The single degree of freedom of folding into an energy-absorbing tube allows for the infinite expansion of paper-cutting structures and their expansion methods.

Abstract

This invention relates to a single-degree-of-freedom infinitely expandable paper-cutting structure that can be folded into an energy-absorbing tube, and its expansion method. It includes a type of triangular module with three connecting sides and a type of hexagonal module with four connecting sides. The base of a non-edge triangular module is connected to the base of another triangular module; the top base of a non-edge hexagonal module is connected to the top base of another hexagonal module; and the bottom base of a non-edge hexagonal module is connected to the bottom base of another hexagonal module. The lower right side of a non-edge hexagonal module is connected to the left side of a triangular module, and its lower left side is connected to the right side of another triangular module. Connecting these four hexagonal modules and two triangular modules sequentially to form a single closed loop creates a hollow quadrilateral, forming the basic unit of the paper-cutting structure. This paper-cutting structure has a revolute joint at the connecting sides, providing a single degree of freedom during folding and unfolding, and has the advantages of good operability and good repeatable folding and unfolding capabilities.

Description

Technical Field

[0001] This invention relates to a single-degree-of-freedom paper-cutting structure that can be infinitely expanded into an energy-absorbing tube, and a method for expanding it. Background Technology

[0002] In practical engineering, thin-walled tube energy-absorbing devices are widely used in vehicles such as automobiles, airplanes, and trains to absorb impact energy and reduce damage from collisions. For decades, energy-absorbing devices in vehicles have mostly used square and round tubes, but these tubes do not offer good crashworthiness. Therefore, some have proposed incorporating origami patterns into the structure to improve the energy-absorbing performance of the tubes. Among these origami patterns, the diamond-shaped pattern significantly improves the energy-absorbing performance of the tubes.

[0003] Origami-patterned energy-absorbing tubes offer good energy absorption due to the plastic hinges connecting the panels, and the simple graphic panels are easy to manufacture. However, because the overall structure's connections resemble origami creases, it is difficult to assemble the tubular structure from the basic components, thus limiting the widespread application of this type of origami-patterned energy-absorbing tube. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a single-degree-of-freedom paper-cutting structure that can be infinitely expanded by folding into an energy-absorbing tube and a method for expanding it, which is not only structurally reasonable, but also has good repeatability in folding and unfolding.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: a single-degree-of-freedom infinitely expandable paper-cutting structure folded into an energy-absorbing tube, including a type of triangular module with 3 connecting sides and a type of hexagonal module with 4 connecting sides. The two types of modules are connected by several connecting sides. The hexagonal module includes an upper base, a lower base, a lower left waist edge and a lower right waist edge adjacent to the lower base, and an upper left waist edge and an upper right waist edge adjacent to the upper base. The two base edges, the lower left waist edge, and the lower right waist edge serve as connecting sides. All three sides of the triangular module serve as connecting sides. When the connecting sides are not at the edge of the paper-cutting structure, they connect and only connect two adjacent modules. The base edge of a non-edge triangular module is connected to the base edge of another triangular module, and these two triangular modules are identical. The hexagonal module is not at the edge... The top edge of the hexagonal module is connected to the top edge of another hexagonal module. The bottom edge of the non-edge hexagonal module is connected to the bottom edge of another hexagonal module, and these two hexagonal modules are identical. The lower right side of the non-edge hexagonal module is connected to the left side of a triangle module, and its lower left side is connected to the right side of another triangle module. By connecting the four hexagonal modules and two triangle modules in sequence to form a single closed loop, a hollow quadrilateral will be generated, forming the basic unit of the paper-cutting structure. The quadrilateral is always composed of the adjacent top edges of the four hexagonal modules and is arranged continuously in the horizontal direction. When unfolded into a plane, the multiple hollow quadrilaterals are arranged in a "well" shape. All module connecting edges are provided with rotating joints for movable connection, and the connecting edges overlap in pairs.

[0006] Furthermore, the bottom edge of the triangular module and the bottom edge of the hexagonal module are on the same horizontal line. The upper left waist edge and the lower left waist edge of the hexagonal module are adjacent, and the upper right waist edge and the lower right waist edge are adjacent. The angles between the bottom edge and the two lower waist edges are the left bottom angle and the right bottom angle, respectively. The angles between the top edge and the two upper waist edges are the left top angle and the right top angle, respectively. The angle between the two left waist edges is the left waist angle, and the angle between the two right waist edges is the right waist angle.

[0007] Furthermore, the side lengths of the triangular and hexagonal modules satisfy the following conditions: ① Modules of the same type are completely identical, that is, all triangular modules are completely identical, and all hexagonal modules are completely identical; the lower left side of the hexagonal module is the same length as the right side of the triangular module, and the lower right side of the hexagonal module is the same length as the left side of the triangular module; when the overall structure is unfolded into a plane, the angle bisectors of the vertices of all triangular modules are perpendicular to the upper base connecting side of any adjacent hexagonal module; under this condition, the basic unit is centrally symmetrical, its hollowed-out quadrilateral is a rhombus, and the rhombuses in the overall structure are congruent.

[0008] Furthermore, the lengths of the sides of the triangular and hexagonal modules satisfy the following condition ②: Each type of module can have multiple types, that is, the paper-cutting structure contains multiple triangular modules and multiple hexagonal modules; all triangular modules are isosceles triangles, and the upper and lower bases of all hexagonal modules are parallel and equidistant; when connected, the left side of any triangular module is equal in length to the lower right side of the hexagonal module it is connected to, and the right side of any triangular module is equal in length to the lower left side of the hexagonal module it is connected to; when the overall structure is unfolded into a plane, the upper bases of all hexagonal modules are parallel or collinear, and along the direction perpendicular to the base, they are all the same type of triangular or hexagonal module, and the basic unit under this condition is axially symmetric about the upper base.

[0009] Furthermore, under either of the above two conditions, all modules are movably connected via revolute joints, and the connecting edges coincide in pairs. When the overall structure unfolds into a planar state, the top base edges of all hexagons with four connecting edges are parallel or collinear, and along the direction perpendicular to the bottom connecting edge, they are all triangular or hexagonal modules of the same type.

[0010] The expansion method of the single-degree-of-freedom paper-cut structure that can be infinitely expanded by folding it into an energy-absorbing tube: When unfolded into a plane, the basic unit can be expanded laterally along the direction parallel to the bottom edge, and at the same time, it can be expanded longitudinally along the direction perpendicular to the bottom connecting edge.

[0011] Furthermore, any basic element exhibits kinematic bifurcation when unfolded into a planar state, possessing four single-degree-of-freedom motion modes. These include the Miura-ori mode with motion in two directions, the mode with motion only at the bottom connecting edge, and the mode with motion at all revolute joints.

[0012] Furthermore, in the unfolded planar state, within the expanded structure, when any unit's motion mode is the Miura-ori mode, any unit extending longitudinally has the same motion mode, and any unit extending laterally has either one of the Miura-ori modes of motion in the two directions; when any unit's motion mode is a mode with only the rotational joint motion at the bottom connecting edge, any unit extending longitudinally can maintain a planar state or have the same motion mode, and any unit extending laterally has the same motion mode; when any unit's motion mode is a mode with all rotational joint motions, any unit in its structure has the same motion mode.

[0013] Furthermore, when unfolded into a planar state, the overall structure exhibits bifurcated motion, with two types of single-degree-of-freedom motion modes during the unfolding process. One type of single-degree-of-freedom motion mode follows the Miura-ori pattern, while the other unfolds into a near-cylindrical structure. Specifically, when both conditions are simultaneously satisfied—that is, when there is only one type of hexagonal module with four connecting sides and one type of isosceles triangle module with three connecting sides in condition ②, and the angles are arbitrary—the above motion laws can be satisfied. A single-degree-of-freedom unfolding into a toroidal closed tubular structure can be achieved only when the hexagon with four connecting sides and the isosceles triangle with three connecting sides satisfy a definite angular relationship.

[0014] Compared with existing technologies, this invention has the following advantages: The single-degree-of-freedom, infinitely expandable paper-cut structure of this invention, folded into an energy-absorbing tube, possesses expandability. During folding, it operates with a single degree of freedom; when unfolded, it is planar, facilitating processing and installation. Based on determined angular relationships, the folded structure is a closed-loop tubular structure, suitable for use as an energy-absorbing device in automobiles, airplanes, trains, etc. The expandability of this structure facilitates the industrial manufacturing of this type of energy-absorbing tube. The overall structure of this invention is simple, consisting of an isosceles triangle with three connecting sides and an axisymmetric hexagon with four connecting sides connected together. Units can be assembled according to user needs, providing expandability and applicability to long-scale spatial expansion.

[0015] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the planar state of the structure that satisfies condition ① according to the present invention;

[0017] Figure 2 This is a schematic diagram of the unfolded state of the structure that satisfies condition ① according to the present invention;

[0018] Figure 3 This is a schematic diagram of the planar state of the structure that satisfies condition ② according to the present invention;

[0019] Figure 4 This is a schematic diagram of the unfolded state of the structure that satisfies condition ② according to the present invention;

[0020] Figure 5 This is a schematic diagram of an isosceles triangle structure with three connecting sides when both conditions described in this invention are met simultaneously.

[0021] Figure 6 This is a schematic diagram of a hexagonal structure with 4 connecting sides that is symmetrical when both conditions described in this invention are met simultaneously.

[0022] Figure 7This is a schematic diagram of the basic unit structure when both conditions described in this invention are met simultaneously;

[0023] Figure 8 This is a schematic diagram of the mechanism in the fully expanded state of the horizontally extended 3 units of Embodiment 1 of the present invention;

[0024] Figure 9 This is a schematic diagram of a fully folded, annularly sealed tubular structure with three laterally extended units according to Embodiment 1 of the present invention.

[0025] Figure 10 This is a schematic diagram of a Miura-like structure formed by folding three units laterally in Embodiment 1 of the present invention.

[0026] Figure 11 This is a schematic diagram of the mechanism in the fully expanded state of the lateral expansion of two units according to Embodiment 2 of the present invention;

[0027] Figure 12 This is a schematic diagram of a fully folded, annularly sealed tubular structure with two laterally extended units, as shown in Embodiment 2 of the present invention.

[0028] Figure 13 This is a schematic diagram of a Miura-like structure formed by folding two units laterally in Embodiment 2 of the present invention.

[0029] In the diagram: 1 - Triangle module, 2 - Hexagonal module, AB - Connecting base of triangle connecting unit, BC - Connecting side of triangle connecting unit, AC - Connecting side of triangle connecting unit, DE - Bottom base, EF - Bottom left waist, FG - Top left waist, GH - Top base, HI - Top right waist, ID - Bottom right waist, T1 - First triangle connector, T2 - Second triangle connector, T3 - Third triangle connector, T4 - Fourth triangle connector, T5 - Fifth triangle connector, T6 - Sixth triangle connector, T7 - ​​Seventh triangle connector, T8 - Eighth triangle connector, T9 - Ninth triangle connector, T10 - Tenth triangle connector, T11 - Eleventh triangle connector T12 - Twelfth Triangular Connector, T13 - Thirteenth Triangular Connector, T14 - Fourteenth Triangular Connector, H1 - First Hexagonal Connecting Unit, H2 - Second Hexagonal Connecting Unit, H3 - Third Hexagonal Connecting Unit, H4 - Fourth Hexagonal Connecting Unit, H5 - Fifth Hexagonal Connecting Unit, H6 - Sixth Hexagonal Connecting Unit, H7 - Seventh Hexagonal Connecting Unit, H8 - Eighth Hexagonal Connecting Unit, H9 - Ninth Hexagonal Connecting Unit, H10 - Sixteenth Hexagonal Connecting Unit, H11 - Eleventh Hexagonal Connecting Unit, H12 - Twelfth Hexagonal Connecting Unit, H13 - Thirteenth Hexagonal Connecting Unit, H14 - Fourteenth Hexagonal Connecting Unit, H15 - Fifteenth Hexagonal Connecting Unit Units: H16 - Sixteenth hexagonal connection unit, R1 - First revolute joint, R2 - Second revolute joint, R3 - Third revolute joint, R4 - Fourth revolute joint, R5 - Fifth revolute joint, R6 - Sixth revolute joint, R7 - Seventh revolute joint, R8 - Eighth revolute joint, R9 - Ninth revolute joint, R10 - Tenth revolute joint, R11 - Eleventh revolute joint, R12 - Twelfth revolute joint, R13 - Thirteenth revolute joint, R14 - Fourteenth revolute joint, R15 - Fifteenth revolute joint, R16 - Sixteenth revolute joint, R17 - Seventeenth revolute joint, R18 - Eighteenth revolute joint, R19 - Nineteenth revolute joint, R20 - Twentieth revolute joint, R21 - Twenty-first revolute joint, R22 - Twenty-second revolute joint, R23 - ... 23rd revolute joint, R24th revolute joint, R25th revolute joint, R26th revolute joint, R27th revolute joint, R28th revolute joint, R29th revolute joint, R30th revolute joint, R31st revolute joint, R32nd revolute joint, R33rd revolute joint, R34th revolute joint, R35th revolute joint, R36th revolute joint, R37th revolute joint, R38th revolute joint, R39th revolute joint, R40th revolute joint, R41st revolute joint, R42nd revolute joint, h1 - hexagonal connection element of Example 2.h2 - Hexagonal connection element for Example 2, h3 - Hexagonal connection element for Example 2, h4 - Hexagonal connection element for Example 2, h5 - Hexagonal connection element for Example 2, h6 - Hexagonal connection element for Example 6, t1 - Triangular connection element for Example 2, t2 - Triangular connection element for Example 2, t3 - Triangular connection element for Example 2, t4 - Triangular connection element for Example 4, r1 - Revolute joint for Example 2, r2 - Revolute joint for Example 2, r3 - Revolute joint for Example 2, r4 - Revolute joint for Example 4, r5 - Revolute joint for Example 2, r6 - Revolute joint for Example 6, r7 - Revolute joint for Example 2, r8 - Revolute joint for Example 2, r9 - Revolute joint for Example 2, r10 - Revolute joint for Example 2, r11 - Revolute joint for Example 11. Detailed Implementation

[0030] To make the above features and advantages of the present invention more apparent and understandable, Embodiments 1 and 2 are provided below, and are described in detail with reference to the accompanying drawings. Example 1

[0031] like Figures 1-13 As shown, the single-degree-of-freedom paper-cutting structure, folded into an energy-absorbing tube, can be infinitely expanded. It includes a triangular module 1 with three connecting edges and a hexagonal module 2 with four connecting edges. Both types of modules are connected by several connecting edges. The hexagonal module includes an upper base GH, a lower base DE, a lower left waist edge EF and a lower right waist edge ID adjacent to the lower base, and an upper left waist edge FG and an upper right waist edge HI adjacent to the upper base. The two base edges, the lower left waist edge, and the lower right waist edge serve as connecting edges. All three sides of the triangular module serve as connecting edges. When these connecting edges are not at the edge of the paper-cutting structure, they connect and only connect two adjacent modules. The base edge of a non-edge triangular module is connected to the base edge of another triangular module, and these two triangular modules are identical. The upper base edge of a non-edge hexagonal module is connected to the upper base edge of another hexagonal module. The bottom edge of the hexagonal module at the edge is connected to the bottom edge of another hexagonal module, and these two hexagonal modules are identical. The lower right waist edge of the non-edge hexagonal module is connected to the left side of a triangle module, and its lower left waist edge is connected to the right side of another triangle module. A hollow quadrilateral will be generated between the four hexagonal modules and two triangle modules that are connected in sequence to form a single closed loop, forming the basic unit of the paper-cutting structure. The quadrilateral is always composed of the adjacent upper waist edges of the four hexagonal modules and is arranged continuously in the horizontal direction. When unfolded into a plane, the multiple hollow quadrilaterals are arranged in a "well" shape, that is, the triangle modules are all arranged continuously in the same horizontal direction, and the two triangle modules with three connecting edges in the basic unit are not adjacent. All module connecting edges are provided with rotating joints for movable connection, and the connecting edges overlap in pairs.

[0032] In this embodiment of the invention, the base of the triangular module and the bottom base of the hexagonal module are on the same horizontal line. The upper left waist side and the lower left waist side of the hexagonal module are adjacent, and the upper right waist side and the lower right waist side are adjacent. The angles between the bottom base side and the two lower left and right waist sides are the left bottom angle and the right bottom angle, respectively. The angles between the top base side and the two upper left and right waist sides are the left top angle and the right top angle, respectively. The angle between the two left waist sides is the left waist angle, and the angle between the two right waist sides is the right waist angle.

[0033] In this embodiment of the invention, the side lengths of the triangular module and the hexagonal module satisfy the following conditions: ① Modules of the same type are completely identical, that is, all triangular modules are completely identical, and all hexagonal modules are completely identical; the lower left side of the hexagonal module is the same length as the right side of the triangular module, and the lower right side of the hexagonal module is the same length as the left side of the triangular module; when the overall structure is unfolded into a plane, the angle bisectors of the vertices of all triangular modules are perpendicular to the upper base connecting edge of any adjacent hexagonal module; under this condition, the basic unit is centrally symmetrical, its hollowed-out quadrilateral is a rhombus, and the rhombuses in the overall structure are congruent.

[0034] In this embodiment of the invention, the lengths of the sides of the triangular and hexagonal modules satisfy the following condition ②: each type of module can have multiple types, that is, the paper-cutting structure contains multiple triangular modules and multiple hexagonal modules; all triangular modules are isosceles triangles, and the upper and lower bases of all hexagonal modules are parallel and equidistant; when connected, the left side of any triangular module is equal in length to the lower right side of the hexagonal module it is connected to, and the right side of any triangular module is equal in length to the lower left side of the hexagonal module it is connected to; when the overall structure is unfolded into a plane, the upper bases of all hexagonal modules are parallel or collinear, and along the direction perpendicular to the base, they are all the same type of triangular or hexagonal module, and the basic unit under this condition is axially symmetric about the upper base.

[0035] In this embodiment of the invention, both conditions ① and ② are satisfied simultaneously. All modules are movably connected via rotating joints, and the connecting edges overlap pairwise. When the overall structure unfolds into a planar state, the top base edges of all hexagons with four connecting edges are parallel or collinear, and along the direction perpendicular to the bottom connecting edge, they are all the same type of triangular or hexagonal module. That is... Figure 5 , Figure 6 As shown, AC=BC=EF=DI, connecting edges DE and GH are perpendicular to the axis of symmetry, and connecting edges EF and ID are symmetric about the axis of symmetry. Figure 8As shown, the AB connecting side of triangle is connected to and coincides with the AB connecting side of an adjacent identical triangle; the DE connecting side of hexagon is connected to and coincides with the DE connecting side of an adjacent identical hexagon; the GH connecting side of hexagon is connected to and coincides with the GH connecting side of an adjacent identical hexagon; the EF connecting side of hexagon is connected to and coincides with the BC connecting side of an adjacent triangle; and the ID connecting side of hexagon is connected to and coincides with the AC connecting side of an adjacent triangle.

[0036] In this embodiment of the invention, each isosceles triangle with three connecting sides is movably connected to an adjacent identical isosceles triangle with three connecting sides through a revolute joint with the same number.

[0037] In this embodiment of the invention, each of the four axisymmetric hexagons with four connecting sides is movably connected to an adjacent identical hexagon with four axisymmetric connecting sides through a revolute joint with the same number.

[0038] In this embodiment of the invention, a hexagon with four connecting sides that are symmetrical is connected to an adjacent isosceles triangle with three connecting sides by a rotating joint with the same number.

[0039] In this embodiment of the invention, under either of the two conditions described above, all modules are movably connected via rotating joints, and the connecting edges overlap in pairs. When the overall structure is unfolded into a planar state, the upper base edges of all hexagons with four connecting edges are parallel or collinear, and along the direction perpendicular to the bottom connecting edge, they are all triangular or hexagonal modules of the same type.

[0040] The single-degree-of-freedom expansion method of the paper-cutting structure, which can be infinitely expanded when folded into an energy-absorbing tube, means that when unfolded into a planar state, the basic unit can be expanded laterally along the direction parallel to the bottom edge, and at the same time, it can be expanded longitudinally along the direction perpendicular to the bottom connecting edge, depending on the user's needs.

[0041] In this embodiment of the invention, any basic unit, when unfolded into a planar state, exhibits kinematic bifurcation and has four single-degree-of-freedom motion modes. These include the Miura-ori mode with motion in two directions, the mode with motion only at the bottom connecting edge, and the mode with motion at all rotating joints.

[0042] In this embodiment of the invention, when unfolded into a planar state, in the expanded structure, when any unit's motion mode is the Miura-ori mode, any unit extending longitudinally has the same motion mode, and any unit extending laterally has the same motion mode as the Miura-ori mode in both directions; when any unit's motion mode is a mode with only the rotational joint at the bottom connecting edge moving, any unit extending longitudinally can maintain a planar state or have the same motion mode, and any unit extending laterally has the same motion mode as the Miura-ori mode; when any unit's motion mode is a mode with all rotational joints moving, any unit in the structure has the same motion mode as the Miura-ori mode.

[0043] In this embodiment of the invention, when unfolded into a planar state, the overall structure exhibits kinematic bifurcation. The unfolding process involves two types of single-degree-of-freedom motion modes: one resembling the Miura origami pattern, and the other unfolding into a near-cylindrical structure. The above motion laws can be satisfied when the angles of a hexagon with four connecting sides and an isosceles triangle with three connecting sides are arbitrary. A single-degree-of-freedom unfolding into a toroidal, closed tubular structure can be achieved only when a specific angular relationship is satisfied. Specifically, in this embodiment, when the vertex angle of the triangle ∠ACB = 90° and the vertex angle of the hexagon ∠EFG = ∠HID = 112.5°, a single-degree-of-freedom unfolding into a toroidal, closed tubular structure can be achieved. Figure 9 The diagram shows a closed-loop tubular structure. Figure 10 As shown, this structure can move in a single degree of freedom in the Miura origami pattern.

[0044] Figure 8 The diagram shows the mechanism in its fully unfolded state according to an embodiment of the present invention. The first hexagonal connecting unit H1 with four connecting sides, the first triangular connecting member T1 with three connecting sides, and the fifth hexagonal connecting unit H5 with four connecting sides are movably connected through the first revolute joint R1 and the seventh revolute joint R7, respectively.

[0045] The second hexagonal connecting unit H2 with 4 connecting sides is movably connected to the first triangular connecting member T1 with 3 connecting sides, the second triangular connecting member T2 with 3 connecting sides, and the sixth hexagonal connecting unit H6 with 4 connecting sides through the second revolute joint R2, the third revolute joint R3, and the eighth revolute joint R8, respectively.

[0046] The third hexagonal connecting unit H3 with 4 connecting sides is movably connected to the second triangular connecting member T2 with 3 connecting sides, the third triangular connecting member T3 with 3 connecting sides, and the seventh hexagonal connecting unit H7 with 4 connecting sides through the fourth revolute joint R4, the fifth revolute joint R5, and the ninth revolute joint R9, respectively.

[0047] The fourth hexagonal connecting unit H4 with 4 connecting sides is movably connected to the third triangular connecting member T3 with 3 connecting sides and the eighth hexagonal connecting unit H8 with 4 connecting sides through the sixth revolute joint R6 and the tenth revolute joint R10, respectively.

[0048] The fifth hexagonal connecting unit H5 with 4 connecting sides is movably connected to the first hexagonal connecting unit H1 with 4 connecting sides, the fourth triangular connecting member T4 with 3 connecting sides, and the ninth hexagonal connecting unit H9 with 4 connecting sides through the seventh revolute joint R7, the eleventh revolute joint R11, and the eighteenth revolute joint R18, respectively.

[0049] The sixth hexagonal connecting unit H6 with 4 connecting sides is movably connected to the fourth triangular connecting member T4 with 3 connecting sides, the second hexagonal connecting unit H2 with 4 connecting sides, the fifth triangular connecting member T5 with 3 connecting sides, and the sixteenth hexagonal connecting unit H10 with 4 connecting sides through the twelfth revolute joint R12, the eighth revolute joint R8, the thirteenth revolute joint R13, and the twentieth revolute joint R20, respectively.

[0050] The seventh hexagonal connecting unit H7 with 4 connecting sides is movably connected to the fifth triangular connecting member T5 with 3 connecting sides, the third hexagonal connecting unit H3 with 4 connecting sides, the sixth triangular connecting member T6 with 3 connecting sides, and the eleventh hexagonal connecting unit H11 with 4 connecting sides through the fourteenth revolute joint R14, the ninth revolute joint R9, the fifteenth revolute joint R15, and the twenty-second revolute joint R22, respectively.

[0051] The eighth hexagonal connecting unit H8 with 4 connecting sides is movably connected to the sixth triangular connecting member T6 with 3 connecting sides, the fourth hexagonal connecting unit H4 with 4 connecting sides, the seventh triangular connecting member T7 with 3 connecting sides, and the twelfth hexagonal connecting unit H12 with 4 connecting sides through the sixteenth revolute joint R16, the tenth revolute joint R10, the seventeenth revolute joint R17, and the twenty-fourth revolute joint R24, respectively.

[0052] The ninth hexagonal connecting unit H9 with 4 connecting sides is movably connected to the fifth hexagonal connecting unit H5 with 4 connecting sides, the eighth triangular connecting unit T8 with 3 connecting sides, and the thirteenth hexagonal connecting unit H13 with 4 connecting sides through the eighteenth revolute joint R18, the twenty-sixth revolute joint R26, and the thirty-third revolute joint R33, respectively.

[0053] The sixteenth hexagonal connecting unit H10 with 4 connecting sides is movably connected to the eighth triangular connecting member T8 with 3 connecting sides, the sixth hexagonal connecting unit H6 with 4 connecting sides, the ninth triangular connecting member T9 with 3 connecting sides, and the fourteenth hexagonal connecting unit H14 with 4 connecting sides through the twenty-seventh revolute joint R27, the twentieth revolute joint R20, the twenty-eighth revolute joint R28, and the thirty-fourth revolute joint R34, respectively.

[0054] The eleventh hexagonal connecting unit H11 with 4 connecting sides is movably connected to the ninth triangular connecting member T9 with 3 connecting sides, the seventh hexagonal connecting unit H7 with 4 connecting sides, the tenth triangular connecting member T10 with 3 connecting sides, and the fifteenth hexagonal connecting unit H15 with 4 connecting sides through the twenty-ninth revolute joint R29, the twenty-second revolute joint R22, the thirtieth revolute joint R30, and the thirty-fifth revolute joint R35, respectively.

[0055] The twelfth hexagonal connecting unit H12 with 4 connecting sides is movably connected to the tenth triangular connecting member T10 with 3 connecting sides, the eighth hexagonal connecting unit H8 with 4 connecting sides, the eleventh triangular connecting member T11 with 3 connecting sides, and the sixteenth hexagonal connecting unit H16 with 4 connecting sides through the thirty-first revolute joint R31, the twenty-fourth revolute joint R24, the thirty-second revolute joint R32, and the thirty-sixth revolute joint R36, respectively.

[0056] The thirteenth hexagonal connecting unit H13 with 4 connecting sides is movably connected to the ninth hexagonal connecting unit H9 with 4 connecting sides and the twelfth triangular connecting member T12 with 3 connecting sides through the thirty-third revolute joint R33 and the thirty-seventh revolute joint R37, respectively.

[0057] The fourteenth hexagonal connecting unit H14 with 4 connecting sides is movably connected to the twelfth triangular connecting member T12 with 3 connecting sides, the sixteenth triangular connecting unit H10 with 4 connecting sides, and the thirteenth triangular connecting member T13 with 3 connecting sides through the thirty-eighth revolute joint R38, the thirty-fourth revolute joint R34, and the thirty-ninth revolute joint R39, respectively.

[0058] The fifteenth hexagonal connecting unit H15 with 4 connecting sides is movably connected to the thirteenth triangular connecting member T13 with 3 connecting sides, the eleventh hexagonal connecting unit H11 with 4 connecting sides, and the fourteenth triangular connecting member T14 with 3 connecting sides through the fortieth revolute joint R40, the thirty-fifth revolute joint R35, and the forty-first revolute joint R41, respectively.

[0059] The sixteenth hexagonal connecting unit H16 with 4 connecting sides is movably connected to the fourteenth triangular connecting member T14 with 3 connecting sides and the twelfth hexagonal connecting unit H12 with 4 connecting sides through the forty-second revolute joint R42 and the thirty-sixth revolute joint R36, respectively.

[0060] The first triangular connector T1 with three connecting sides is movably connected to the first hexagonal connector H1 with four connecting sides and the second hexagonal connector H2 with four connecting sides through the first revolute joint R1 and the second revolute joint R2, respectively.

[0061] The second triangular connector T2 with three connecting sides is movably connected to the second hexagonal connector H2 with four connecting sides and the third hexagonal connector H3 with four connecting sides through the third revolute joint R3 and the fourth revolute joint R4, respectively.

[0062] The third triangular connector T3 with three connecting sides is movably connected to the third hexagonal connector H3 with four connecting sides and the fourth hexagonal connector H4 with four connecting sides through the fifth revolute joint R5 and the sixth revolute joint R6, respectively.

[0063] The fourth triangular connector T4 with three connecting sides is movably connected to the fifth hexagonal connector H5 with four connecting sides, the sixth hexagonal connector H6 with four connecting sides, and the eighth triangular connector T8 with three connecting sides through the eleventh revolute joint R11, the twelfth revolute joint R12, and the nineteenth revolute joint R19, respectively.

[0064] The fifth triangular connector T5 with three connecting sides is movably connected to the sixth hexagonal connector H6 with four connecting sides, the seventh hexagonal connector H7 with four connecting sides, and the ninth triangular connector T9 with three connecting sides through the thirteenth revolute joint R13, the fourteenth revolute joint R14, and the twenty-first revolute joint R21, respectively.

[0065] The sixth triangular connector T6 with three connecting sides is movably connected to the seventh hexagonal connector H7 with four connecting sides, the eighth hexagonal connector H8 with four connecting sides, and the tenth triangular connector T10 with three connecting sides through the fifteenth revolute joint R15, the sixteenth revolute joint R16, and the twenty-third revolute joint R23, respectively.

[0066] The seventh triangular connector T7 with three connecting sides is movably connected to the eighth hexagonal connector H8 with four connecting sides and the eleventh triangular connector T11 with three connecting sides through the seventeenth revolute joint R17 and the twenty-fifth revolute joint R25, respectively.

[0067] The eighth triangular connector T8 with three connecting sides is movably connected to the ninth hexagonal connector H9 with four connecting sides, the fourth triangular connector T4 with three connecting sides, and the sixteenth triangular connector H10 with four connecting sides through the twenty-sixth revolute joint R26, the nineteenth revolute joint R19, and the twenty-seventh revolute joint R27, respectively.

[0068] The ninth triangular connector T9 with three connecting sides is movably connected to the sixteenth polygonal connector H10 with four connecting sides, the fifth triangular connector T5 with three connecting sides, and the eleventh hexagonal connector H11 with four connecting sides through the twenty-eighth revolute joint R28, the twenty-first revolute joint R21, and the twenty-ninth revolute joint R29, respectively.

[0069] The tenth triangular connector T10 with three connecting sides is movably connected to the eleventh hexagonal connector H11 with four connecting sides, the sixth triangular connector T6 with three connecting sides, and the twelfth hexagonal connector H12 with four connecting sides through the thirtieth revolute joint R30, the twenty-third revolute joint R23, and the thirty-first revolute joint R31, respectively.

[0070] The eleventh triangular connector T11 with three connecting sides is movably connected to the twelfth hexagonal connector H12 with four connecting sides and the seventh triangular connector T7 with three connecting sides through the thirty-second revolute joint R32 and the twenty-fifth revolute joint R25, respectively.

[0071] The twelfth triangular connector T12 with three connecting sides is movably connected to the thirteenth hexagonal connector H13 with four connecting sides and the fourteenth hexagonal connector H14 with four connecting sides through the thirty-seventh revolute joint R37 and the thirty-eighth revolute joint R38, respectively.

[0072] The thirteenth triangular connector T13 with three connecting sides is movably connected to the fourteenth hexagonal connector H14 with four connecting sides and the fifteenth hexagonal connector H15 with four connecting sides through the thirty-ninth revolute joint R39 and the fortieth revolute joint R40, respectively.

[0073] The fourteenth triangular connector T14 with three connecting sides is movably connected to the fifteenth hexagonal connector H15 with four connecting sides and the sixteenth hexagonal connector H16 with four connecting sides through the forty-first revolute joint R41 and the forty-second revolute joint R42, respectively.

[0074] Figure 9 A schematic diagram of the structure in a fully folded state according to an embodiment of the present invention is shown. The fifth triangular connecting unit T5 is fixed, and the entire mechanism converges inwards towards the paper surface, ultimately achieving a fully folded state.

[0075] During this unfolding process, the void formed by the first hexagonal connecting unit H1, the second hexagonal connecting unit H2, the fifth hexagonal connecting unit H5, and the sixth hexagonal connecting unit H6 gradually shrinks until it disappears.

[0076] The void formed by the second hexagonal connecting unit H2, the third hexagonal connecting unit H3, the sixth hexagonal connecting unit H6, and the seventh hexagonal connecting unit H7 gradually becomes smaller until it disappears.

[0077] The void formed by the third hexagonal connecting unit H3, the fourth hexagonal connecting unit H4, the seventh hexagonal connecting unit H7, and the eighth hexagonal connecting unit H8 gradually becomes smaller until it disappears.

[0078] The void formed by the ninth hexagonal connecting unit H9, the sixteenth hexagonal connecting unit H10, the thirteenth hexagonal connecting unit H13, and the fourteenth hexagonal connecting unit H14 gradually becomes smaller until it disappears.

[0079] The void formed by the sixteenth hexagonal connecting unit H10, the eleventh hexagonal connecting unit H11, the fourteenth hexagonal connecting unit H14, and the fifteenth hexagonal connecting unit H15 gradually becomes smaller until it disappears.

[0080] The void formed by the eleventh hexagonal connecting unit H11, the twelfth hexagonal connecting unit H12, the fifteenth hexagonal connecting unit H15, and the sixteenth hexagonal connecting unit H16 gradually becomes smaller until it disappears.

[0081] Example 2:

[0082] A single-degree-of-freedom, infinitely expandable paper-cutting structure that folds into an energy-absorbing tube includes a triangular module with three connecting edges and a hexagonal module with four connecting edges. The two types of modules are joined together by several connecting edges. The hexagonal module includes an upper base, a lower base, a lower left waist edge and a lower right waist edge adjacent to the lower base, and an upper left waist edge and an upper right waist edge adjacent to the upper base. The two base edges, the lower left waist edge, and the lower right waist edge serve as connecting edges. All three sides of the triangular module serve as connecting edges. When the connecting edges are not at the edge of the paper-cutting structure, they connect and only connect two adjacent modules. The base edge of a non-edge triangular module is connected to the base edge of another identical triangular module. The top base of a non-edge hexagonal module is connected to the top base of another hexagonal module, and the bottom base of a non-edge hexagonal module is connected to the bottom base of another hexagonal module. These two hexagonal modules are identical. The lower right side of a non-edge hexagonal module is connected to the left side of a triangle module, and its lower left side is connected to the right side of another triangle module. By connecting these four hexagonal modules and two triangle modules in sequence to form a single closed loop, a hollow quadrilateral will be generated, forming the basic unit of the paper-cutting structure. The two triangle modules with three connecting sides in the basic unit are not adjacent. All modules are connected by rotating joints for movable connection, and the connecting sides overlap in pairs.

[0083] In this embodiment of the invention, the base of the triangular module and the bottom base of the hexagonal module are on the same horizontal line. The upper left waist side and the lower left waist side of the hexagonal module are adjacent, and the upper right waist side and the lower right waist side are adjacent. The angles between the bottom base side and the two lower left and right waist sides are the left bottom angle and the right bottom angle, respectively. The angles between the top base side and the two upper left and right waist sides are the left top angle and the right top angle, respectively. The angle between the two left waist sides is the left waist angle, and the angle between the two right waist sides is the right waist angle.

[0084] In this embodiment of the invention, the side lengths of the triangular module and the hexagonal module satisfy the following conditions: ① Modules of the same type are completely identical, that is, all triangular modules are completely identical, and all hexagonal modules are completely identical; the lower left side of the hexagonal module is the same length as the right side of the triangular module, and the lower right side of the hexagonal module is the same length as the left side of the triangular module; when the overall structure is unfolded into a plane, the angle bisectors of the vertices of all triangular modules are perpendicular to the upper base connecting edge of any adjacent hexagonal module; under this condition, the basic unit is centrally symmetrical, its hollowed-out quadrilateral is a rhombus, and the rhombuses in the overall structure are congruent.

[0085] In this embodiment of the invention, the lengths of the sides of the triangular and hexagonal modules satisfy the following condition ②: each type of module can have multiple types, that is, the paper-cutting structure contains multiple triangular modules and multiple hexagonal modules; all triangular modules are isosceles triangles, and the upper and lower bases of all hexagonal modules are parallel and equidistant; when connected, the left side of any triangular module is equal in length to the lower right side of the hexagonal module it is connected to, and the right side of any triangular module is equal in length to the lower left side of the hexagonal module it is connected to; when the overall structure is unfolded into a plane, the upper bases of all hexagonal modules are parallel or collinear, and along the direction perpendicular to the base, they are all the same type of triangular or hexagonal module, and the basic unit under this condition is axially symmetric about the upper base.

[0086] In this embodiment of the invention, each isosceles triangle with three connecting sides is movably connected to an adjacent identical isosceles triangle with three connecting sides through a revolute joint with the same number.

[0087] In this embodiment of the invention, each of the four axisymmetric hexagons with four connecting sides is movably connected to an adjacent identical hexagon with four axisymmetric connecting sides through a revolute joint with the same number.

[0088] In this embodiment of the invention, a hexagon with four connecting sides that are symmetrical is connected to an adjacent isosceles triangle with three connecting sides by a rotating joint with the same number.

[0089] In this embodiment of the invention, under any of the above conditions, all modules are movably connected via rotating joints, and the connecting edges coincide in pairs. When the overall structure is unfolded into a planar state, the upper base edges of all hexagons with four connecting edges are parallel or collinear, and along the direction perpendicular to the bottom connecting edge, they are the same type of triangular or hexagonal module.

[0090] In this embodiment of the invention, any basic unit, when unfolded into a planar state, exhibits kinematic bifurcation and has four single-degree-of-freedom motion modes. These include the Miura-ori mode with motion in two directions, the mode with motion only at the bottom connecting edge, and the mode with motion at all rotating joints.

[0091] The single-degree-of-freedom expansion method of the paper-cutting structure, which can be infinitely expanded when folded into an energy-absorbing tube, means that when unfolded into a planar state, the basic unit can be expanded laterally along the direction parallel to the bottom edge, and at the same time, it can be expanded longitudinally along the direction perpendicular to the bottom connecting edge, depending on the user's needs.

[0092] In this embodiment of the invention, when unfolded into a planar state, in the expanded structure, when any unit's motion mode is the Miura-ori mode, any unit extending longitudinally has the same motion mode, and any unit extending laterally has the same motion mode as the Miura-ori mode in both directions; when any unit's motion mode is a mode with only the rotational joint at the bottom connecting edge moving, any unit extending longitudinally can maintain a planar state or have the same motion mode, and any unit extending laterally has the same motion mode as the Miura-ori mode; when any unit's motion mode is a mode with all rotational joints moving, any unit in the structure has the same motion mode as the Miura-ori mode.

[0093] In this embodiment of the invention, when unfolded into a planar state, the overall structure exhibits kinematic bifurcation. The unfolding process involves two types of single-degree-of-freedom motion modes: one resembling the Miura origami pattern, and the other unfolding into a near-cylindrical structure. When the angles of a hexagon with four connecting sides and an isosceles triangle with three connecting sides are arbitrary, the above motion laws can be satisfied. A single-degree-of-freedom unfolding into a toroidal, closed tubular structure can be achieved only when a specific angular relationship is satisfied. Specifically, in this embodiment, when the vertex angle of the triangle ∠ACB = 60° and the vertex angle of the hexagon ∠EFG = ∠HID = 120°, single-degree-of-freedom unfolding can be achieved, resulting in a toroidal, closed tubular structure. Figure 12 The diagram shows a closed-loop tubular structure. Figure 13 As shown, this structure can move in a single degree of freedom in the Miura origami pattern.

[0094] Figure 11 The diagram shows the mechanism in its fully unfolded state according to an embodiment of the present invention. The first hexagonal connecting unit h1 with four connecting sides, the first triangular connecting member t1 with three connecting sides, and the fourth hexagonal connecting unit h4 with four connecting sides are movably connected through the first rotating joint r1 and the fifth rotating joint r5, respectively.

[0095] The second example 2 hexagonal connecting unit h2 with 4 connecting sides is movably connected to the first example 2 triangular connecting member t1 with 3 connecting sides, the second example 2 triangular connecting member t2 with 3 connecting sides, and the fifth example 2 hexagonal connecting unit h5 with 4 connecting sides through the second example 2 revolute joint r2, the third example 2 revolute joint r3, and the sixth example 2 revolute joint r6, respectively.

[0096] The third example 2 hexagonal connecting unit h3 with 4 connecting sides is movably connected to the second example 2 triangular connecting member t2 with 3 connecting sides and the sixth example 2 hexagonal connecting unit h6 with 4 connecting sides through the fourth example 2 revolute joint r4 and the seventh example 2 revolute joint r7, respectively.

[0097] The fourth example 2 hexagonal connecting unit h4 with 4 connecting sides, the first example 2 hexagonal connecting unit h1 with 4 connecting sides, and the third example 2 triangular connecting member t3 with 3 connecting sides are movably connected through the fifth example 2 revolute joint r5 and the eighth example 2 revolute joint r8, respectively.

[0098] The fifth example 2 hexagonal connecting unit h5 with 4 connecting sides is movably connected to the third example 2 triangular connecting member t3 with 3 connecting sides, the fourth example 2 triangular connecting member t4 with 3 connecting sides, and the second example 2 hexagonal connecting unit h2 with 4 connecting sides through the ninth example 2 revolute joint r9, the tenth example 2 revolute joint r10, and the sixth example 2 revolute joint r6, respectively.

[0099] The sixth example 2 hexagonal connecting unit h6 with 4 connecting sides is movably connected to the fourth example 2 triangular connecting member t4 with 3 connecting sides and the third example 2 hexagonal connecting unit h3 with 4 connecting sides through the eleventh example 2 revolute joint r11 and the seventh example 2 revolute joint r7, respectively.

[0100] The first example 2 triangular connector t1 with 3 connecting sides is movably connected to the first example 2 hexagonal connector h1 with 4 connecting sides and the second example 2 hexagonal connector h2 with 4 connecting sides through the first example 2 revolute joint r1 and the second example 2 revolute joint r2, respectively.

[0101] The second example 2 triangular connector t2 with 3 connecting sides is movably connected to the second example 2 hexagonal connector h2 with 4 connecting sides and the third example 2 hexagonal connector h3 with 4 connecting sides through the third example 2 revolute joint r3 and the fourth example 2 revolute joint r4, respectively.

[0102] The triangular connector t3 of Example 2 with 3 connecting sides is movably connected to the hexagonal connector h4 of Example 2 with 4 connecting sides and the hexagonal connector h5 of Example 2 with 4 connecting sides through the revolute joint r8 of Example 2 and the revolute joint r9 of Example 2, respectively.

[0103] The fourth example 2 triangular connector t4 with 3 connecting sides is movably connected to the fifth example 2 hexagonal connector h5 with 4 connecting sides and the sixth example 2 hexagonal connector h6 with 4 connecting sides through the tenth example 2 revolute joint r10 and the eleventh example 2 revolute joint r11, respectively.

[0104] During this unfolding process, the voids formed by the first example of two hexagonal connecting units h1, the second example of two hexagonal connecting units h2, the fourth example of two hexagonal connecting units h4, and the fifth example of two hexagonal connecting units h5 gradually become smaller until they disappear.

[0105] The holes enclosed by the second hexagonal connecting unit h2, the third hexagonal connecting unit h3, the fifth hexagonal connecting unit h5, and the sixth hexagonal connecting unit h6 gradually become smaller until they disappear.

[0106] The hexagon with four connecting sides and axis symmetry, and the isosceles triangle with three connecting sides in this invention, can have their shape, size, dimensions, and materials varied according to the requirements of the actual application. The materials can be foldable materials such as cardboard or rigid materials such as metal.

[0107] This invention features a simple structure and can connect multiple triangular and hexagonal units according to user needs, offering unlimited expandability. Furthermore, the entire mechanism operates with a single degree of freedom during folding and unfolding, transforming a flat cardboard into a closed, toroidal tubular structure based on defined angular relationships. It boasts advantages such as good operability, excellent unfolding capability, and the ability to be repeatedly folded.

[0108] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive various other forms of single-degree-of-freedom infinitely expandable paper-cutting structures and their expansion methods for forming energy-absorbing tubes. All equivalent variations and modifications made within the scope of the claims of this invention should be considered within the scope of this invention.

Claims

1. A single-degree-of-freedom paper-cutting structure that can be infinitely expanded into an energy-absorbing tube, characterized by: This includes two types of modules: a triangular module with three connecting edges and a hexagonal module with four connecting edges. Several of each type are arranged and connected by these connecting edges. The hexagonal module includes a top base, a bottom base, a lower left waist edge and a lower right waist edge adjacent to the bottom base, and an upper left waist edge and an upper right waist edge adjacent to the top base. The two bottom edges, the lower left waist edge, and the lower right waist edge serve as connecting edges. All three sides of the triangular module serve as connecting edges. When these connecting edges are not at the edge of the paper-cut structure, they connect and only connect two adjacent modules. The base edge of a non-edge triangular module is connected to the base edge of another identical triangular module. The top edge of a non-edge hexagonal module... The bottom edge of the hexagonal module is connected to the top bottom edge of another hexagonal module. The bottom bottom edge of the non-edge hexagonal module is connected to the bottom bottom edge of another hexagonal module, and these two hexagonal modules are identical. The lower right side of the non-edge hexagonal module is connected to the left side of a triangle module, and its lower left side is connected to the right side of another triangle module. By connecting the four hexagonal modules and two triangle modules in sequence to form a single closed loop, a hollow quadrilateral will be generated, forming the basic unit of the paper-cutting structure. When unfolded into a plane, the multiple hollow quadrilaterals are arranged in a "well" shape. All module connecting edges are equipped with rotating joints for movable connection, and the connecting edges overlap in pairs.

2. The single-degree-of-freedom, infinitely expandable paper-cutting structure folded into an energy-absorbing tube according to claim 1, characterized in that: The upper left waist edge of the hexagonal module is adjacent to the lower left waist edge, and the upper right waist edge is adjacent to the lower right waist edge. The angles between the lower bottom edge and the two lower waist edges are the left bottom angle and the right bottom angle, respectively. The angles between the upper bottom edge and the two upper waist edges are the left top angle and the right top angle, respectively. The angle between the two left waist edges is the left waist angle, and the angle between the two right waist edges is the right waist angle.

3. The single-degree-of-freedom, infinitely expandable paper-cutting structure folded into an energy-absorbing tube according to claim 1, characterized in that: The side lengths of the triangular and hexagonal modules satisfy the following conditions: when modules of the same type are completely identical, that is, all triangular modules are completely identical and all hexagonal modules are completely identical; the lower left side of the hexagonal module is the same length as the right side of the triangular module, and the lower right side of the hexagonal module is the same length as the left side of the triangular module; when the overall structure is unfolded into a plane, the angle bisectors of the vertices of all triangular modules are perpendicular to the upper base of any adjacent hexagonal module; under this condition, the basic unit is centrally symmetrical, its hollowed-out quadrilateral is a rhombus, and the rhombuses in the overall structure are congruent.

4. The single-degree-of-freedom, infinitely expandable paper-cutting structure folded into an energy-absorbing tube according to claim 1, characterized in that: The lengths of the sides of the triangular and hexagonal modules satisfy the following conditions: when each type of module has multiple types, i.e., the paper-cutting structure contains multiple triangular modules and multiple hexagonal modules; all triangular modules are isosceles triangles, and the top and bottom sides of all hexagonal modules are parallel and equidistant; when connected, the left side of any triangular module is equal in length to the lower right side of the hexagonal module it is connected to, and the right side of any triangular module is equal in length to the lower left side of the hexagonal module it is connected to; when the overall structure is unfolded into a plane, the top sides of all hexagonal modules are parallel or collinear, and along the direction perpendicular to the bottom side, they are all the same type of triangular or hexagonal module, and the basic unit under this condition is axially symmetric about the top side.

5. A method for extending a single-degree-of-freedom infinitely expandable paper-cutting structure folded into an energy-absorbing tube as described in any of claims 1-4, characterized in that: When unfolded into a planar state, the basic unit can be extended laterally along the direction parallel to the bottom edge, and at the same time, it can be extended longitudinally along the direction perpendicular to the bottom connecting edge.

6. The method for extending a single-degree-of-freedom, infinitely expandable paper-cutting structure folded into an energy-absorbing tube according to claim 5, characterized in that: Any basic unit, when unfolded into a planar state, exhibits kinematic bifurcations and has four single-degree-of-freedom motion modes; these include the Miura-ori mode with motion in two directions, the mode with only the rotational joint motion at the bottom connecting edge, and the mode with all rotational joint motions.

7. The method for extending a single-degree-of-freedom, infinitely expandable paper-cut structure folded into an energy-absorbing tube according to claim 6, characterized in that: In the unfolded planar state, within the expanded structure, when any unit's motion mode is the Miura-ori mode, any unit extending longitudinally has the same motion mode, and any unit extending laterally has either one of the Miura-ori modes of motion in the two directions; when any unit's motion mode is a mode with only the rotational joints at the bottom connecting edge, any unit extending longitudinally can maintain a planar state or have the same motion mode, and any unit extending laterally has the same motion mode; when any unit's motion mode is a mode with all rotational joints moving, any unit in the structure has the same motion mode.

8. The method for extending a single-degree-of-freedom, infinitely expandable paper-cutting structure folded into an energy-absorbing tube according to claim 7, characterized in that: When unfolded into a planar state, the folding and unfolding process has two types of single-degree-of-freedom motion modes; One type of single-degree-of-freedom motion mode exhibits the Miura-ori pattern, while the other type unfolds into a cylindrical structure.

Images