Polyhedral multistable structure based on curved paper folding

Abstract

The invention discloses a polyhedral multistable structure based on curved paper folding. The polyhedral multistable structure comprises a first substructure and a second substructure, the first substructure is a polyhedral frame formed by connecting eight rigid triangular panels through revolute pairs, the rigid triangular panels are regular triangles, and the side length of each rigid triangular panel is a; the second substructure is composed of six deformable curved line paper folding units, each curved line paper folding unit is formed by connecting every two of three curved edge panels through rotating pairs on the curved edges to form a spatial quadrilateral contour, and the side length of the spatial quadrilateral contour is a; the first substructure and the second substructure are connected through a common revolute pair to form a polyhedral multistable structure with a first stable state, a second stable state and a third stable state, and the structure can be subjected to stable state conversion along two different paths.

Description

Technical Field

[0001] The present invention relates to the technical field of polyhedron multi-stable folding and unfolding, and in particular to a polyhedron multi-stable structure based on zigzag origami and having different implementation paths depending on different loading positions. Background Art

[0002] Polyhedral foldable structures and multistable structures, two major research areas in engineering, achieve unique functional advantages through geometric design and nonlinear mechanical manipulation, respectively. Traditional polyhedral foldable structures, such as the Hoberman sphere mechanism, connect rigid panels via rotatable hinges to form a spatial mechanism with well-defined kinematic properties, enabling efficient folding and unfolding. They are widely used in aerospace antennas, deployable buildings, and other fields. These structures are renowned for their excellent geometric deformation capabilities, precisely controllable motion trajectories, and high load-bearing capacity. Multistable structures, such as bistable composite materials and origami metamaterials, on the other hand, utilize material or geometric nonlinearity to enable controllable switching between different stable configurations, achieving programmable control of mechanical properties. These structures can exist in multiple equilibrium positions corresponding to energy minima and can transition between these states under the action of external forces. They exhibit nonlinear mechanical response, energy absorption and release, and programmable variable stiffness.

[0003] Polyhedral multistable structures are an important new type of engineering structure, characterized by the ability to control their mechanical properties through the design of their geometric structure and the way they fold. The performance of this type of structure does not depend entirely on the physical properties of the material itself, but is determined by its geometric configuration. Polyhedral multistable structures can switch between multiple stable states under the action of different external forces and maintain mechanical stability in these states. With their unique folding and unfolding capabilities, this type of structure can achieve efficient geometric deformation within a limited space, and through special geometric configuration design, it can achieve effective control of Poisson's ratio, flexibility and stiffness. It combines the characteristics of the geometric structure with the characteristics of the material itself. Through programmable geometric design, it can achieve flexible control of the mechanical properties of the overall structure, thus showing broad application prospects in cutting-edge fields such as aerospace, construction engineering, and flexible robotics. Summary of the Invention

[0004] The present invention aims to overcome the shortcomings of the existing technology by providing a polyhedral multistable structure based on zigzag paper. This structure has three stable states: unfolded, folded, and self-locking, and can be controllably transitioned between these states. By constraining the zigzag paper with a rigid frame, it ensures structural flexibility while providing good load-bearing capacity. It also features a simple structure, easy manufacturing, and adjustable parameters. Based on these advantages, this invention has significant significance and broad application prospects in fields such as aerospace, intelligent robotics, and deformable architecture.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A polyhedral multistable structure based on zigzag origami, comprising:

[0007] A first substructure is a polyhedral frame formed by eight rigid triangular panels connected by revolute joints, wherein the rigid triangular panels are regular triangles with a side length of a;

[0008] The second substructure consists of six deformable origami units. Each unit consists of three curved panels connected in pairs by revolute pairs on the curved edges to form a spatial quadrilateral outline. The side length of the spatial quadrilateral outline is a.

[0009] The first substructure and the second substructure are connected by a common revolute pair to form a polyhedral multi-stable structure with a first stable state, a second stable state and a third stable state. The structure can undergo stable state conversion along two different paths:

[0010] Path 1 is the transition from the first stable state to the second stable state. The first substructure rotates and contracts around the revolving pair toward the center, driving the curved edge panels of each curved origami unit in the second substructure to rotate relative to each other around their curved edge revolving pair and fold, ultimately reaching the second stable state.

[0011] Path 2 is when the first stable state is converted to the third stable state, the second substructure jumps, each zigzag origami unit bulges outward to trigger self-locking, and finally reaches the third stable state.

[0012] Furthermore, the first stable state is an unfolded state, presenting a truncated octahedron configuration, with the first substructure and the second substructure being rotationally symmetrically distributed, and the polyhedral multistable structure is in an initial stable equilibrium state;

[0013] The second stable state is a folded state, which is a regular octahedron configuration. The first substructure and the second substructure are axially symmetrical. At this time, the second substructure is completely folded along the curved crease and stored inside the first substructure.

[0014] The third stable state is a self-locking state. Driven by an external load, the origami units of the second substructure unfold and stretch outward under the rigid constraint of the first substructure, forming a geometric interlock. When the rigid triangular panel is vertically loaded, the reverse constraint of the origami units cannot trigger the structural contraction, and the first and second substructures are rotationally symmetrically distributed.

[0015] Furthermore, the thickness of the rigid triangular panel is an arbitrary value greater than zero; while maintaining the structural functional integrity, the spatial quadrilateral outline angle θ of the curved origami unit is in the range of [0.62, 0.75] radians, and the curvature κ of the curved edge is in the range of (0, 0.6 / a].

[0016] Furthermore, each rigid triangular panel of the first substructure is connected to other rigid triangular panels and the second substructure through at least three rotating pairs, and the rotating pairs are one of hinges, hinges or bearings; the rotating pairs between the curved edge panels in the second substructure are obtained by additional processing.

[0017] Furthermore, the structure has the ability to be densely packed in both plane and three dimensions, and adjacent structures can be linked by rotational pairs to form a continuous deformation array to adapt to different application requirements.

[0018] The present invention also provides an application of a polyhedral multistable structure, which is applied to deployable spacecraft structures, shape-variable robot joints, reconfigurable building structures, and metamaterial devices with adjustable mechanical properties.

[0019] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0020] 1. Programmable Multi-Stability: The proposed structure possesses three stable states (expanded, folded, and self-locking), and the transitions between these states can be precisely controlled by external loads. By programming the key geometric parameters of the origami unit, specifically selecting the angle of the spatial quadrilateral outline (e.g., [0.62, 0.75] radians) and the curvature of the curved edge (e.g., (0, 0.6 / a]) within the valid parameter range, the structure's stable-state characteristics and transition paths can be effectively controlled, achieving customized mechanical properties to meet the needs of different operating conditions.

[0021] 2. Unifying High Load-Bearing Capacity with High Deformation Capacity: This invention achieves both high load-bearing capacity and high deformation capacity by combining a rigid polyhedral frame with flexible origami elements. In the deployed and self-locking states, the rigid frame provides the primary load-bearing path and structural stability. During folding, the origami elements allow for large-angle rotation and a wide range of geometric deformation, enabling the structure to effectively switch between bearing operational loads (deployed / self-locking states) and achieving compact storage (folded state).

[0022] 3. Path-dependent load response selectivity: The structure exhibits unique path-dependent characteristics, exhibiting different response patterns to loads in different directions or positions. For example, applying a compressive load to the first substructure tends to trigger overall collapse (path one), while loading a specific position on the second substructure can trigger its outward bulge and self-locking state (path two). This selective response provides the basis for intelligent control and functional switching of the structure in complex environments.

[0023] 4. High folding / deployment ratio: The structure can achieve a significant volume change from the unfolded state (truncated octahedron configuration) to the folded state (regular octahedron configuration with the secondary substructure stored inside), achieving a high volume compression ratio (or packaging efficiency). This is of great significance for space-constrained applications such as satellite deployable components, portable equipment, or temporary building structures.

[0024] 5. Passive Geometric Self-Locking Enhances Stability: The self-locking state (third stable state) utilizes a geometric interlocking mechanism formed by the outward expansion of the second substructure to resist deformation in a specific load direction without the need for continuous external energy input. This passive stability mechanism improves the reliability and energy efficiency of the structure after deployment or under load.

[0025] 6. Potential Energy Absorption: During steady-state transitions (especially the sudden-jump behavior in Path 2), the structure must overcome an energy barrier, a process accompanied by energy absorption or release. By adjusting geometric parameters, the height and shape of the energy barrier can be manipulated, giving the structure potential for impact energy absorption, vibration suppression, or controlled energy release (e.g., actuation).

[0026] 7. High Reliability and Durability: The origami-based design boasts high reliability. It demonstrates excellent durability under repeated use and heavy loads, effectively preventing structural failure due to fatigue or deformation. The rational configuration of the revolute pairs ensures excellent stability and efficiency under various operating conditions. The revolute pair size can be adjusted to meet specific requirements, allowing for the installation of the drive in any desired location.

[0027] 8. Simple structure and easy to manufacture: The present invention adopts a design based on origami principles, with a relatively simple structure, a small number of components, and clear connection methods. This allows the structure to be manufactured and assembled at low cost and high efficiency through standardized origami techniques and existing manufacturing technologies (such as laser cutting, 3D printing, etc.), reducing production difficulty and cost.

[0028] 9. Broad Application Prospects: The multistable deployable structure proposed in this invention has broad application prospects, including in aerospace, robotics, architecture, metamaterials, and intelligent devices. This structure offers significant advantages in applications requiring a balance of load-bearing capacity, deformability, space utilization, and programmability. For example, it could be used to design deployable spacecraft structures with self-locking capabilities, shape-shifting robotic joints, reconfigurable architectural structures, and metamaterials with adjustable mechanical properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1-1 Schematic diagram of the structure of the polyhedron multistable structure in this embodiment.

[0030] Figure 1-2 to Figure 1-3 Schematic diagram of the first substructure consisting of rigid triangular panels.

[0031] Figure 2-1 to Figure 2-6 Schematic diagram of the second substructure composed of deformable curved pattern units.

[0032] Figure 3-1 to Figure 3-3 Schematic diagram of the transition process from the expanded state to the folded state, where Figure 3-2 is the intermediate state, Figure 3-3 Schematic diagram of the folded state.

[0033] Figure 4-1 to Figure 4-2 Schematic diagram of the transition process from the unfolded state to the self-locking state, where Figure 4-2 Schematic diagram of self-locking state.

[0034] Figure 5 Schematic diagram of the dense combination of multiple structural units in plane and height.

[0035] Reference numerals: A1 - first surface of the first substructure, A2 - second surface of the first substructure, A3 - third surface of the first substructure, A4 - fourth surface of the first substructure, A5 - fifth surface of the first substructure, A6 - sixth surface of the first substructure, A7 - seventh surface of the first substructure, A8 - eighth surface of the first substructure;

[0036] M1-first substructure first rotation pair, M2-first substructure second rotation pair, M3-first substructure third rotation pair, M4-first substructure fourth rotation pair, M5-first substructure fifth rotation pair, M6-first substructure sixth rotation pair, M7-first substructure seventh rotation pair, M8-first substructure eighth rotation pair, M9-first substructure ninth rotation pair, M10-first substructure tenth rotation pair, M11-first substructure eleventh rotation pair, M12-first substructure twelfth rotation pair, M13-first substructure tenth rotation pair Three rotation pairs, M14 - the fourteenth rotation pair of the first substructure, M15 - the fifteenth rotation pair of the first substructure, M16 - the sixteenth rotation pair of the first substructure, M17 - the seventeenth rotation pair of the first substructure, M18 - the eighteenth rotation pair of the first substructure, M19 - the nineteenth rotation pair of the first substructure, M20 - the twentieth rotation pair of the first substructure, M21 - the twenty-first rotation pair of the first substructure, M22 - the twenty-second rotation pair of the first substructure, M23 - the twenty-third rotation pair of the first substructure, M24 - the twenty-fourth rotation pair of the first substructure;

[0037] B1-first side of the second substructure, B2-second side of the second substructure, B3-third side of the second substructure, B4-fourth side of the second substructure, B5-fifth side of the second substructure, B6-sixth side of the second substructure, B7-seventh side of the second substructure, B8-eighth side of the second substructure, B9-ninth side of the second substructure, B10-tenth side of the second substructure, B11-eleventh side of the second substructure, B12-twelfth side of the second substructure, B13-thirteenth side of the second substructure, B14-fourteenth side of the second substructure, B15-fifteenth side of the second substructure, B16-sixteenth side of the second substructure, B17-seventeenth side of the second substructure, B18-eighteenth side of the second substructure;

[0038] N1-the first rotation pair of the second substructure, N2-the second rotation pair of the second substructure, N3-the third rotation pair of the second substructure, N4-the fourth rotation pair of the second substructure, N5-the fifth rotation pair of the second substructure, N6-the sixth rotation pair of the second substructure, N7-the seventh rotation pair of the second substructure, N8-the eighth rotation pair of the second substructure, N9-the ninth rotation pair of the second substructure, N10-the tenth rotation pair of the second substructure, N11-the eleventh rotation pair of the second substructure, N12-the twelfth rotation pair of the second substructure, N13-the thirteenth rotation pair of the second substructure, N14-the fourteenth rotation pair of the second substructure, N15-the fifteenth rotation pair of the second substructure, N16-the sixteenth rotation pair of the second substructure, N17-the seventeenth rotation pair of the second substructure, N18-the eighteenth rotation pair of the second substructure, N19-the nineteenth rotation pair of the second substructure, N 20-the twentieth rotational pair of the second substructure, N21-the twenty-first rotational pair of the second substructure, N22-the twenty-second rotational pair of the second substructure, N23-the twenty-third rotational pair of the second substructure, N24-the twenty-fourth rotational pair of the second substructure, N25-the twenty-fifth rotational pair of the second substructure, N26-the twenty-sixth rotational pair of the second substructure, N27-the twenty-seventh rotational pair of the second substructure, N28-the twenty-eighth rotational pair of the second substructure, N29-the twenty-ninth rotational pair of the second substructure, N30-the thirtieth rotational pair of the second substructure, N31-the thirty-first rotational pair of the second substructure, N32-the thirty-second rotational pair of the second substructure, N33-the thirty-third rotational pair of the second substructure, N34-the thirty-fourth rotational pair of the second substructure, N35-the thirty-fifth rotational pair of the second substructure, N36-the thirty-sixth rotational pair of the second substructure. DETAILED DESCRIPTION

[0039] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0040] This embodiment provides a polyhedron multistable structure based on zigzag paper. Figure 1-1, including two substructures, a first substructure and a second substructure; wherein the first substructure is composed of eight faces, and the second substructure is composed of six curved pattern units. The first substructure is connected to the second substructure.

[0041] The first substructure is a regular triangular rigid panel with a preset side length a, and its thickness is an arbitrary value greater than zero; the second substructure's deformable zigzag paper unit has a spatial quadrilateral profile with a specific angle and is composed of three curved-edge panels. To meet the geometric coordination relationship, the side length of the spatial quadrilateral profile of the zigzag paper unit is a, the profile angle θ of the zigzag paper unit can be adjusted in the range of [0.62, 0.75] radians, and the curved edge curvature κ can be adjusted in the range of (0, 0.6 / a].

[0042] The structure has three stable states: unfolded, folded, and self-locking. The transition from unfolded to folded occurs when the first substructure rotates and contracts toward the center of the structure, while the second substructure folds along the curved creases. The transition from unfolded to self-locking occurs when the second substructure bulges outward under the rigid constraints of the first.

[0043] Example 1: Transition from Expanded to Collapsed

[0044] The structure of the present invention includes two substructures, wherein: the first substructure includes eight surfaces, namely the first substructure first surface A1, the first substructure second surface A2, the first substructure third surface A3, the first substructure fourth surface A4, the first substructure fifth surface A5, the first substructure sixth surface A6, the first substructure seventh surface A7, and the first substructure eighth surface A8.

[0045] See Figure 1-2 to Figure 1-3 As shown, the first substructure includes twenty-four rotation pairs, namely the first rotation pair M1 of the first substructure, the second rotation pair M2 of the first substructure, the third rotation pair M3 of the first substructure, the fourth rotation pair M4 of the first substructure, the fifth rotation pair M5 of the first substructure, the sixth rotation pair M6 of the first substructure, the seventh rotation pair M7 of the first substructure, the eighth rotation pair M8 of the first substructure, the ninth rotation pair M9 of the first substructure, the tenth rotation pair M10 of the first substructure, the eleventh rotation pair M11 of the first substructure, the twelfth rotation pair M12 of the first substructure, and the The first substructure has a thirteenth rotational pair M13, the first substructure has a fourteenth rotational pair M14, the first substructure has a fifteenth rotational pair M15, the first substructure has a sixteenth rotational pair M16, the first substructure has a seventeenth rotational pair M17, the first substructure has an eighteenth rotational pair M18, the first substructure has a nineteenth rotational pair M19, the first substructure has a twentieth rotational pair M20, the first substructure has a twenty-first rotational pair M21, the first substructure has a twenty-second rotational pair M22, the first substructure has a twenty-third rotational pair M23, and the first substructure has a twenty-fourth rotational pair M24.

[0046] See Figure 2-1 to Figure 2-6 As shown, the second substructure includes eighteen surfaces, namely the second substructure first surface B1, the second substructure second surface B2, the second substructure third surface B3, the second substructure fourth surface B4, the second substructure fifth surface B5, the second substructure sixth surface B6, the second substructure seventh surface B7, the second substructure eighth surface B8, the second substructure ninth surface B9, the second substructure tenth surface B10, the second substructure eleventh surface B11, the second substructure twelfth surface B12, the second substructure thirteenth surface B13, the second substructure fourteenth surface B14, the second substructure fifteenth surface B15, the second substructure sixteenth surface B16, the second substructure seventeenth surface B17, and the second substructure eighteenth surface B18.

[0047] The second substructure includes thirty-six rotation pairs, namely the first rotation pair N1 of the second substructure, the second rotation pair N2 of the second substructure, the third rotation pair N3 of the second substructure, the fourth rotation pair N4 of the second substructure, the fifth rotation pair N5 of the second substructure, the sixth rotation pair N6 of the second substructure, the seventh rotation pair N7 of the second substructure, the eighth rotation pair N8 of the second substructure, the ninth rotation pair N9 of the second substructure, the tenth rotation pair N10 of the second substructure, the eleventh rotation pair N11 of the second substructure, the twelfth rotation pair N12 of the second substructure, the thirteenth rotation pair N13 of the second substructure, the fourteenth rotation pair N14 of the second substructure, the fifteenth rotation pair N15 of the second substructure, the sixteenth rotation pair N16 of the second substructure, the seventeenth rotation pair N17 of the second substructure, the eighteenth rotation pair N18 of the second substructure, and the nineteenth rotation pair N19 of the second substructure. Rotational pair N19, the twentieth rotational pair N20 of the second substructure, the twenty-first rotational pair N21 of the second substructure, the twenty-second rotational pair N22 of the second substructure, the twenty-third rotational pair N23 of the second substructure, the twenty-fourth rotational pair N24 of the second substructure, the twenty-fifth rotational pair N25 of the second substructure, the twenty-sixth rotational pair N26 of the second substructure, the twenty-seventh rotational pair N27 of the second substructure, the twenty-eighth rotational pair N28 of the second substructure, the twenty-ninth rotational pair N29 of the second substructure, the thirtieth rotational pair N30 of the second substructure, the thirty-first rotational pair N31 of the second substructure, the thirty-second rotational pair N32 of the second substructure, the thirty-third rotational pair N33 of the second substructure, the thirty-fourth rotational pair N34 of the second substructure, the thirty-fifth rotational pair N35 of the second substructure, and the thirty-sixth rotational pair N36 of the second substructure.

[0048] The second surface B2 of the second substructure is adjacent to the first surface B1 of the second substructure and is connected to each other through the first rotation pair N1 of the second substructure; the second surface B2 of the second substructure is adjacent to the third surface B3 of the second substructure and is connected to each other through the second rotation pair N2 of the second substructure; the fifth surface B5 of the second substructure is adjacent to the fourth surface B4 of the second substructure and is connected to each other through the third rotation pair N3 of the second substructure; the fifth surface B5 of the second substructure is adjacent to the sixth surface B6 of the second substructure and is connected to each other through the fourth rotation pair N4 of the second substructure; the eighth surface B8 of the second substructure is adjacent to the seventh surface B7 of the second substructure and is connected to each other through the fifth rotation pair N5 of the second substructure; the eighth surface B8 of the second substructure is adjacent to the ninth surface B9 of the second substructure and is connected to each other through the sixth rotation pair N6 of the second substructure; the eleventh surface B11 of the second substructure is adjacent to the fourth surface B4 of the second substructure and is connected to each other through the third rotation pair N3 of the second substructure; The tenth surface B10 of the second substructure is adjacent and connected to each other through the seventh rotation pair N7 of the second substructure; the eleventh surface B11 of the second substructure is adjacent to the twelfth surface B12 of the second substructure and connected to each other through the eighth rotation pair N8 of the second substructure; the fourteenth surface B14 of the second substructure is adjacent to the thirteenth surface B13 of the second substructure and connected to each other through the ninth rotation pair N9 of the second substructure; the fourteenth surface B14 of the second substructure is adjacent to the fifteenth surface B15 of the second substructure and connected to each other through the tenth rotation pair N10 of the second substructure; the seventeenth surface B17 of the second substructure is adjacent to the sixteenth surface B16 of the second substructure and connected to each other through the eleventh rotation pair N11 of the second substructure; the seventeenth surface B17 of the second substructure is adjacent to the eighteenth surface B18 of the second substructure and connected to each other through the twelfth rotation pair N12 of the second substructure.

[0049] The first surface A1 of the first substructure is adjacent to the fourth surface B4 of the second substructure and is connected to each other through the first substructure first rotation pair M1 (the second substructure nineteenth rotation pair N19); the first surface A1 of the first substructure is adjacent to the third surface B3 of the second substructure and is connected to each other through the first substructure second rotation pair M2 (the second substructure fifteenth rotation pair N15); the first surface A1 of the first substructure is adjacent to the ninth surface B9 of the second substructure and is connected to each other through the first substructure third rotation pair M3 (the second substructure twenty-third rotation pair N23); the second surface A2 of the first substructure is adjacent to the first surface B1 of the second substructure and is connected to each other through the first substructure fourth rotation pair M4 (the second substructure thirteenth rotation pair N13); the second surface A1 of the first substructure is adjacent to the first surface B1 of the second substructure and is connected to each other through the first substructure fourth rotation pair M4 (the second substructure thirteenth rotation pair N13); The surface A2 is adjacent to the fourth surface B4 of the second substructure and is connected to each other through the fifth rotational pair M5 of the first substructure (the seventeenth rotational pair N17 of the second substructure); the second surface A2 of the first substructure is adjacent to the twelfth surface B12 of the second substructure and is connected to each other through the sixth rotational pair M6 of the first substructure (the twenty-seventh rotational pair N27 of the second substructure); the third surface A3 of the first substructure is adjacent to the third surface B3 of the second substructure and is connected to each other through the seventh rotational pair M7 of the first substructure (the sixteenth rotational pair N16 of the second substructure); the third surface A3 of the first substructure is adjacent to the seventh surface B7 of the second substructure and is connected to each other through the eighth rotational pair M8 of the first substructure (the twenty-first rotational pair N21 of the second substructure); the third surface A3 of the first substructure and The thirteenth surface B13 of the second substructure is adjacent and connected to each other through the ninth rotational pair M9 of the first substructure (the thirty-first rotational pair N31 of the second substructure); the fourth surface A4 of the first substructure is adjacent to the sixth surface B6 of the second substructure and connected to each other through the tenth rotational pair M10 of the first substructure (the twentieth rotational pair N20 of the second substructure); the fourth surface A4 of the first substructure is adjacent to the ninth surface B9 of the second substructure and connected to each other through the eleventh rotational pair M11 of the first substructure (the twenty-fourth rotational pair N24 of the second substructure); the fourth surface A4 of the first substructure is adjacent to the eighteenth surface B18 of the second substructure and connected to each other through the twelfth rotational pair M12 of the first substructure (the thirty-fifth rotational pair N35 of the second substructure); the fifth surface A4 of the first substructure is adjacent to the sixth surface B6 of the second substructure and connected to each other through the tenth rotational pair M10 of the first substructure (the twentieth rotational pair N20 of the second substructure); The surface A5 is adjacent to the sixth surface B6 of the second substructure and is connected to each other through the thirteenth rotational pair M13 of the first substructure (the eighteenth rotational pair N18 of the second substructure); the fifth surface A5 of the first substructure is adjacent to the twelfth surface B12 of the second substructure and is connected to each other through the fourteenth rotational pair M14 of the first substructure (the twenty-eighth rotational pair N28 of the second substructure); the fifth surface A5 of the first substructure is adjacent to the sixteenth surface B16 of the second substructure and is connected to each other through the fifteenth rotational pair M15 of the first substructure (the thirty-third rotational pair N33 of the second substructure); the sixth surface A6 of the first substructure is adjacent to the tenth surface B10 of the second substructure and is connected to each other through the sixteenth rotational pair M16 of the first substructure (the twenty-fifth rotational pair N25 of the second substructure);The sixth surface A6 of the first substructure is adjacent to the first surface B1 of the second substructure and is connected to each other through the seventeenth rotation pair M17 of the first substructure (the fourteenth rotation pair N14 of the second substructure); the sixth surface A6 of the first substructure is adjacent to the thirteenth surface B13 of the second substructure and is connected to each other through the eighteenth rotation pair M18 of the first substructure (the twenty-ninth rotation pair N29 of the second substructure); the seventh surface A7 of the first substructure is adjacent to the seventh surface B7 of the second substructure and is connected to each other through the nineteenth rotation pair M19 of the first substructure (the twenty-second rotation pair N22 of the second substructure); the seventh surface A7 of the first substructure is adjacent to the eighteenth surface B18 of the second substructure and is connected to each other through the twentieth rotation pair M20 of the first substructure (the thirty-sixth rotation pair N36 of the second substructure); The seventh surface A7 of the structure is adjacent to the fifteenth surface B15 of the second substructure and is connected to each other via the twenty-first rotational pair M21 of the first substructure (the thirty-second rotational pair N32 of the second substructure); the eighth surface A8 of the first substructure is adjacent to the tenth surface B10 of the second substructure and is connected to each other via the twenty-second rotational pair M22 of the first substructure (the twenty-sixth rotational pair N26 of the second substructure); the eighth surface A8 of the first substructure is adjacent to the sixteenth surface B16 of the second substructure and is connected to each other via the twenty-third rotational pair M23 of the first substructure (the thirty-fourth rotational pair N34 of the second substructure); and the eighth surface A8 of the first substructure is adjacent to the fifteenth surface B15 of the second substructure and is connected to each other via the twenty-fourth rotational pair M24 of the first substructure (the thirtieth rotational pair N30 of the second substructure).

[0050] See Figure 3-1 to Figure 3-3, and simultaneously apply compressive loading to all surface normal directions of the first substructure, the structure will transform from an unfolded state to a folded state. During this process, the first substructure begins to rotate and shrink around its rotation pair toward the center of the structure. Specifically, the first surface of the first substructure rotates toward the center of the structure around the first rotational pair of the first substructure (which is also the nineteenth rotational pair of the second substructure), the second rotational pair (which is also the fifteenth rotational pair of the second substructure) and the third rotational pair (which is also the twenty-third rotational pair of the second substructure); the second surface of the first substructure rotates toward the center of the structure around the fourth rotational pair of the first substructure (which is also the thirteenth rotational pair of the second substructure), the fifth rotational pair (which is also the seventeenth rotational pair of the second substructure) and the sixth rotational pair (which is also the twenty-seventh rotational pair of the second substructure); the third surface of the first substructure rotates toward the center of the structure around the seventh rotational pair of the first substructure (which is also the sixteenth rotational pair of the second substructure), the eighth rotational pair (which is also the twenty-first rotational pair of the second substructure) and the ninth rotational pair (which is also the thirty-first rotational pair of the second substructure); the fourth surface of the first substructure rotates toward the center of the structure around the tenth rotational pair of the first substructure (which is also the twentieth rotational pair of the second substructure), the eleventh rotational pair (which is also the twenty-fourth rotational pair of the second substructure) and the twelfth rotational pair (which is also the thirty-fifth rotational pair of the second substructure); The five surfaces rotate toward the center of the structure around the 13th rotational pair of the first substructure (which is also the 18th rotational pair of the second substructure), the 14th rotational pair (which is also the 28th rotational pair of the second substructure) and the 15th rotational pair (which is also the 33rd rotational pair of the second substructure); the sixth surface of the first substructure rotates toward the center of the structure around the 16th rotational pair of the first substructure (which is also the 25th rotational pair of the second substructure), the 17th rotational pair (which is also the 14th rotational pair of the second substructure) and the 18th rotational pair (which is also the 29th rotational pair of the second substructure); the seventh surface of the first substructure rotates toward the center of the structure around the 19th rotational pair of the first substructure (which is also the 22nd rotational pair of the second substructure), the 20th rotational pair (which is also the 36th rotational pair of the second substructure) and the 21st rotational pair (which is also the 32nd rotational pair of the second substructure); the eighth surface of the first substructure rotates toward the center of the structure around the 22nd rotational pair of the first substructure (which is also the 26th rotational pair of the second substructure), the 23rd rotational pair (which is also the 34th rotational pair of the second substructure) and the 24th rotational pair (which is also the 30th rotational pair of the second substructure) At the same time, under the action of the rigid constraint of the first substructure, the six curved units of the second substructure fold and deform along the preset curved creases. Specifically, the three faces of each curved unit rotate relative to each other around the curved edge rotation pair between them, so that the curved unit transitions from the unfolded state to the folded state. Finally, when all the rigid triangular faces of the first substructure are tightly fitted and the second substructure folds and shrinks to the inside of the regular octahedron formed by the first substructure, the entire structure enters the folded state ( Figure 3-3 ). In the folded state, the first substructure and the second substructure are spatially axially symmetrically distributed.

[0051] Example 2: Conversion from the unfolded state to the self-locking state

[0052] See Figure 4-1 to Figure 4-2, when all the vertices of the curved surface of the second substructure are compressed and loaded in sequence along the direction coinciding with the line connecting the upper and lower vertices of the curved surface of the second substructure, the structure will transform from the expanded state to the self-locking state. In this process, the second substructure begins to bulge outward under the rigid constraint of the first substructure. Specifically, for each curved unit: the curved unit composed of the first, second and third surfaces of the second substructure, its first surface rotates around the two rotational pairs connecting the first surface of the first substructure and itself (i.e. the thirteenth rotational pair and the fourteenth rotational pair of the second substructure), its third surface rotates around the two rotational pairs connecting the second surface of the first substructure and itself (i.e. the fifteenth rotational pair and the sixteenth rotational pair of the second substructure), and its second surface rotates around its own first rotational pair and second rotational pair; the curved unit composed of the fourth, fifth and sixth surfaces of the second substructure, its fourth surface rotates around the two rotational pairs connecting the first substructure (i.e. the seventeenth rotational pair of the second substructure The sixth face of the curved pattern unit composed of the seventh, eighth, and ninth faces of the second substructure rotates around the two rotational pairs connecting the first substructure (i.e., the twenty-first and twenty-second rotational pairs of the second substructure), the sixth face of the curved pattern unit rotates around the two rotational pairs connecting the first substructure (i.e., the nineteenth and twenty-fourth rotational pairs of the second substructure), and the fifth face of the curved pattern unit rotates around its own third and fourth rotational pairs. The seventh face of the curved pattern unit composed of the seventh, eighth, and ninth faces of the second substructure rotates around the two rotational pairs connecting the first substructure (i.e., the twenty-first and twenty-second rotational pairs of the second substructure), the ninth face of the curved pattern unit rotates around the two rotational pairs connecting the first substructure (i.e., the twenty-third and twenty-fourth rotational pairs of the second substructure), and the eighth face of the curved pattern unit rotates around its own fifth and sixth rotational pairs. The curved pattern unit composed of the tenth, eleventh, and twelfth surfaces of the second substructure has its tenth surface rotated around the two rotational pairs connecting the first substructure (i.e., the twenty-fifth and twenty-sixth rotational pairs of the second substructure), its twelfth surface rotates around the two rotational pairs connecting the first substructure (i.e., the twenty-seventh and twenty-eighth rotational pairs of the second substructure), and its eleventh surface rotates around its own seventh and eighth rotational pairs; the curved pattern unit composed of the thirteenth, fourteenth, and fifteenth surfaces of the second substructure has its thirteenth surface rotated around the two rotational pairs connecting the first substructure (i.e., the twenty-ninth and thirtieth rotational pairs of the second substructure). Its fifteenth face rotates around the two revolving pairs connecting the first substructure (i.e., the 31st and 32nd revolving pairs of the second substructure), and its fourteenth face rotates around its own ninth and tenth revolving pairs. The curved pattern unit, composed of the sixteenth, seventeenth, and eighteenth faces of the second substructure, has its sixteenth face rotate around the two revolving pairs connecting the first substructure (i.e., the 33rd and 34th revolving pairs of the second substructure), its eighteenth face rotates around the two revolving pairs connecting the first substructure (i.e., the 35th and 36th revolving pairs of the second substructure), and its seventeenth face rotates around its own eleventh and twelfth revolving pairs. All of these faces rotate away from the center of the structure, and the three curved edge faces of the curved pattern unit undergo a steady-state jump from concave to convex.Finally, when all the units of the second substructure reach the outward-stretched state, the entire structure enters a self-locking state (. Figure 4-2 ). In the self-locking state, the first substructure and the second substructure are distributed in rotational symmetry in space.

[0053] Example 3: Tiling of polyhedral multistable structures

[0054] See Figure 5 As shown, the polyhedral multistable structure of this embodiment has the ability to be densely packed in both planar and three-dimensional space, and adjacent structures are linked by rotational pairs to form a continuously deformed array. In the plane, the units tend to form hexagonal dense packing. When the array as a whole deforms cooperatively (for example, each unit switches between stable states), the center spacing of adjacent units also changes dynamically, and the range of change depends on the geometric design parameters of the unit and the deformation state it is in (for example, changing between fully expanded and fully folded states). In the three-dimensional direction, dense packing can be achieved by stacking the planar array layer by layer, and theoretically there is no limit to the number of stacked layers.

[0055] In summary, the multi-stable polyhedron structure provided in this embodiment can achieve the steady-state performance required by the present invention as long as the above-mentioned constraints are met, that is, as long as the connection method of the revolute pair is met. This structure can ensure reliable conversion between stable working states. The revolute pair can be a hinge, hinge or bearing, and its specific size can be determined according to actual needs; the geometric parameters of the curved edge can be optimized according to the required steady-state characteristics; the thickness of the rigid surface of the first substructure can be freely selected as needed. The structure has the characteristics of simple composition, easy manufacturing, and controllable motion, and is suitable for engineering applications in the fields of aerospace, intelligent robots, etc.

[0056] The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention. The above specific embodiments are merely illustrative and not restrictive. Without departing from the scope of the present invention and the scope of protection of the claims, those skilled in the art may make various specific modifications based on the teachings of the present invention, all of which fall within the scope of protection of the present invention.

Claims

1. A polyhedral multistable structure based on origami, characterized in that: include: A first substructure is a polyhedral frame formed by eight rigid triangular panels connected by revolute joints, wherein the rigid triangular panels are regular triangles with a side length of a; The second substructure consists of six deformable origami units. Each unit consists of three curved panels connected in pairs by revolute pairs on the curved edges to form a spatial quadrilateral outline. The side length of the spatial quadrilateral outline is a. The first substructure and the second substructure are connected by a common revolute pair to form a polyhedral multi-stable structure with a first stable state, a second stable state and a third stable state. The structure can undergo stable state conversion along two different paths: Path 1 is the transition from the first stable state to the second stable state. The first substructure rotates and contracts around the revolving pair toward the center, driving the curved edge panels of each curved origami unit in the second substructure to rotate relative to each other around their curved edge revolving pair and fold, ultimately reaching the second stable state. Path 2 is when the first stable state is converted to the third stable state, the second substructure jumps, each zigzag origami unit bulges outward to trigger self-locking, and finally reaches the third stable state.

2. The polyhedron multistable structure based on zigzag origami according to claim 1, characterized in that: The first stable state is the unfolded state, which is a truncated octahedron configuration. The first substructure and the second substructure are rotationally symmetrically distributed. At this time, the polyhedral multistable structure is in the initial stable equilibrium state. The second stable state is a folded state, which is a regular octahedron configuration. The first substructure and the second substructure are axially symmetrical. At this time, the second substructure is completely folded and stored inside the first substructure. The third stable state is a self-locking state. Driven by an external load, the origami units of the second substructure unfold and stretch outward under the rigid constraint of the first substructure, forming a geometric interlock. When the rigid triangular panel is vertically loaded, the reverse constraint of the origami units cannot trigger the structural contraction, and the first and second substructures are rotationally symmetrically distributed.

3. The polyhedron multistable structure based on zigzag origami according to claim 1 or 2, characterized in that: The thickness of the rigid triangular panel is an arbitrary value greater than zero; while maintaining the structural functional integrity, the spatial quadrilateral outline angle θ of the curved origami unit is in the range of [0.62, 0.75] radians, and the curvature κ of the curved edge is in the range of (0, 0.6 / a].

4. The polyhedron multistable structure based on zigzag origami according to claim 1 or 2, characterized in that: Each rigid triangular panel of the first substructure is connected to other rigid triangular panels and the second substructure through at least three rotating pairs, and the rotating pairs are one of hinges, hinges or bearings; the rotating pairs between the curved edge panels in the second substructure are obtained by additional processing.

5. The polyhedron multistable structure based on zigzag origami according to claim 1 or 2, characterized in that: The structure has the ability to be paved in both plane and three dimensions, and adjacent structures can be linked by rotational pairs to form a continuous deformation array to adapt to different application requirements.

6. An application of a polyhedral multistable structure, based on the polyhedral multistable structure according to any one of claims 1 to 5, characterized in that: It is used in deployable spacecraft structures, shape-shifting robotic joints, reconfigurable building structures, and metamaterial devices with adjustable mechanical properties.

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