using the relationship between the plane angle and the folding angle of the BOIII mechanism, another isomeric tetrahedron O1-ABCD of BOIII can be further constructed.

[0047] Further, please refer to Figure 5 , on the basis of the known first basic tetrahedron O-ABCD, the coordinates of the vertices of the next adjacent BOIII mechanism can be determined by the following way for the construction of the lateral extension: Extend the adjacent base DC of the tetrahedron O-ABCD to point E such that ∠COE = ∠DOC = α O ; Similarly, extend the adjacent base BC of the tetrahedron O-ABCD to point G such that ∠COG = ∠BOC = β O . The included angle between side OA and OC is θ. Rotate the side length OC around the normal vector of OAC by θ, and the ray where a vertex F of the next BOIII mechanism is located is in this direction. Using the side length OC, α O , β O , π - β c , π - α c can construct the vertices of the next BOIII mechanism. Finally, connect point O with each point and connect the bottom points in sequence to obtain the laterally extended tetrahedron O-CEFG. Repeat this process, taking the geometric parameters of the pipeline formed by each layer of tetrahedrons as the input of the next layer and calculating layer by layer, and finally complete the design of the entire laterally extended pipeline. In this process, through strict geometric constraints and progressive calculation methods, the continuity, structural consistency and rigid foldability of each layer of pipelines can be ensured.

[0048] Even further, on the basis of the lateral extension of the pipeline, the pipeline can be extended along the axial direction. First, according to the initial designed angle and the geometric relationship between the basic tetrahedron O-ABCD and the isomeric tetrahedron O1-ABCD in the BOIII mechanism. By extending the four side edges of the corresponding pipeline of the isomeric tetrahedron O1-ABCD, the side edges intersect at a point O1 in space. Connect the intersection point O1 with the four points ABCD on the bottom surface of the original tetrahedron. Since the position coordinates of each point have been obtained, the α O1 and β O1 of the new tetrahedron can be calculated. The angle of the new tetrahedron at point A1 is equal to α A and α B , by specifying the length of the extended side O1A1 and the included angle α between the extended side O1A1 and the connected base A1B1A1 , the positions of the vertices and side lengths of the extended frustum unit corresponding to the new layer of the pipeline can be calculated. In the new tetrahedron, removing the heterogeneous tetrahedron O1-ABCD, the remaining frustum is the axially extended tetrahedron ABCD-A1B1C1D1. Repeating this process, based on the geometric information of the previous layer of the pipeline each time, the coordinates of all vertices in the axially extended pipeline can be calculated layer by layer. If the α i at point A A and β A are adjusted during the extension, when the pipeline extends along the inner side, a spiral or Z-shaped pipeline can also be generated. This design method is simple and intuitive, and can flexibly construct complex three-dimensional pipeline structures.

[0049] In this way, by calculating according to S2 and S3 multiple times, the lateral extension structural structure of the rigid foldable multi-pipeline can be obtained. By changing the size of the designed initial value, various different rigid foldable multi-pipeline structures can be simulated.

[0050] In one embodiment, step S1 further includes:

[0051] S11. Obtain the angle α O between the first side OA and the second side OB, the angle β O between the second side OB and the third side OC, the angle α A between the first side OA and the first base AB, and the supplementary angle β A between the first heterogeneous side O1A and the first base AB in the basic tetrahedron O-ABCD and the first rotation angle and the second rotation angle based on the first side OA and the second side OB in the initial plane triangle OAB;

[0052] S12. According to the sum of the opposite angles at the second vertex B of the second side OB and the fourth vertex D of the fourth side OD in the basic tetrahedron O-ABCD being π, determine the angles of each vertex in the basic tetrahedron O-ABCD, and calculate and determine the lengths of each side length in the basic tetrahedron O-ABCD by giving the first side OA with a basic length.

[0053] Specifically, in the embodiment of the present invention, by determining the basic angles α O , β O , α A and β AAnd the dihedral angle between the two planes OAD and OAB of the tetrahedron. Through the formed tetrahedron relationship (in the same tetrahedron, the plane angles formed by the two opposite side faces and the vertex are equal) and the fact that at points B and D are foldable vertices, and the sum of the opposite angles at these two points is π, the angles at other vertices can be calculated. Therefore, based on the given basic length OA, the lengths of all the side lengths of the tetrahedron can be confirmed through calculation, and thus the coordinates of each point of the tetrahedron can be obtained.

[0054] In this way, by determining the angles and side lengths, the angles of each face of the tetrahedron and the dihedral angles between adjacent planes can be calculated through calculation, and finally the model of the tetrahedron can be obtained. Since both the angles and side lengths can be changed, pipes of different sizes and lengths can be designed to meet different situations, improving the flexibility and diversity of the design.

[0055] In one embodiment, step S2 further includes:

[0056] S21. Taking the second base BC and the third base CD of the bottom surface of the basic tetrahedron O - ABCD as the extension reference, extend along the direction of the third base DC to form the third extended side CE and obtain the fifth side OE, so that the included angle between the third side OC and the fifth side OE is equal to the included angle between the third side OC and the fourth side OD (according to the angle relationship in the basic tetrahedron, the plane angle ∠COG is equal to the plane angle ∠AOD, that is, β O ), extend along the direction of the second base BC to form the second extended side CG and obtain the sixth side OG, so that the included angle between the third side OC and the sixth side OG is equal to the included angle between the third side OC and the second side OB (according to the angle relationship in the basic tetrahedron, the plane angle ∠COE is equal to the plane angle ∠AOB, that is, α O ); According to the included angle θ between the first side OA and the third side OC, rotate the third side OC around the normal vector of the plane formed by the first side OA and the third side OC with the origin O by θ to obtain the direction of the seventh side OF, and based on the relationship between the first side OA and the third side OC in the basic tetrahedron O - ABCD, determine the relationship between the third side OC and the seventh side OF in the laterally extended tetrahedron O - CEFG. According to the third side OC, the fifth side OE, the sixth side OG and the seventh side OF, determine the constructed laterally extended tetrahedron O - CEFG;

[0057] S22. According to the lengths of each side and the formed plane angles in the laterally extended tetrahedron O - CEFG, calculate the side lengths and angles of the next BOIII mechanism of the lateral extension through trigonometric functions, and determine the positions of each vertex of the newly constructed BOIII mechanism.

[0058] S23. During the lateral extension process, based on the previous BOIII mechanism, by repeating the calculation process of step S21, determine the vertex positions of each vertex of the next BOIII mechanism for lateral extension.

[0059] Please refer to the appendix Figure 7 , in an embodiment, the basic tetrahedron and the heterogeneous tetrahedron of the BOIII mechanism include two types of planar triangles. The three interior angles of the first type of planar triangle are α O , α A and α B , and the three interior angles of the second type of planar triangle are α O , π - β B and π - α A , where α O is the planar angle at the tip, and the planar angles satisfy the relational expression α B = π - α O - α A and where

[0060] Specifically, in an embodiment of the present invention, the BOIII mechanism can be composed of 4 triangles at the front end and 4 basic units of planar quadrilaterals connected thereto. Please refer to the appendix Figure 5 , which shows the double - tubular structure formed after the double - rigid - fold tubular structure extends along the axial direction. The left - hand and right - hand figures respectively show the crease diagrams of the upper and lower layers of the tubular structure. Each ring - shaped unit is a truncated cone based on BOIII. The previous ring - shaped unit intersects with the next ring - shaped unit, and the conical part of the tip of the next ring - shaped unit is removed. By analogy, a multi - foldable bent - pipe structure with a curved axis can be obtained, and the front end can be closed.

[0061] In an embodiment, the contours formed by multiple axially - extended tetrahedrons for the tubular structure include a spiral shape and a Z - shape. By judging according to the sign of the α + β - π angle of the corresponding - position vertex A i in multiple axially - extended tetrahedrons, if the signs of the α + β - π angles at adjacent A points are the same, the tubular structure formed by multiple axially - extended tetrahedrons is spiral - shaped; if the signs of the α + β - π angles at adjacent A points are opposite, the tubular structure formed by multiple axially - extended tetrahedrons is Z - shaped.

[0062] Specifically, in the embodiments of the present invention, a continuous tubular profile is formed by axially extending tetrahedrons stacked layer by layer and connected axially by sharing vertices and edges. Each tetrahedron has a specific vertex marker (such as vertex Ai, where i is the layer number), and its position changes with the extension direction. During continuous rotation in the same direction, a cumulative angular offset will occur. For example, each layer rotates clockwise around the axis by a fixed angle, and the projection of vertex Ai forms an equiangular spiral-shaped path on a plane perpendicular to the axis. Alternating the rotation direction will cause vertex Ai to swing periodically on both sides of the axis. For example, the odd-numbered layers rotate clockwise by a fixed angle, and the even-numbered layers rotate counterclockwise by a fixed angle, forming a zigzag Z-shaped path.

[0063] More specifically, the formed spiral tubular structure can induce fluid to rotate and flow, reducing resistance (such as a spiral pipe pump), and can also be used in the extension mechanism of plant tendrils for soft robots. The formed Z-shaped tubular structure can be compressed and unfolded along the axis (such as a folding solar panel bracket), and can also dissipate energy through plastic deformation under impact, for applications such as anti-collision beam design.

[0064] In this way, by determining the angular signs of adjacent vertices Ai, the global morphology of the axially extending tetrahedron structure can be precisely controlled. The spiral and Z-shaped forms are achieved through continuous rotation in the same direction and alternating rotation in opposite directions respectively, and their mathematical modeling and parameter optimization provide a flexible design basis for engineering applications. This mechanism has important application values in fields such as microfluidic devices and aerospace deployable structures.

[0065] In one embodiment, the vertices of the axially extending tetrahedron are flattenable vertices, and the relationship between the folding angle at the flattenable vertex and the plane angle of the axially extending tetrahedron satisfies:

[0066]

[0067] Specifically, in the embodiments of the present invention, α and α represent two adjacent plane angles of a planar quadrilateral (as shown in the flattened view in Figure 4 . ρ to ρ represent the folding angles of the four creases during the folding process (as shown in the folding view in Figure 4 . The relationship associates the plane angle with the folding angle through trigonometric relationships, ensuring the coordinated movement of the vertices of the four creases during folding. The negative sign "-" indicates that the folding directions of adjacent creases are opposite (such as one folding upward and the other folding downward).

[0068] More specifically, in the spiral or Z-shaped profile formed by multiple axially extending tetrahedrons, by adjusting the plane angles α A and β A, combined with the above relationships, the helical shape (the signs of all point A are the same) or the zigzag shape (the signs of adjacent point A are opposite) can be formed axially in the tubular structure. The relational equation also ensures that each frustum unit has only a single rigid degree of freedom, simplifying the folding control of its multi-tubular structure. By giving the initial plane angles (α O , β O , α A and β A ), the folding angle parameters can be calculated to generate tubular structures of different shapes. The relationship is the mathematical basis for judging whether the structure meets the rigid foldability, verifying the folding feasibility, and avoiding folding failures caused by geometric conflicts in practical applications.

[0069] Please refer to the appendix Figure 4 . Its unfolded diagram and folding diagram intuitively show the corresponding relationship between the plane angle α and the folding angle ρ. The relational equations (1) and (2) are derived from this geometric model. Please refer to the appendix Figure 7 . Its helical and zigzag tubular structures are finally combined with the above equations by adjusting the α and β parameters to generate tubular structures with complex contours.

[0070] In this way, by proposing the relationship as the core mathematical constraint for the folding movement of the frustum unit, through the dynamic balance between the plane angle and the folding angle, it is ensured that the structure remains rigid and the movement is controllable during the folding and unfolding process.

[0071] Please refer to Figure 6 and Figure 7 . In one embodiment, step S4 further includes:

[0072] S41. Based on the generation process of S2 - S3, by adjusting the size of the first side OA, the included angle α O between the second side OB and the first side OA, the included angle β O between the second side OB and the third side OC, and the set values of the first rotation angle and the second rotation angle in the initial plane triangle OAB, basic unit variants of the laterally extended tetrahedron O - CEFG and the axially extended tetrahedron ABCD - A'B'C'D' are generated;

[0073] S42. Combine the basic unit variants generated in S41 into a multi-tubular structure through symmetric operations, and obtain a helical tubular structure or a zigzag tubular structure through optimizing the set values;

[0074] S43. Verify the rigidity and motion compatibility of the tubular structure under different set values through dynamic folding simulation of the tubular structure model generated in S42.

[0075] Specifically, in the embodiments of the present invention, based on the generation logic of the laterally extended tetrahedron and the axially extended tetrahedron in steps S2 - S3, by adjusting the dimensions (side lengths OA, OB, AB) of the initial planar triangle OAB, modifying the first / second rotation angles, and the included angle α between the second side OB and the first side OA O and the included angle β between the second side OB and the third side OC O , a variety of basic unit variants (such as short and thick type, slender type, high folding angle type) are generated. Through symmetric operations such as mirroring, translation, or rotation on the basic unit variants generated in S41, they are combined into complex multi - tubular structures (such as spiral tubular structures or Z - shaped tubular structures), and the overall rigidity is ensured through global parameter optimization.

[0076] Furthermore, through dynamic folding simulation of the model generated in S42, the rigidity and motion compatibility of the structure under different parameters are verified. For example, single - variable parameters are set for testing, the folding angle changes of each side surface in the tetrahedron under different side - length parameters and vertex - angle parameters are observed, and the vertex displacement trajectories are recorded for analysis. The side - length parameters and vertex - angle parameters can also be adjusted to analyze their influence on the folding lever arm (for example, the longer the side length, the smaller the vertex angle needs to be to maintain stability). The stress - concentration areas can also be calculated (such as whether the bending moments at vertices C and E exceed the limit). In this way, the relationship between the BOIII mechanism parameters and the performance parameters is obtained.

[0077] It should be noted that the initial side - length parameters and vertex - angle parameters adjusted in S41 directly affect the expansion result of the multi - tubular structure in S42, and the verification result in S43 can feedback the parameters of the optimized setting value in S42. That is to say, through the steps of S41, the design freedom for generating tubular structures is provided to support the morphology of customized basic unit variants; through the symmetric operations of S42, the modeling complexity is reduced and the construction efficiency of the tubular structure is improved; through the verification of S43, the physical prototype trial - and - error of the tubular structure is avoided, and feasible solutions are directly screened through simulation. For example, applied in the design of medical stents, through the steps of S41, basic unit variant structures with different diameters / angles are generated, then combined into bifurcated vascular stents through the steps of S42, and the reliability of folding and deployment after implantation is verified through the steps of S43. For example, applied in space deployable structures, through the steps of S42, a lightweight grid structure is generated, and then the folding dynamics under zero gravity is simulated through the steps of S43.

[0078] In one embodiment, the present invention further provides a construction of a rigid foldable multi-tubular structure. According to the set third type of Bricard octahedron BOIII mechanism, the given basic tetrahedron in the BOIII mechanism is laterally extended, and the position coordinates of each point of its lateral extension are determined through the mathematical relationship of the BOIII mechanism. A heterogeneous tetrahedron of the BOIII mechanism is extended laterally on the basis of the basic tetrahedron of the BOIII mechanism, and is combined with the basic tetrahedron of the BOIII mechanism to form a composite mechanism of the BOIII mechanism.

[0079] By axially extending the composite mechanism of the BOIII mechanism, a number of frustum units connected axially and laterally are obtained. The adjacent side lengths of the frustum units in the axial direction are not equal, so that the tubular structure formed by connecting a number of frustum units in the axial direction is spiral or Z-shaped (the contour shape of the tubular structure depends on the α+β-π sign of point A i If the signs at each A point are the same, it is spiral; if the signs of adjacent A i point A i+1 points are opposite, it is Z-shaped). The side lengths of the frustum units in the lateral direction are not equal, so that the tubular structure of the frustum units is continuous and foldable in the lateral direction.

[0080] In one embodiment, the BOIII mechanism includes two frustum units. Each frustum unit includes four side faces. The BOIII mechanism is connected pairwise in the lateral and axial directions. The lengths of the sides of the laterally extended frustum unit are restricted by the side lengths of the previous frustum unit; the axially extended frustum units are rotationally connected between the side edges of the side faces to form the side wall of the foldable tubular structure. Between the axially adjacent frustum units, the tubular structure is formed by rotational connection between the side edges of the plane quadrilateral side faces in the lateral direction. The tetrahedron extended laterally in the frustum unit has the extension lines of the side edges in the axial direction of its side faces intersecting at a point at the small end, so that the frustum unit forms a spherical four-rotary pair mechanism. The plane quadrilateral side face closed at the small end of the frustum unit includes a vertex structure with equal opposite angles and a vertex structure with complementary opposite angles. The plane quadrilateral side face in the frustum unit is a general quadrilateral.

[0081] In summary, an extension method for constructing a rigid foldable multi-tubular structure and a tubular structure provided by the present invention construct a three-dimensional tetrahedron from the side lengths, interior angles, and dihedral angles of a set plane triangle by setting the parameters of a basic tetrahedron and the steps of lateral extension, axial extension, and iterative expansion; then extend the bottom edge of the tetrahedron and determine new vertices through geometric constraints to generate adjacent laterally extended tetrahedrons; then determine the isomeric tetrahedrons of the basic tetrahedron through the geometric constraints of the BOIII mechanism, and determine the axially extended tetrahedrons based on the isomeric tetrahedrons; by repeating the steps of lateral extension and axial extension and modifying the initial side length and angle parameters, a multi-foldable tubular structure is generated to meet different engineering requirements, enabling the tip of the tubular structure to be designed to be closed or not according to needs, having a small volume when folded for easy storage and transportation, and having single and multiple pipe spaces when unfolded. The planar quadrilateral side of the frustum unit in the entire tubular structure has a single rigid degree of freedom, with advantages such as simple motion control and high reliability.

[0082] The above embodiments are only illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Any person familiar with this technology can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes completed by those with ordinary knowledge in the technical field without departing from the spirit and technical ideas disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. A method for constructing a rigid foldable multi-tubular structure, characterized in that: include: S1. Based on the given initial plane triangle (OAB), determine its origin (O), the first side (OA) and the second side (OB), by setting the length of the third side (OC), the first rotation angle and the angle β between the second side (OB) and the third side (OC) O , rotate around the second side (OB) to determine the position of the third vertex (C); by setting the length of the fourth side (OD), the second rotation angle, and the angle β between the first side (OA) and the fourth side (OD) O , rotate around the first edge (OA) to determine the position of the fourth vertex (D), and determine the basic tetrahedron (O-ABCD) to be constructed according to the first edge (OA), the second edge (OB), the third edge (OC) and the fourth edge (OD); then, according to the parameter relationship of the third type of Bricard octahedron BOIII mechanism, construct the heterogeneous tetrahedron (O1-ABCD) based on the basic tetrahedron (O-ABCD); S2. Taking the second base side (BC) and the third base side (CD) of the bottom surface of the basic tetrahedron (O-ABCD) as extension references, extending along the direction of the third base side (DC) to form a third extended side (CE) and obtain the fifth side (OE), extending along the direction of the second base side (BC) to form a second extended side (CG) and obtain the sixth side (OG), and based on the angle (θ) relationship formed by the first side (OA) and the third side (OC) in the basic tetrahedron (O-ABCD), determining the angle (θ) relationship between the third side (OC) and the seventh side (OF) in the transversely extended tetrahedron (O-CEFG), and determining the constructed transversely extended tetrahedron (O-CEFG) according to the third side (OC), the fifth side (OE), the sixth side (OG) and the seventh side (OF); S3, based on extending the four edges of the isomeric tetrahedron (O1-ABCD), determining the axially extended isomeric tetrahedron (O1-A1B1C1D1), and setting the length of the extended edge (O1A1) and the angle α between the extended edge (O1A1) and the connected bottom edge (A1B1) A , removing the isomeric tetrahedron (O1-ABCD) from the axially extended isomeric tetrahedron (O1-A1B1C1D1) to obtain the axially extended tetrahedron (ABCD-A1B1C1D1); S4, repeat the generation process of the transversely extended tetrahedron (O-CEFG) and the axially extended tetrahedron (ABCD-A1B1C1D1) in S2-S3, by changing the initial plane triangle (OAB), the first rotation angle, and the angle α between the first side (OA) and the second side (OB) of the second rotation O and the angle β between the second side (OB) and the third side (OC) O By setting the parameter values, a variety of foldable multi-tubular structures with different rigidity are generated.

2. The stretching method according to claim 1, characterized in that: The step S1 further comprises: S11. Obtain the angle α between the first edge (OA) and the second edge (OB) of the basic tetrahedron (O-ABCD) and the isomeric tetrahedron (O1-ABCD) O , the angle β between the second side (OB) and the third side (OC) O , the angle α between the first side (OA) and the first base (AB) A and the complementary angle β between the first isomorphic side (O1A) and the first base (AB) A and a first rotation angle and a second rotation angle based on a first side (OA) and a second side (OB) in the initial planar triangle (OAB); S12. Determine the angles of each vertex in the basic tetrahedron (O-ABCD) based on the sum of the opposite angles at the second vertex (B) of the second side (OB) and the fourth vertex (D) of the fourth side (OD) as π, and calculate and determine the length of each side in the basic tetrahedron (O-ABCD) by giving the basic length of the first side (OA).

3. The stretching method according to claim 1, characterized in that: The step S2 further comprises: S21. Taking the second base side (BC) and the third base side (CD) of the bottom face of the basic tetrahedron (O-ABCD) as extension references, extend along the direction of the third base side (DC) to form a third extended side (CE), obtain a fifth side (OE), make the angle between the third side (OC) and the fifth side (OE) equal to the angle between the third side (OC) and the fourth side (OD), extend along the direction of the second base side (BC) to form a second extended side (CG), obtain a sixth side (OG), make the third side (OC) and The angle of the sixth side (OG) is equal to the angle between the third side (OC) and the second side (OB); and based on the angle (θ) between the first side (OA) and the third side (OC) in the basic tetrahedron (O-ABCD), the angle (θ) between the third side (OC) and the seventh side (OF) in the laterally extended tetrahedron (O-CEFG) is determined, and the laterally extended tetrahedron (O-CEFG) is constructed based on the third side (OC), the fifth side (OE), the sixth side (OG) and the seventh side (OF); S22. According to the length of each side in the laterally extended tetrahedron (O-CEFG) and the plane angle formed, the side length and angle of the next laterally extended BOIII mechanism are calculated by trigonometric functions, and the positions of each vertex of the newly constructed BOIII mechanism are determined. S23. During the lateral extension process, based on the previous BOIII mechanism, the calculation process of step S21 is repeated to determine the positions of the vertices of the next BOIII mechanism to be extended laterally.

4. The stretching method according to claim 1, characterized in that: The basic tetrahedron and isomeric tetrahedron of BOIII structure include two types of planar triangles. The three internal angles of the first type of planar triangle are α O , α A and α B , the three interior angles of the second type plane triangle are α O ,π-β B and π-α A , where α O is the plane angle at the tip, and the plane angles satisfy the relationship 5. The stretching method according to claim 1, characterized in that: The contours of the tubular structure formed by the plurality of axially extending tetrahedrons include spiral and zigzag shapes, and the corresponding vertices A in the plurality of axially extending tetrahedrons are i The sign of the α+β-π angle at adjacent vertices A is used to determine. If the signs of the α+β-π angles at adjacent vertices A are the same, the tubular structure formed by multiple axially extending tetrahedrons is spiral. If the signs of the α+β-π angles at adjacent vertices A are opposite, the tubular structure formed by multiple axially extending tetrahedrons is Z-shaped.

6. The stretching method according to claim 5, characterized in that: The vertices of the axially extended tetrahedron are flattenable vertices, and the relationship between the folding angle at the flattenable vertex and the plane angle of the axially extended tetrahedron satisfies:

7. The stretching method according to claim 1, characterized in that: The step S4 further comprises: S41, based on the generation process of S2-S3, by adjusting the length of the first side (OA) in the initial plane triangle (OAB), the angle α between the second side (OB) and the first side (OA) O and the setting value of the first rotation angle, generating basic unit variants of different forms of laterally extended tetrahedron (O-CEFG) and axially extended tetrahedron (ABCD-ABCD); S42, combining the basic unit variants generated in S41 into multiple tubular structures through symmetry operations, and obtaining a spiral tubular structure or a Z-shaped tubular structure by optimizing the setting value; S43. By performing a dynamic folding simulation on the tubular structure model generated by S42, the rigidity and motion compatibility of the tubular structure under different setting values ​​are verified.

8. A tubular structure, characterized in that: According to the set third-class Bricard octahedron BOIII mechanism, the given basic tetrahedron in the BOIII mechanism is extended laterally, and the position coordinates of each point of the lateral extension are determined by the mathematical relationship of the BOIII mechanism. A heterogeneous tetrahedron of the BOIII mechanism is extended in the lateral direction of the basic tetrahedron, and combined with the basic tetrahedron of the BOIII mechanism to form a composite mechanism of the BOIII mechanism.

9. The tubular structure according to claim 8, characterized in that By axially extending the composite structure of the BOIII structure, a plurality of truncated cone units connected in the axial and transverse directions are obtained, and the adjacent sides of the truncated cone units in the axial direction are of different lengths, so that the tubular structure formed by connecting the plurality of truncated cone units in the axial direction is spiral or Z-shaped, and the side lengths of the truncated cone units in the transverse direction are not equal, so that the tubular structure of the truncated cone units is continuous in the transverse direction and has foldability.

10. The tubular structure according to claim 9, characterized in that The BOIII mechanism includes two truncated cone units, each of which includes four side surfaces. The BOIII mechanism is connected in pairs in the transverse and axial directions. The length of each side of the transversely extending truncated cone unit is constrained by the length of the side surface of the previous truncated cone unit. The axially extending truncated cone unit is connected by rotating between the side surfaces to form the side wall of the foldable tubular structure.

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