Polyhedral metamorphic paper folding mechanism

Abstract

The invention discloses a polyhedral metamorphic paper folding mechanism which is a closed body formed by six same surface units. The surface unit has an initial form and a structural form, the initial form is a square sheet, and the square sheet has four vertex angles and two diagonal lines; the surface unit comprises a square central area, four same sharp corners formed by folding top corners along diagonal lines, and four same trapezoidal surfaces formed by folding inwards along four edges of the square central area; the bending directions of the sharp corners and the trapezoidal surfaces are the same; the lower bottom of the trapezoidal surface is the edge of the square central area, and the upper bottom of the trapezoidal surface is positioned on the edge of the square sheet; the six surface units are mutually connected in a structural form, two upper bottoms of the trapezoidal surfaces of two adjacent surface units form line connection, and the tips of the three sharp corners of three adjacent surface units form point connection. The polyhedral metamorphic paper folding mechanism is simple in structure, high in strength, capable of being repeatedly used and high in motion precision.

Description

Technical Field

[0001] The present invention relates to a polyhedron variable cell origami mechanism. Background Art

[0002] As an ancient art form, origami technology has been widely applied in engineering and scientific fields in recent years, especially in mechanical design and structural engineering. Due to its unique geometric characteristics and foldability, origami structures exhibit superior deformability and lightweight characteristics. The rigid-flexible coupling mechanism significantly enhances the capabilities of traditional rigid structures in stress distribution, energy absorption, and shape adjustment by introducing flexible elements into the system. This property makes it particularly suitable for applications that require high compliance and versatility. Through reasonable rigid-flexible coupling design, origami mechanisms can achieve more complex and diverse deformation modes, thus expanding the application scope of origami technology and promoting its applications in fields such as robotics, aerospace, and architecture.

[0003] As a type of origami mechanism, polyhedron origami mechanisms are important research objects in the fields of mechanical engineering and robotics, and their geometric characteristics and kinematic behaviors have broad potential in multiple application fields. Such mechanisms are based on polyhedron geometric structures and form a mechanical system capable of achieving complex motions through the combination of rigid body connectors and movable hinges. Due to the unique geometric relationships between the vertices, edges, and faces of polyhedra, polyhedron origami mechanisms usually have high symmetry and modular characteristics, providing flexibility and the possibility of structural optimization for mechanical design.

[0004] The disadvantages of existing origami mechanisms mainly focus on the following aspects:

[0005] 1. High structural complexity

[0006] Polyhedron origami mechanisms usually require complex designs and precise manufacturing, involving multiple connection surfaces and folding angles, and are difficult to manufacture.

[0007] Reason: Origami mechanisms require the structure to maintain controllability of geometric shape during the unfolding and contraction processes and need to meet strict kinematic constraints.

[0008] 2. Insufficient mechanical strength

[0009] Some origami mechanisms are prone to deformation or damage during loading or long-term use.

[0010] Reason: The material selection and connection design of the mechanism usually sacrifice strength to ensure flexibility, especially the vulnerability of thin materials and connection nodes is prominent.

[0011] 3. Limited repeat use performance

[0012] Due to the gradual fatigue of materials during multiple folding and unfolding processes, the service life is affected.

[0013] Reason: The folded part is repeatedly stressed, and fatigue damage or fracture is likely to occur, especially in the area where the focusing stress is concentrated.

[0014] 4. Low motion accuracy

[0015] After some origami mechanisms are unfolded, they may not be able to fully return to the designed shape, affecting the application accuracy.

[0016] Reason: The error accumulation between connection points and the variability of the flexible material itself.

[0017] Therefore, providing a polyhedron variable cell origami mechanism with a simple structure, high strength, reusable, and high motion accuracy has become a problem that the industry needs to solve. Summary of the Invention

[0018] To solve the deficiencies in the prior art, the main purpose of the present invention is to provide a polyhedron variable cell origami mechanism with a simple structure, high strength, reusable, and high motion accuracy.

[0019] To achieve the above main purpose, the present invention discloses a polyhedron variable cell origami mechanism, which is a closed body composed of six identical face units; the face unit has an initial form and a constructed form, the initial form is a square thin sheet, and the square thin sheet has four vertices and two diagonals;

[0020] The constructed form of the face unit includes: a central region of the square, four identical sharp corners formed by folding the vertices along the diagonal, and four identical trapezoidal faces formed by folding inward along the four sides of the central region of the square; the folding directions of the sharp corners and the trapezoidal faces are the same; the lower base of the trapezoidal face is the side of the central region of the square, and the upper base of the trapezoidal face is located on the side of the square thin sheet;

[0021] The six face units are connected to each other in the constructed form, the two upper bases of the trapezoidal faces of two adjacent face units form a line connection, and the tips of the three sharp corners of three adjacent face units form a point connection.

[0022] The polyhedron variable cell origami mechanism of the present invention has unconventional mechanical properties such as quasi-zero stiffness, positive stiffness, bistability, negative Poisson's ratio, positive Poisson's ratio, and zero Poisson's ratio. In addition, through the combination at the deformation bifurcation point, programmable Poisson's ratio and variable stiffness metamaterials are networked and applied to the design of damping materials. The present invention opens up a new path for designing multifunctional mechanical metamaterials based on a single structure and can be used in flexible joints, soft robots, etc.

[0023] According to a specific embodiment of the present invention, three adjacent face units are connected into a single loop; in the single loop, each face unit provides two trapezoidal faces separated by 90° for connection with the other two face units; the single loop includes three line connections and one point connection; that is, the single loop includes three faces and one vertex.

[0024] According to a specific embodiment of the present invention, in the single loop, the three line connections are symmetrically constrained about its central axis; the central axis is the axis connecting the point connection and the center of the closed body; the central symmetry constraint means that the folding angles of the three line connections are the same in real time. In the present invention, this configuration is called Configuration One (CP configuration, cube path); in this configuration, the mechanism always maintains good symmetry during the movement process.

[0025] According to a specific embodiment of the present invention, the same constraints as those of the single loop are set on all loops of the polyhedron variable cell origami mechanism.

[0026] According to a specific embodiment of the present invention, in the single loop, two line connections are provided with fixed constraints; the fixed constraints fix the angle between the two trapezoidal faces involved in the line connection to 180°. In the present invention, this configuration is called Configuration Two (LP configuration, long srtip path); in this configuration, the dimensions of the mechanism in the two horizontal directions change in opposite directions during the movement process.

[0027] According to a specific embodiment of the present invention, the same constraints as those of the single loop are set on all loops of the polyhedron variable cell origami mechanism.

[0028] According to a specific embodiment of the present invention, elastomeric connectors are provided at the line connections without constraints to obtain elastic joints.

[0029] According to a specific embodiment of the present invention, in the single loop, one line connection is provided with a fixed constraint; the other two line connections are provided with plane symmetry constraints about their middle planes;

[0030] The fixed constraint fixes the angle between the two trapezoidal faces involved in the line connection to 180°;

[0031] The middle plane passes through the line connection with the fixed constraint and the center of the closed body;

[0032] The plane symmetry constraint means that the folding angles of the two line connections are the same in real time.

[0033] In the present invention, this configuration is called Configuration Three (FP configuration, flat path); in this configuration, the dimension of the mechanism in the horizontal direction remains unchanged during the movement process.

[0034] According to a specific embodiment of the present invention, on all loops of the polyhedron variable-cell origami mechanism, the same constraints as those of a single loop are set.

[0035] According to a specific embodiment of the present invention, at the line joints without constraints, elastomeric connectors are set to obtain elastic joints.

[0036] Based on the bifurcation characteristics of the polyhedron origami mechanism and its different ways of changing geometric dimensions during movement, elastomers are added at the line joints without constraints to form elastic joints, thereby completing the rigid-flexible coupling design of the mechanism. When the mechanism is initially in the same configuration (at the bifurcation point), when different bifurcation paths are selected, its mechanical properties will have different changes, which are mainly reflected in the overall stiffness of the mechanism, that is, a variable stiffness mechanism can be realized through the reconfigurability of the mechanism. This variable stiffness property can realize a quasi-zero stiffness mechanism, which has good shock absorption and buffering characteristics. In the rigid-flexible coupling design, the rigid mechanism has significant advantages in terms of accuracy and strength, but it is easily limited in complex dynamic environments. The flexible mechanism, due to its material properties, has excellent adaptability and deformability, but is relatively insufficient in terms of load-bearing capacity and stability. The rigid-flexible coupling mechanism combines the structural strength of the traditional rigid mechanism and the adaptability advantages of the flexible mechanism.

[0037] The present invention has the following beneficial effects:

[0038] The polyhedron variable-cell origami mechanism of the present invention becomes a single-degree-of-freedom mechanism with different motion paths after adding different constraints. Compared with the traditional polyhedron origami mechanism, the polyhedron variable-cell origami mechanism of the present invention has significant innovation. The designed polyhedron origami mechanism of the present invention has the characteristic of reconfigurability. By adjusting the constraint conditions of the polyhedron origami mechanism, the mechanism can have at least 3 different motion bifurcation paths and there is a common bifurcation point. The polyhedron origami mechanism in the present invention has more motion modes than the traditional origami mechanism, thereby increasing the versatility and adaptability of the mechanism. By adding elastomeric units at the connecting joints, the rigid joints are transformed into flexible joints, and the mechanism itself thus has a certain stiffness, so it has a wider application prospect in the fields of deformable and flexible mechanisms, etc.

[0039] In order to more clearly illustrate the purpose, technical solution and advantages of the present invention, the present invention will be further described in detail below with reference to the drawings and specific embodiments. Description of the Drawings

[0040] Figure 1A It is the crease design drawing of the square thin sheet in Embodiment 1;

[0041] Figure 1B It is the schematic diagram of the structural form of the face unit in Embodiment 1;

[0042] Figure 2A It is a schematic diagram of the connection mode of the surface units in Embodiment 1;

[0043] Figure 2B It is a schematic diagram of the overall structure of the polyhedron variable-cell origami mechanism in Embodiment 1;

[0044] Figure 3A It is a schematic diagram of the structure of a single loop in Embodiment 1;

[0045] Figure 3B It is Figure 3A a simplified model diagram of

[0046] Figure 4 It is a schematic diagram of the constraint mode of a single loop in Embodiment 1;

[0047] Figure 5 It is a schematic diagram of the constraint mode of a single loop in Embodiment 2;

[0048] Figure 6 It is a schematic diagram of the constraint mode of a single loop in Embodiment 3;

[0049] Figure 7 It is a comparison diagram of the deformation paths of Embodiments 1 - 3;

[0050] Figure 8 It is a kinematic relationship diagram of Embodiments 1 - 3;

[0051] Figure 9A It is a rigid-flexible coupling design diagram of the polyhedron variable-cell origami mechanism in Embodiment 4;

[0052] Figure 9B It is the simulation value and experimental value of the force-displacement curve of the polyhedron variable-cell origami mechanism in Embodiment 4 under axial load;

[0053] Figure 10A It is a rigid-flexible coupling design diagram of the polyhedron variable-cell origami mechanism in Embodiment 5;

[0054] Figure 10B It is the simulation value and experimental value of the force-displacement curve of the polyhedron variable-cell origami mechanism in Embodiment 5 under axial load. Specific implementation mode

[0055] In the following description, many specific details are elaborated in combination with the embodiments to facilitate a full understanding of the present invention. However, it should be understood that the following embodiments and detailed descriptions are only for illustrative purposes and do not limit the protection scope of the present invention.

[0056] Embodiment 1 (Configuration 1, CP)

[0057] This embodiment discloses a polyhedron variable-cell origami mechanism, which is a closed body composed of six identical surface units (such asFigure 2B as shown); the surface unit has an initial form and a constructed form, the initial form being a square thin sheet (such as Figure 1A shown), the square thin sheet having four vertex angles and two diagonals; creases are designed inside the square thin sheet, and at the position of vertex 1 of the polygon, a 7R spherical mechanism is locally formed.

[0058] such as Figure 1A and 1B shown, the constructed form of the surface unit includes: a square central region 2, four identical pointed corners 3 formed by folding the vertex angles along the diagonals, and four identical trapezoidal surfaces 4 formed by folding inwards along the four sides of the square central region; the folding directions of the pointed corners 3 and the trapezoidal surfaces 4 are the same; the lower base 42 of the trapezoidal surface is the side of the square central region, and the upper base 41 of the trapezoidal surface is located on the side of the square thin sheet;

[0059] such as Figure 2A and Figure 3A shown, six surface units are connected to each other in the constructed form, and the two upper bases of the trapezoidal surfaces of two adjacent surface units form a line connection A, and the tips of the three pointed corners of three adjacent surface units form a point connection B.

[0060] such as Figure 3A and Figure 3B shown, three mutually adjacent surface units are connected into a single loop; in the single loop, each surface unit provides two trapezoidal surfaces separated by 90° for connection with the other two surface units; the single loop includes three line connections and one point connection; that is, the single loop includes three surfaces and one vertex. Such as Figure 3B shown, taking the smallest loop in the polyhedron variable-cell origami mechanism for analysis, the geometric angles θ1 - θ3 of the mechanism are defined, and the kinematic relationship closed-loop equation is established according to the D-H method to obtain the mathematical model of the mechanism.

[0061] such as Figure 4 shown, in the single loop, the three line connections A are symmetrically constrained about their central axis C; the central axis C is the axis connecting the point connection and the center of the closed body; the central symmetry constraint means that the folding angles of the three line connections A are the same in real time.

[0062] On all the loops of the polyhedron variable-cell origami mechanism, the same constraints as those of the single loop are set; that is to say, there are a total of eight central axes C.

[0063] Embodiment 2 (Configuration 2, LP)

[0064] such as Figure 5 shown, the difference between this embodiment and Embodiment 1 is that: in the single loop, two line connections are provided with a fixed constraint D; this fixed constraint fixes the angle between the two trapezoidal surfaces involved in this line connection to 180°.

[0065] On all the loops of the polyhedral metamorphic origami mechanism, the same constraints as those on the single loop are set.

[0066] Embodiment 3 (Configuration 2, FP)

[0067] As Figure 6 shown, the difference between this embodiment and Embodiment 1 is that: in the single loop, a fixed constraint E is set for one wire connection; for the other two wire connections F, a plane symmetry constraint about the middle plane G thereof is set; the fixed constraint E fixes the included angle between the two trapezoidal faces involved in this wire connection to 180°; the middle plane G passes through the wire connection of the fixed constraint and the center of the closed body; the plane symmetry constraint means that the folding angles of the two wire connections F are the same in real time.

[0068] On all the loops of the polyhedral metamorphic origami mechanism, the same constraints as those on the single loop are set.

[0069] Comparison of Embodiment 1 - Embodiment 3

[0070] The deformation paths of the three configurations of Embodiment 1 - Embodiment 3 are as Figure 7 shown. It should be noted that the deformation path of each configuration is unique; the so-called "bifurcation point" means that all three deformation paths have the state of "bifurcation point".

[0071] During the deformation process of the three configurations, the variation relationships of θ1, are as Figure 8 shown.

[0072] The CP module maintains the symmetry of a cube during the movement, and θ1~θ3 and have the same variation; when θ1 increases, it is denoted as CP1, and when θ1 = 360°, the CP module reaches the minimum volume; when θ1 decreases, it is denoted as CP2, and when θ1 = 100.63°, the CP module reaches the maximum volume.

[0073] Similarly, during the movement of the LP module, only the side surface maintains the symmetry of a square, and there is When θ1 = 360°, the LP1 module has the maximum lateral distance of 129.6 mm, and when θ1 = 123.12°, the LP2 module reaches the end point of the movement.

[0074] During the movement of the FP module, only the upper and lower surfaces maintain the symmetry of a square, and θ1 = θ2, When θ1 = 262.78°, the FP1 module reaches the end point of the movement, and when θ1 = 118.39°, the FP2 module reaches the end point of the movement.

[0075] The geometric dimensions of the three configurations vary with θ1: The length, width, and height of the CP module are always equal, first increasing and then decreasing as θ1 increases; the length of the LP module first decreases and then increases as θ1 increases, and the variation patterns of the height and width are the same as those of the CP module; the height of the FP module first increases and then decreases as θ1 increases, while its length and width remain unchanged.

[0076] The three motion branches of CP, LP, and FP have a common configuration, which corresponds to the motion bifurcation point of the polyhedral origami. For a certain motion branch, at this point, the creases where θ1-θ3 are located in the polyhedral origami can be folded inward or outward, forming six motion paths: CP1, CP2, LP1, LP2, FP1, and FP2. According to the setting method of the constraints, only the case where the side plates fold inward or outward simultaneously relative to the polyhedral module is considered.

[0077] Example 4 (Rigid-flexible Coupled Configuration II, LP)

[0078] As Figure 9A shown, the difference between this example and Example 2 is that at the line connections without constraints, elastomeric connectors H are provided to obtain elastic joints.

[0079] Figure 9B are the simulation values and experimental values of the force-displacement curve under axial load in this example. As can be seen from Figure 9B it, the LP1 module in this example has a longer axial movement distance (about 58 mm), which is determined by its bifurcation path; at the same time, in the middle and front stages of the movement (when the longitudinal strain is less than 0.5), the applied uniaxial load basically remains at 2.5 N, which shows the characteristic of quasi-zero stiffness, meaning that the LP1 module in this example has a good shock absorption and buffering effect.

[0080] Example 5 (Rigid-flexible Coupled Configuration III, FP)

[0081] As Figure 10A shown, the difference between this example and Example 3 is that at the line connections without constraints, elastomeric connectors K are provided to obtain elastic joints.

[0082] Figure 10B are the simulation values and experimental values of the force-displacement curve under axial load in this example. As can be seen from Figure 9B it, the FP2 module in this example shows a shorter axial movement distance (about 19 mm), and its force-displacement curve maintains a linear increase during the movement. Compared with the LP1 module in Example 4, the FP2 module in this example requires a greater uniaxial load at the same longitudinal strain.

[0083] Although the present invention has been depicted through the embodiments above, the above embodiments are only used to exemplarily describe the feasible embodiments of the present invention, rather than to limit the protection scope of the present invention. Any equivalent substitution or change made by those skilled in the art in accordance with the present invention shall equally be covered by the protection scope defined by the claims of the present invention.

Claims

1. A polyhedron variable-cell origami mechanism, which is a closed body composed of six identical face units; characterized in that, The surface unit has an initial form and a structural form. The initial form is a square sheet, and the square sheet has four vertices and two diagonals. The structural form of the surface unit includes: a central square region, four identical pointed corners formed by folding the vertices along the diagonals, and four identical trapezoidal surfaces formed by folding inward along the four sides of the central square region; the folding directions of the pointed corners and the trapezoidal surfaces are the same; the lower base of the trapezoidal surface is the side of the central square region, and the upper base of the trapezoidal surface is located on the side of the square sheet. Six of the surface units are connected to each other in the structural form. The two upper bases of the trapezoidal surfaces of two adjacent surface units form a line connection, and the tips of the three pointed corners of three adjacent surface units form a point connection.

2. The polyhedral variable-cell origami mechanism according to claim 1, characterized in that, Three mutually adjacent surface units are connected into a single loop; in the single loop, each surface unit provides two trapezoidal surfaces separated by 90° for connection with the other two surface units; the single loop includes three line connections and one point connection.

3. The polyhedron variable cell origami mechanism according to claim 2, wherein In the single loop, the three line connections are symmetrically constrained about its central axis; the central axis is the axis connecting the point connection and the center of the closed body; the central symmetry constraint means that the folding angles of the three line connections are the same in real time.

4. The polyhedron variable-cell origami mechanism according to claim 3, characterized in that On all loops of the polyhedral metamorphic origami mechanism, the same constraints as those of the single loop are set.

5. The polyhedral variable-cell origami mechanism according to claim 2, wherein In the single loop, two of the line connections are provided with fixed constraints; the fixed constraints fix the angle between the two trapezoidal surfaces involved in the line connection to 180°.

6. The variable-cell origami mechanism of a polyhedron according to claim 5, wherein, On all loops of the polyhedral metamorphic origami mechanism, the same constraints as those of the single loop are set.

7. The polyhedral variable-cell origami mechanism according to claim 6, characterized in that, At the line connections without constraints, elastomeric connectors are provided to obtain elastic joints.

8. The polyhedron variable-cell origami mechanism according to claim 2, wherein In the single loop, one of the line connections is provided with a fixed constraint; the other two line connections are provided with a plane symmetry constraint about their mid-planes. The fixed constraint fixes the angle between the two trapezoidal surfaces involved in the line connection to 180°. The mid-plane passes through the line connection with the fixed constraint and the center of the closed body.

9. The polyhedron variable-cell origami mechanism according to claim 8, wherein, The plane symmetry constraint means that the folding angles of the two line connections are the same in real time.

10. The polyhedron variable-cell origami mechanism according to claim 9, wherein On all loops of the polyhedral metamorphic origami mechanism, the same constraints as those of the single loop are set. At the line connections without constraints, elastomeric connectors are provided to obtain elastic joints.

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