Multi-stable linkages and folding methods

Abstract

This invention discloses a multistable connecting joint and a folding method. The multistable folding joint is based on a single-vertex six-fold origami configuration, with vertical panels set at the edges of the planar fold structure to form a connecting unit with spatial folding and rotation capabilities. The folding joint mainly consists of oppositely arranged rigid body units and folding units between them. Through the coordinated design of the fold configuration and panel layout, the joint can form multiple stable configurations under different folding states. The folding method of this invention, through the design of the fold geometry and panel spatial arrangement, achieves reversible transformation between multiple stable states of the folding joint, and maintains structural stability without the need for additional locking mechanisms. This method enables the configuration design of multistable folding joints under different initial configuration conditions, and is suitable for the design and application of reconfigurable origami mechanisms and deformable structures.

Description

Technical Field

[0001] This invention belongs to the technical field of origami structures and reconfigurable mechanisms, specifically a multistable folding joint. Background Technology

[0002] With the rapid development of flexible structures, deployable structures, and reconfigurable robotics, traditional rigid articulated structures are struggling to meet the demands of complex structural designs in terms of lightweighting, repeatable folding, and multi-stable state maintenance. In recent years, origami geometry has been introduced into the field of mechanical structure design, enabling programmability and reconfigurability of structural forms through the control of crease geometry and panel connections. Typical structures such as Miura origami, Waterbomb origami, and Kresling origami have been widely applied in flexible mechanisms and spatial deployment systems. However, existing origami structures typically only exhibit monostable or bistable characteristics, with a limited number of stable states and a single folding path, making it difficult to achieve stable multi-stable state maintenance and reversible multi-path transformation. Furthermore, traditional origami structures are mostly planar folding patterns, lacking vertical constraints, making it difficult to form multi-stable forms with out-of-plane rotation capabilities during spatial folding. They also have limitations in modular expansion and array construction. Therefore, there is an urgent need for a joint folding method that can achieve multi-stable reversible folding in space, possess multi-path transformation capabilities, and be scalable into modular arrays to meet the diverse needs of flexible connections, deformable mechanisms, and reconfigurable systems. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a multistable connection joint with multistable states and a folding method.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A multi-stable connection joint consists of a first folded surface, two second folded surfaces, and two driving surfaces; The first folded surface is a first rectangle, which is a square and has three creases intersecting at the center of the first rectangle. Two of these creases are along the diagonal direction and are the first creases. The remaining crease is parallel to the first side of the first rectangle and is the second crease. The second folded surface is a second rectangle with a third crease, a fourth crease, and a fifth crease; the third crease and the fifth crease are symmetrical about the fourth crease; the third crease and the fifth crease connect the midpoint of one side of the second rectangle to the two vertices of the opposite side; The driving surface is connected to the second side of the first rectangle, and the second side of the first rectangle is connected to the first side of the first rectangle; one of the two adjacent sides of the second rectangle is connected to the first side of the first rectangle, and the other is connected to the driving surface; the third crease and the fifth crease intersect with the first crease, and the fourth crease intersects with the second crease; The first, third, fourth, and fifth creases are valley creases; the second crease is a mountain crease.

[0005] The folding method based on the above-mentioned multistable joints includes: Define parameters: Angle between the two driving surfaces α , used to describe the overall torsion angle between two rigid body elements; The side length of the first rectangle is 2. l ; The included angle between the two first sides of the first rectangle β This reflects the opening and closing angle of the creases during the twisting process of the module; The distance between the midpoints of the two first sides of the first rectangle d , characterizing the horizontal expansion and contraction state of the connecting structure; The angles between the two first sides of the first rectangle and the two planes formed by the center of the first rectangle are respectively... gamma ; The angle between the folded sub-face intersecting the driving surface on the second rectangle and the driving surface. ; The included angle between a side of the second rectangle that intersects the driving surface and a side that intersects the first rectangle. rho ; The angle between the intersection of the two sides of the second rectangle and the creases EF and EI of the two adjacent sides. rho ; fold: The defined parameters for different steady states are shown in the table below.

[0006] The connecting joint is geometrically composed of two rigid body elements and an intermediate folding element, passing through the angle between plane ABLG and plane EDJI. α Describe the overall torsional angle between rigid body elements, the angle between crease AB and DE. β The distance between vertices P and Q reflects the degree of opening and closing of the crease during the folding process. d Characterizes the expansion and contraction state of the connection structure in the horizontal direction. Through α , β and dThe geometric coupling transformation enables a continuous folding process from the initial folded state to an intermediate stable state and then to the fully unfolded state, maintaining the multi-stability characteristics of the structure under different paths. This folding method can achieve energy balance and shape preservation between steady states without relying on external locking mechanisms. Its energy potential curve exhibits a multi-peak distribution, with each steady state corresponding to an energy minimum. By adjusting the crease arrangement angle, vertical panel height, or panel material stiffness, the number of steady states, the sequence of shape switching, and the energy required for transformation can be flexibly controlled, achieving structural designability and controllability.

[0007] The beneficial effects of this invention are: by introducing a vertical panel, the folding unit gains spatial rotation capability, significantly expanding the geometric function of the traditional Waterbomb crease; through parameters α , β , d The method achieves quadruple stability and multi-path reversible deformation through joint control, ensuring the structure remains stable under different morphologies. It features self-locking without additional locking mechanisms and offers advantages such as repeatable folding, shape retention, and adjustable energy. Furthermore, multiple such connecting joints can be modularly combined to form two-dimensional or three-dimensional array structures, which can be used to construct origami mechanisms that are deployable, retractable, or reconfigurable. This method is applicable to fields such as flexible connection systems, spatial unfolding structures, and deformable robots, and has promising engineering application prospects and promotional value. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the planar fold lines of the present invention; Figure 2 This is a three-dimensional schematic diagram of the present invention; Figure 3 This is a top view of the fully unfolded state of the present invention; Figure 4 This is a parameter characterization diagram of the present invention; Figure 5 These are the four steady-state diagrams of this invention; Figure 6 This is a diagram illustrating the motion process from steady state one to steady state two according to the present invention; Figure 7 This is a motion process diagram from steady state one to steady state four of the present invention; Figure 8 This is a diagram illustrating the motion process from steady state two to steady state three according to the present invention; Figure 9 This is a diagram illustrating the motion process from steady state two to steady state four according to the present invention; Figure 10 This is a diagram illustrating the motion process from steady state three to steady state four according to the present invention; Figure 11 strain energy U Follow gamma The trend of change. Detailed Implementation

[0009] The design method will be further explained below with reference to specific embodiments and the accompanying drawings: This embodiment provides a multistable connection joint. Figure 1 This is a crease diagram of the multistable connection joint of the present invention, demonstrating the planar configuration based on a single-vertex six-crease Waterbomb folding scheme. The diagram radiates outwards from the center point O as the fold vertex, with six crease lines OA, OB, OC, OD, OE, and OF arranged symmetrically to form three pairs of intersecting symmetrical creases. The boundaries are defined by straight lines LK, KJ, J'I', IH, HG, G'L', BL', BL, DJ, DJ', EI, EI', AG, AG'. Creases BK, KC, KD, OB, OD, OA, OE, HA, HF, and HE are valley creases, while creases AB, BC, CD, DE, EF, and FA are mountain creases.

[0010] Figure 2 This is a three-dimensional schematic diagram of the invention, showing the three-dimensional configuration after folding. It forms a structure that is closed on five sides and open on one side. [The diagram shows...] Figure 1 After folding the planar crease diagram, boundaries AG' and AG are overlapped and glued together, boundaries EI' and EI are overlapped and glued together, boundaries DJ' and DJ are overlapped and glued together, and boundaries EI' and EI are overlapped and glued together. This three-dimensional structure demonstrates the spatial geometry of the folded Waterbomb unit, providing a basic structural foundation for realizing multi-stable connection joints.

[0011] Figure 3 This is a schematic diagram illustrating the connection of two rigid bodies according to the present invention, where 1 and 3 are rigid bodies and 2 is a multistable connection joint.

[0012] Figure 4 This is a parameter characterization of the present invention, and the defined parameters include: (a) the angle between plane ABLG and plane EDJI. α (a) The angle between the crease AB and DE, used to describe the overall torsion angle between two rigid body elements; β (c) The angle of the crease opening and closing of the module during the torsion process; d (d) The angle between plane ABO and plane DEO, representing the horizontal expansion and contraction state of the connecting structure; gamma (e) The angle between plane EIH and the adjacent rigid body vertical plane EDJI. (f) Angle between crease EF and EI rho The above six parameters collectively reflect the spatial orientation and local folding characteristics of the origami connection structure during its configuration evolution. Figure 5These are four steady-state diagrams of the present invention, illustrating four stable equilibrium states of the multistable connecting joint based on Waterbomb folding units. Steady-state one, steady-state two, steady-state three, and steady-state four correspond to different torsional angles. α Crease angle β and vertex spacing d The four steady states are transformed into each other through reversible folding paths, forming multiple motion paths such as Path 1-2, Path 2-3, Path 3-4 and Path 1-4, Path 2-4, thus constructing a reconfigurable motion network with multi-steady-state characteristics.

[0013] The parameters for each of the four steady states are defined in the table below.

[0014] The four steady states correspond to different geometric configurations; the first steady state corresponds to the torsional state, the second steady state corresponds to the fully extended state, the third steady state corresponds to the fully contracted state, and the fourth steady state corresponds to the bending state.

[0015] Figure 6 This is a motion diagram of the steady-state transition from steady state one to steady state two, illustrating the dynamic change process (Path 1-2) of the connecting joint transitioning from a torsional state to full deployment. During the rotation from steady state one to steady state two, the entire rotational motion is broken down into three parts: Step 1 involves the relative rotation of all cuboids and the plane around the crease AD; Step 2 involves the rotation of the two cuboids around the axes DE and AB; and Step 3 involves the rotation of the plane EIH around the EI axis. , .

[0016] During this process, the two rigid body elements undergo torsional motion around the central vertex, and the structure transitions from a compact form to an unfolded form, demonstrating the continuous deformation characteristics and geometric reversibility of the multi-stable structure.

[0017] Figure 7 This is a motion diagram illustrating the transition from steady state one to steady state four of the present invention, showing the transformation path (Path 1-4) of the structure from a bending state to a torsional state. In the motion paths 1-4, it is assumed that points H, K, and O coincide throughout the entire transformation process, and points I and F, and points C and L also remain coincident. The rigid body and its connected planes rotate about the crease AD axis, and the transformation process occurs through the dihedral angle between plane ABO and plane DEO. gamma Describe it. , , α = gamma .

[0018] During this process, the two rigid body elements connecting the joints twist around the central folding vertex. As the folding angle gradually increases, the structure gradually transitions from the initial bending shape to a torsional symmetry steady state, realizing a continuous deformation process from in-plane folding to out-of-plane torsion.

[0019] Figure 8 This is a motion diagram illustrating the transition from steady state two to steady state three of the present invention, showing the transformation path (Path 2–3) of the structure from a fully unfolded state to a fully contracted state. Path 2–3 corresponds to the planar unfolding path from steady state two to steady state three. In this transformation path, the reconfigurable multistable origami module undergoes linear stretching / contraction morphological changes. It is assumed that during the path movement, the in-plane angles… α Angle with crease β The perpendicular distance between the two cuboids remains at 0. d The distance between vertices P and Q can be expressed as: ; During this process, the distance between the two rigid bodies continuously decreases until the multistable joint is fully contracted.

[0020] Figure 9 This is a diagram illustrating the motion process from steady state four to steady state two in this invention, showing the transition of the structure from a bending steady state to a fully deployed steady state (Path 2–4). Path 2–4 corresponds to the bending path from the second steady state to the fourth steady state. Assume that during the path motion, the distance between vertices… d =2 l And the angle of the crease β =0 remains unchanged, dihedral angle α With fold angle rho Geometric relationship between them: α= π-2 rho.

[0021] In this path, the two side panels connecting the joint twist synchronously until they are fully extended.

[0022] Figure 10 This is a motion diagram illustrating the transition from steady state three to steady state four in this invention, showing the process of the structure changing from a fully folded state to a bending steady state (Path 3–4). Path 3–4 corresponds to the bending path from steady state three to steady state four; in this transition path, a dihedral angle is assumed. β The angle between plane ABG and DEI is always 0, and points H, K, and O remain coincident throughout the movement. α The path makes equal angles with both planes AOE and ABO, therefore the following relationship holds: , .

[0023] Figure 11This is an energy curve diagram between the four steady states of this invention. It shows the energy conversion between each path. The strain energy on the motion path is characterized by the change in the distance between points F and H during the motion. If the distance between F and H changes on a certain path, it indicates that strain has occurred in the structure along this path, and this path can be classified as a steady-state transition path. If the distance between F and H remains unchanged, it is considered a rigid path, and no strain is generated during the entire motion process. Among the five paths, Path 1-2, Path 2-3, and Path 2-4 are identified as steady-state transition paths; while the energy curves of Path 1-4 and Path 3-4 coincide with the coordinate axis, with an energy of 0, indicating rigid paths, during which no strain energy is generated inside the origami structure. The analysis results show that the proposed reconfigurable multi-stable origami module has four steady states. The corresponding strain energy U It can be represented as: ,in U This represents the strain energy generated by the deformation of FH. The trend of strain energy variation is plotted based on parameter changes under different states.

[0024] In summary, the present invention achieves this through... Figures 1 to 11 The system demonstrates the structural configuration and morphological evolution of a multistable folding joint. The accompanying figures visually illustrate the geometric laws governing the joint's transformation from crease design and three-dimensional unfolding to multistable transitions, verifying the structural rationality and innovation of this invention's folding joint in achieving reversible deformation and maintaining multistable states.

Claims

1. A multi-stable connection joint, characterized in that: It consists of a first folding surface, two second folding surfaces, and two driving surfaces; The first folded surface is a first rectangle, which is a square and has three creases intersecting at the center of the first rectangle. Two of these creases are along the diagonal direction and are the first creases. The remaining crease is parallel to the first side of the first rectangle and is the second crease. The second folded surface is a second rectangle with a third crease, a fourth crease, and a fifth crease; the third crease and the fifth crease are symmetrical about the fourth crease; the third crease and the fifth crease connect the midpoint of one side of the second rectangle to the two vertices of the opposite side; The driving surface is connected to the second side of the first rectangle, and the second side of the first rectangle is connected to the first side of the first rectangle; one of the two adjacent sides of the second rectangle is connected to the first side of the first rectangle, and the other is connected to the driving surface; the third crease and the fifth crease intersect with the first crease, and the fourth crease intersects with the second crease; The first, third, fourth, and fifth creases are valley creases; the second crease is a mountain crease.

2. The folding method based on the multistable joint as described in claim 1, characterized in that, include: Define parameters: Angle between the two driving surfaces α , used to describe the overall torsion angle between two rigid body elements; The side length of the first rectangle is 2. l ; The included angle between the two first sides of the first rectangle β This reflects the opening and closing angle of the creases during the twisting process of the module; The distance between the midpoints of the two first sides of the first rectangle d , characterizing the horizontal expansion and contraction state of the connecting structure; The angles between the two first sides of the first rectangle and the two planes formed by the center of the first rectangle are respectively... γ ; The angle between the folded sub-face intersecting the driving surface on the second rectangle and the driving surface. ; The included angle between a side of the second rectangle that intersects the driving surface and a side that intersects the first rectangle. ρ ; The angle between the intersection of the two sides of the second rectangle and the creases EF and EI of the two adjacent sides. ρ ; Based on the defined parameters, four steady states are determined: steady state one, steady state two, steady state three, and steady state four. The parameters for each of the four steady states are as follows: The steady-state parameters are: α=0，β= ，d= , γ=0, =0, ρ=0; The steady-state parameters are as follows: α=0，β=0，d= γ= ， = ρ= ； The three steady-state parameters are: α=0，β=0，d= , γ=0, =0, ρ= ； The steady-state parameters are: α= ，β=0，d= γ= ， =0, ρ=0 .

3. The folding method according to claim 2, characterized in that: The four steady states are connected by five controllable deformation paths, which are as follows: Path 1–2 corresponds to the rotational expansion path from steady state one to steady state two; Path 2–3 corresponds to the planar expansion path from steady state two to steady state three; Path 1–4 corresponds to the rotation paths from steady state one to steady state four; Path 2–4 corresponds to the curved path from the second steady state to the fourth steady state.

4. The folding method according to claim 3, characterized in that: During the rotation from steady state one to steady state two, the entire rotational motion can be decomposed into three parts: Step 1: All cuboids and planes are rotated relative to each other about the crease AD. Step 2: Rotate the two cuboids around DE and AB as axes; Step 3: Rotate plane EIH around axis EI; The parameters for the rotation from steady state one to steady state two satisfy: , .

5. The folding method according to claim 3, characterized in that: In the Path 2–3 transformation path, the reconfigurable multistable origami module undergoes linear stretching / shrinking morphological changes; during the path movement, the in-plane angles... α Angle with crease β The perpendicular distance between the two cuboids remains at 0. d for: 。 6. The folding method according to claim 3, characterized in that: In the transformation path of Path 3–4, dihedral angles β The angle between plane ABG and DEI is always 0, and points H, K, and O always coincide during the movement. α The path makes equal angles with both planes AOE and ABO, therefore the following relationship holds: , .

7. The folding method according to claim 3, characterized in that: In the motion path of Path 1-4, points H, K, and O always coincide throughout the transformation process, as do points I and F, and points C and L; the rigid body and the connected planes rotate around the fold line AD axis, and the transformation process passes through the dihedral angle between plane ABO and plane DEO. γ Describe: , , α = γ .

8. The folding method according to claim 3, characterized in that: During the path movement in Path 2–4, the distance between vertices d =2 l And the angle of the crease β =0 remains unchanged, dihedral angle α With fold angle ρ Geometric relationship between them: α= π-2 ρ.

9. The folding method according to claim 3, characterized in that: The change in strain energy along the motion path is characterized by the change in the distance between points F and H during the motion process. U Represented as: in, U This represents the strain energy generated due to the deformation of FH; This represents the change in distance between points F and H; when U When the value is not zero, it indicates that the module has internal stress during the conversion process and needs to input external energy to overcome the energy barrier in order to reach another steady state.

10. The folding method according to claim 9, characterized in that: Based on the changes in the defined parameters, plot the trend of strain energy variation.

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