Optimization Method for Curved Folding and Unfolding Structures Based on Miura Origami and Flexible Hinges

Abstract

The present invention discloses an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges, belonging to the field of folding and unfolding structures. The present invention combines origami technology with flexible hinges to construct a curved folding structure, specifically including: obtaining a curved folding and unfolding origami pattern by combining an ideal surface with a Miura origami pattern, obtaining a curved folding and unfolding structure by combining the curved folding and unfolding origami pattern with soft hinges, and optimizing the obtained curved folding and unfolding structure. In the curved folding and unfolding structure, the crease rods and diagonal braces are connected by flexible hinges to avoid the stress concentration problem at the intersection of traditional origami creases. The curved folding and unfolding structure is pre-assembled on the ground and compressed. When launching is required, it is placed in the rocket launch cabin in a smaller volume, and then self-unfolds after successfully entering the orbit, so as to solve the problem of inconvenient launching of large-scale structures. And because the optimized curved folding and unfolding structure has been pre-assembled, there is no need for on-orbit assembly, and it can actively adapt to the harsh working environment after the rocket enters the orbit.

Description

Technical Field

[0001] The present invention relates to an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges, belonging to the field of folding and unfolding structures. Background Art

[0002] Folding and unfolding structures can be seen everywhere in our daily life and are used to solve the problem of inconvenient storage of large items in daily life. Narrowly defined, a folding and unfolding structure refers to a structure that can be unfolded when in use and folded up when not in use, while broadly defined, a folding and unfolding structure also involves changes in structural functions. Folding and unfolding structures include two categories. One is to achieve folding through ingenious structural design, such as folding mobile phones; the other is to utilize the soft characteristics of materials, such as solar sails and folding tents. The emergence of folding and unfolding structures makes items more portable, effectively reducing the storage and transportation costs of large structures and having broad development prospects.

[0003] Origami is an art activity of folding a two-dimensional plane paper into a three-dimensional state. Origami technology has been widely applied in fields such as aerospace, architecture, and robotics. Traditional origami styles include Yoshimura origami and Miura origami. These origami structures all have the characteristic of folding a large piece of paper into a smaller structure, thus providing rich inspiration for the design of folding structures. However, there are still the following problems in the application of origami structures in the engineering field: First, different from origami art, the origami structures in the engineering field cannot be soft paper anymore, and the stiffness of the material and the overall structure needs to be considered; second, for origami structures with a high degree of folding, the thickness of the paper must be considered, otherwise it is very easy to have problems where the origami structure cannot be folded or unfolded smoothly; finally, origami structures are prone to fatigue damage problems at the crease positions and vertex positions after multiple cycles of folding and unfolding. Summary of the Invention

[0004] To solve the problems in the application of origami styles in the construction of folding and unfolding structures, the purpose of the present invention is to provide an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges. By combining origami technology with flexible hinges, a curved folding structure is constructed to achieve the functions of folding and unfolding, facilitating the storage and transportation of the curved folding and unfolding structure obtained by the optimization method of the curved surface structure based on the origami principle and soft hinges, and the curved folding and unfolding structure obtained by the optimization method of the curved surface structure based on the origami principle and soft hinges is simple and easy to expand.

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

[0006] An optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges of the present invention includes the following steps:

[0007] Step 1: Obtain a curved folding and unfolding origami style by combining an ideal curved surface with the Miura origami style, specifically including the following sub-steps:

[0008] Step 1.1 Determine the directrix of the cylinder, select the control point a on the directrix and the discrete point c outside the directrix; connect these control points and discrete points in sequence to form a broken line segment;

[0009] Step 1.2 Determine the width t of the paper tape, and determine the positions of the remaining points b and d on the paper tape according to the width t of the paper tape;

[0010] Step 1.3 Determine the stretching height H, and stretch the points b and d on the paper tape to a predetermined height to obtain a half Miura structure;

[0011] Step 1.4 For the half Miura structure generated in Step 1.3, mirror it along the horizontal plane to obtain the entire Miura structure;

[0012] Step 1.5 Determine the number of arrays i, and array the Miura structure generated in Step 1.4 along the height direction to obtain a curved surface folding and unfolding origami pattern based on Miura origami;

[0013] Step Two: Construct a curved surface folding and unfolding structure by combining the curved surface folding and unfolding origami pattern with soft hinges, specifically including the following sub-steps:

[0014] Step 2.1 Determine the coordinates of each vertex in the curved surface folding and unfolding origami pattern based on Miura origami obtained in Step One, and the direction vectors formed by adjacent points and opposite points;

[0015] Step 2.2 Determine the spatial positions of the crease rod joints and strut rod joints in each flexible hinge according to the direction vectors obtained in Step 2.1, and determine the cross-sectional dimensions and lengths of the crease rod joints and strut rod joints;

[0016] Step 2.3 Determine the dimensions of the crease rod joint sleeves connected to the crease rod joints and the strut rod joint sleeves connected to the strut rod joints, including: the length of the crease rod joint sleeve, the outer diameter of the crease rod joint sleeve, the inner diameter of the crease rod joint sleeve, the depth of the crease rod joint sleeve, the length of the strut rod joint sleeve, the outer diameter of the strut rod joint sleeve, the inner diameter of the strut rod joint sleeve, the depth of the strut rod joint sleeve;

[0017] Step 2.4 Determine the length and cross-sectional dimensions of the crease rod;

[0018] Step 2.5 Determine the length and cross-sectional dimensions of the strut rod;

[0019] Step 2.6 Assemble the flexible hinge, the crease rod and the strut rod according to the origami pattern to obtain a curved surface folding and unfolding structure based on Miura origami and soft hinges, that is, realize the optimization of the curved surface folding and unfolding structure based on Miura origami and soft hinges.

[0020] It also includes Step 3: According to the curved surface folding and unfolding structure optimized in Step 2, it is pre-fabricated and assembled on the ground and then compressed and stored. When it needs to be launched, it is placed in the rocket launch compartment in a smaller volume and then unfolds itself after successfully entering the orbit, solving the problem of inconvenient launch of large-scale structures. Moreover, the optimized curved surface folding and unfolding structure has been pre-assembled and does not require on-orbit assembly, and can actively adapt to the harsh working environment after the rocket enters the orbit.

[0021] Beneficial effects:

[0022] 1. A method for optimizing a curved surface folding and unfolding structure based on Miura origami and soft hinges according to the present invention can specify the style and height of the directrix of the required curved surface, so as to flexibly create the required curved surface folding and unfolding structure.

[0023] 2. A method for optimizing a curved surface folding and unfolding structure based on Miura origami and soft hinges according to the present invention, through the combination of rigid crease bars, diagonal braces and flexible soft hinges, with the basic component unit being the Miura origami unit, can realize the motion mode of Miura origami. The curved surface folding and unfolding structure obtained by the method for optimizing the curved surface folding and unfolding structure based on the origami principle and soft hinges can be smoothly folded and unfolded in the height direction.

[0024] 3. A method for optimizing a curved surface folding and unfolding structure based on Miura origami and soft hinges according to the present invention. The obtained curved surface folding and unfolding structure has higher stiffness and strength compared with the traditional paper origami structure, and can stably maintain the current configuration after the folding and unfolding structure is unfolded.

[0025] 4. A method for optimizing a curved surface folding and unfolding structure based on Miura origami and soft hinges according to the present invention. In the obtained curved surface folding and unfolding structure, the crease bars and diagonal braces are connected by flexible hinges, avoiding the stress concentration problem at the intersection of traditional origami creases and still not causing fatigue damage after multiple folding and unfolding.

[0026] 5. A method for optimizing a curved surface folding and unfolding structure based on Miura origami and soft hinges according to the present invention. The obtained curved surface folding and unfolding structure can be axially compressed and stored. When it needs to be launched, it is placed in the rocket launch compartment and then unfolds itself after entering the orbit, solving the problem of inconvenient launch of large-scale space structures.

[0027] 6. A method for optimizing a curved surface folding and unfolding structure based on Miura origami and soft hinges according to the present invention. The obtained curved surface folding and unfolding structure is pre-assembled on the ground and then unfolds itself after successfully entering the orbit, without requiring on-orbit assembly, and can actively adapt to the harsh working environment after the rocket enters the orbit. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flowchart of a method for optimizing a curved surface folding and unfolding structure based on Miura origami and soft hinges according to the present invention;

[0029] Figure 2 This is a schematic diagram of Step 1 of an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges of the present invention.

[0030] Among them: Figure 2 (2-1) is a schematic diagram of a flat paper tape of a semi-cylindrical curved folding and unfolding structure obtained by an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges. Figure 2 (2-2) is half of the Miura origami pattern of the origami style of the semi-cylindrical curved folding and unfolding structure obtained by an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges. Figure 2 (2-3) is the complete Miura origami pattern of the semi-cylindrical curved folding and unfolding structure obtained by an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges. Figure 2 (2-4) is the semi-cylindrical curved folding and unfolding origami pattern of the semi-cylindrical curved folding and unfolding structure obtained by an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges.

[0031] Figure 3 This is a schematic diagram of Step 2 of an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges of the present invention;

[0032] Among them: Figure 3 (3-1) is the basic Miura origami unit of the semi-cylindrical curved folding and unfolding structure obtained by an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges. Figure 3 (3-2) is an exploded view of the basic Miura folding structure of the semi-cylindrical curved folding and unfolding structure obtained by an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges. 301 is the upper left flexible hinge, 302 is the upper middle flexible hinge, 303 is the upper right flexible hinge, 304 is the middle left flexible hinge, 305 is the middle middle flexible hinge, 306 is the middle right flexible hinge, 307 is the lower left flexible hinge, 308 is the lower middle flexible hinge, 309 is the lower right flexible hinge. Figure 3 (3-3) is an assembly diagram of the basic Miura folding structure of the semi-cylindrical curved folding and unfolding structure obtained by an optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges.

[0033] Figure 4 This is a schematic diagram of the flexible hinge involved in the embodiment;

[0034] Among them: 401 is the crease rod joint, 402 is the diagonal strut joint, 403 is the crease rod joint bushing, 404 is the diagonal strut joint bushing;

[0035] Figure 5 This is a schematic diagram of the crease rod involved in the embodiment;

[0036] Figure 6 Schematic diagram of the diagonal strut involved in the embodiment;

[0037] Figure 7 Schematic diagram of a curved surface folding and unfolding structure based on Miura origami and soft hinges in the embodiment;

[0038] Figure 8 Schematic diagram of the folding principle of a curved surface folding and unfolding structure based on Miura origami and soft hinges in the embodiment;

[0039] Among them: 801 is the bottom component of the semi-cylindrical surface folding and unfolding structure obtained by the optimization method of the curved surface folding and unfolding structure based on origami principle and soft hinges, and 802 is the top component of the semi-cylindrical surface folding and unfolding structure obtained by the optimization method of the curved surface folding and unfolding structure based on origami principle and soft hinges;

[0040] Figure 9 Schematic diagram of the semi-cylindrical surface folding and unfolding structure obtained by the optimization method of the curved surface folding and unfolding structure based on Miura origami and soft hinges in the embodiment after compression. Detailed implementation method

[0041] To better illustrate the purpose and advantages of the present invention, the following further describes the content of the invention in conjunction with the drawings and examples.

[0042] Example 1:

[0043] The embodiment applies an optimization method of a curved surface folding and unfolding structure based on Miura origami and soft hinges disclosed in this embodiment to optimize the curved surface folding and unfolding mechanism, as Figure 1 shown, and the specific steps are implemented as follows:

[0044] Step 1. Obtain the folding and unfolding origami pattern of the curved surface through the ideal curved surface, as Figure 1 shown, which specifically includes the following sub-steps:

[0045] Step 1.1 Determine the directrix of the cylindrical surface, select the control point a on the directrix and the discrete points c outside the directrix, and sequentially connect these control points and discrete points to form a broken line segment;

[0046] In the embodiment, the curved surface folding and unfolding structure is a semi-cylindrical surface structure, and the directrix of the semi-cylindrical surface is a semi-circular arc line;

[0047] As Figure 2 (2-1) shown, the directrix is a semi-circular arc curve with a radius of R = 80 mm. Select equally spaced control points a1 to a5 on the semi-circular arc curve, and select a series of discrete points c1 to c4 outside the semi-circular arc curve to form the paper tape of the semi-cylindrical surface folding and unfolding structure;

[0048] Step 1.2 Determine the width t of the paper tape, and determine the positions of the remaining points b and d on the paper tape according to the width t of the paper tape;

[0049] As Figure 2 (2-1) shows, in the embodiment, it is determined that the width of the paper tape is t = 65 mm, and the coordinates of the remaining points b1 to b5, d1 to d5 on the paper tape are determined;

[0050] Due to the special geometric property of the paper tape folding in half, a2b2 is the angular bisector of the obtuse angle formed by the ray a2c1 and the ray a2c2, and the angles α formed by a2b2 and the ray a2c1 and the ray a2c2 respectively are as shown in Equation (1):

[0051]

[0052] Among them, a2c1 is a vector starting from a2 and ending at c1, ||a2c1|| is the modulus of the vector a2c1, a2c2 is a vector starting from a2 and ending at c2, and ||a2c2|| is the modulus of the vector a2c2;

[0053] The coordinates of point b2 and the vector Ob2 are as shown in Equation (2):

[0054]

[0055] Among them, Oa2 is a vector starting from the coordinate origin O and ending at a2;

[0056] Taking the origin O as the rotation center, rotate point b2 clockwise to obtain point b1. Taking the origin O as the rotation center, rotate point b2 counterclockwise respectively to obtain points b3, b4, b5;

[0057] According to the special geometric property of the paper tape folding in half, c1d1 is the angular bisector of the obtuse angle formed by the ray a2c1 and the ray c1a1, and ∠a2c1d1 is as shown in Equation (3):

[0058]

[0059] Among them, c1a2 is a vector starting from point c1 and ending at point a2, ||c1a2|| is the modulus of the vector c1a2; c1a1 is a vector starting from c1 and ending at a1, and ||c1a1|| is the modulus of the vector c1a1;

[0060] The coordinates of point d1 and the vector Od1 are as shown in Equation (4):

[0061]

[0062] Among them, Oc1 is a vector starting from point O and ending at c1;

[0063] Taking the origin O as the rotation center, rotate point d1 clockwise to obtain points d2, d3, and d4 respectively;

[0064] Step 1.3 Determine the stretching height H, and stretch the points b and d on the paper tape to a predetermined height to obtain a half Miura structure;

[0065] As Figure 2 (2 - 2) shows that in the embodiment, the stretching length T = 100 mm, stretch point b and point d to the predetermined height T, and obtain a half Miura structure;

[0066] Step 1.4 Mirror the half Miura structure generated in Step 1.3 along the horizontal plane to obtain the entire Miura structure;

[0067] As Figure 2 (2 - 3) shows that mirror the half Miura structure obtained in Step 1.3 along the horizontal plane to obtain the entire Miura structure;

[0068] Step 1.5 Determine the array number i, and array the Miura structure generated in Step 1.4 along the height direction to obtain a curved surface folding and unfolding origami pattern based on Miura origami;

[0069] As Figure 2 (2 - 4) shows that in the embodiment, the array number i = 3, array the entire Miura structure obtained in Step 1.4 along the height direction to obtain a curved surface origami pattern based on Miura origami, and the obtained curved surface origami pattern can be folded and unfolded along the height direction;

[0070] Step Two: Construct a curved surface folding and unfolding structure by combining the Miura origami pattern with soft hinges, as Figure 1 shown, specifically including the following sub - steps:

[0071] Step 2.1 Determine the coordinates of each vertex in the curved surface folding and unfolding origami pattern based on Miura origami obtained in Step One, as well as the direction vectors formed by adjacent points and opposite points;

[0072] In the embodiment, as Figure 3 (3 - 1) shows that for the vertices in a basic Miura unit of the origami pattern obtained in Step One, from left to right and from top to bottom, they are marked as point 1 to point 9;

[0073] Taking point 5 as the coordinate origin, the coordinates of point 1 are (-152.1, -86.3, 100), the coordinates of point 2 are (-62.5, 25.9, 100), the coordinates of point 3 are (-71.1, -50.9, 100), the coordinates of point 4 are (-68.8, -86.3, 100), the coordinates of point 6 are (-12.3, -109.7, 0), the coordinates of point 7 are (-152.1, -86,3, -100), the coordinates of point 8 are (-62.5, 25.9, -100), and the coordinates of point 9 are (-71.1, -50.9, -100);

[0074] Taking point 1 as the starting point, the direction vectors pointing to each adjacent point are: r 12 =(0.6238, 0.7816, 0), r 14 =(0.6394, 0, -0.7688), r 14 =(0.7549, 0.4285, -0.4965);

[0075] Taking point 2 as the starting point, the direction vectors pointing to each adjacent point are: r 21 =(-0.6238, -0.7816, 0), r 23 =(-0.1115, -0.9938, 0), r 24 =(-0.0424, -0.7458, -0.6648), r 25 =(0.5177, -0.2144, -0.8283), r 26 =(0.2855, -0.7714, -0.5688).

[0076] Taking point 3 as the starting point, the direction vectors pointing to each adjacent point are: r 32 =(0.1115, 0.9938, 0), r 35 =(0.5353, 0.3833, -0.7527), r 36 =(0.4521, -0.4521, -0.7688);

[0077] Taking point 4 as the starting point, the direction vectors pointing to each adjacent point are: r 41 =(-0.6394, 0, 0.7688), r 42 =(0.0424, 0.7458, 0.6648), r 45 =(0.6238, 0.7816, 0), r 47 =(-0.6394, 0, -0.7688), r 48 =(0.0424, 0.7458, -0.6648);

[0078] Starting from point 5, the direction vectors pointing to each adjacent point are: r 51 = (-0.7459, -0.4285, 0.4965), r 52 = (-0.5177, 0.2144, 0.8283), r 53 = (-0.5353, -0.3833, 0.7527), r 54 = (-0.6238, -0.7816, 0), r 56 = (-0.1115, -0.9938, 0), r 57 = (-0.7549, -0.4285, -0.4965), r 58 = (-0.5177, 0.2144, -0.8283), r 59 = (-0.5353, -0.3833, -0.7527);

[0079] Starting from point 6, the direction vectors pointing to each adjacent point are: r 62 = (-0.2855, 0.7714, 0.5688), r 63 = (-0.4521, 0.4521, 0.7688), r 65 = (0.1115, 0.9938, 0), r 68 = (-0.2855, 0.7714, -0.5688), r 69 = (-0.4521, 0.4521, -0.7688);

[0080] Starting from point 7, the direction vectors pointing to each adjacent point are: r 74 = (0.6394, 0, 0.7688), r 75 = (0.7549, 0.4285, 0.4965), r 78 = (0.6238, 0.7816, 0);

[0081] Starting from point 8, the direction vectors pointing to each adjacent point are: r 84 = (-0.0424, -0.7458, 0.6648), r 85 = (0.5177, -0.2144, 0.8283), r 86 = (0.2855, -0.7714, 0.5688), r 87 = (-0.6238, -0.7816, 0), r 89 = (-0.1115, -0.9938, 0);

[0082] Starting from point 9, the direction vectors pointing to each adjacent point are: r 95 =(0.5353, 0.3833, 0.7527), r 96 =(0.4521, -0.4521, 0.7688), r 98 =(0.1115, 0.9938, 0);

[0083] Step 2.2 Determine the spatial positions of the crease rod joints and the diagonal brace rod joints in each flexible hinge respectively according to the direction vectors obtained in Step 2.1, and determine the cross-sectional dimensions and lengths of the crease rod joints and the diagonal brace rod joints;

[0084] In the embodiment, as Figure 3 (3-1) shows, starting from 1, along the unit vector r 12 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 301 along the vector r 12 direction; along the unit vector r 14 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 301 along the vector r 14 direction;

[0085] Starting from 2, along the unit vector r 21 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 302 along the vector r 21 direction; along the unit vector r 25 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 302 along the vector r 25 direction; along the unit vector r 23 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 302 along the vector r 23 direction;

[0086] Starting from 3, along the unit vector r 36 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 303 along the vector r 36 direction; along the unit vector r 32 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 303 along the vector r 32 direction;

[0087] Starting from 4, along the unit vector r 41 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 304 along the vector r 41The crease bar joint in the direction; along the unit vector r 45 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 304 along the vector r 45 The crease bar joint in the direction; along the unit vector r 47 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 304 along the vector r 47 The crease bar joint in the direction;

[0088] Starting from 5, along the unit vector r 54 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 305 along the vector r 54 The crease bar joint in the direction; along the unit vector r 52 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 305 along the vector r 52 The crease bar joint in the direction; along the unit vector r 56 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 305 along the vector r 56 The crease bar joint in the direction; along the unit vector r 58 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 305 along the vector r 58 The crease bar joint in the direction;

[0089] Starting from 6, along the unit vector r 63 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 306 along the vector r 63 The crease bar joint in the direction; along the unit vector r 65 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 306 along the vector direction r 65 The crease bar joint; along the unit vector r 69 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 306 along the vector direction r 69 The crease bar joint;

[0090] Starting from 7, along the unit vector r 74 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 307 along the vector r 74 The crease bar joint in the direction; along the unit vector r 78 , a cylinder with a cross-sectional radius of 3 mm and a length of 10 mm, is the crease bar joint of the flexible hinge 307 along the vector r 78 The crease bar joint in the direction;

[0091] Starting from 8, along the unit vector r87 A cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 308 along the vector r 87 direction; along the unit vector r 85 A cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 308 along the vector r 85 direction; along the unit vector r 89 A cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 308 along the vector r 89 direction;

[0092] Starting from 9, along the unit vector r 98 A cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 309 along the vector r 98 direction; along the unit vector r 96 A cylinder with a cross-sectional radius of 3 mm and a length of 10 mm is the crease rod joint of the flexible hinge 309 along the vector r 96 direction;

[0093] Step 2.3 Determine the dimensions of the crease rod joint sleeve connected to the crease rod joint and the strut rod joint sleeve connected to the strut rod joint, including: crease rod joint sleeve length, crease rod joint sleeve outer diameter, crease rod joint sleeve inner diameter, crease rod joint sleeve depth, strut rod joint sleeve length, strut rod joint sleeve outer diameter, strut rod joint sleeve inner diameter, strut rod joint sleeve depth;

[0094] In the embodiment, as Figure 3 (3-1) shows, starting from 1, along the unit vector r 15 A cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut rod joint of the flexible hinge 301 along the vector r 15 direction;

[0095] Starting from 2, along the unit vector r 24 A cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut rod joint of the flexible hinge 302 along the vector r 24 direction; along the unit vector r 26 A cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut rod joint of the flexible hinge 302 along the vector r 26 direction;

[0096] Starting from 3, along the unit vector r 35 A cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut rod joint of the flexible hinge 303 along the vector r 35 direction;

[0097] Starting from 4, along the unit vector r 42 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 304 along the vector r 42 direction; along the unit vector r 48 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 304 along the vector r 48 direction;

[0098] Starting from 5, along the unit vector r 51 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 305 along the vector r 51 direction; along the unit vector r 53 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 305 along the vector r 53 direction; along the unit vector r 57 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 305 along the vector r 57 direction; along the unit vector r 59 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 305 along the vector r 59 direction;

[0099] Starting from 6, along the unit vector r 62 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 306 along the vector r 62 direction; along the unit vector r 68 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 306 along the vector r 68 direction;

[0100] Starting from 7, along the unit vector r 75 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 307 along the vector r 75 direction;

[0101] Starting from 8, along the unit vector r 84 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the strut joint of the flexible hinge 308 along the vector r 84 direction; along the unit vector r 86, a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the joint of the diagonal strut of the flexible hinge 308 along the vector r 86 direction;

[0102] Starting from 9, along the unit vector r 95 , a cylinder with a cross-sectional radius of 1.5 mm and a length of 15 mm is the joint of the diagonal strut of the flexible hinge 309 along the vector r 95 direction;

[0103] In the embodiment, the length of the sleeve of the crease rod of the flexible hinge is 10 mm, the outer diameter is 6 mm, the inner diameter is 3.9 mm, and the hole depth is 10 mm;

[0104] In the embodiment, the length of the sleeve of the diagonal strut of the flexible hinge is 8 mm, the outer diameter is 5 mm, the inner diameter is 2.9 mm, and the hole depth is 7 mm;

[0105] In the embodiment, the flexible hinge is as shown in Figure 4 , 401 is the joint of the crease rod, 402 is the joint of the diagonal strut, 403 is the sleeve of the crease rod joint, and 404 is the sleeve of the diagonal strut joint;

[0106] Step 2.4 Determine the length of the crease rod and the cross-sectional dimensions of the crease rod;

[0107] In the embodiment, as shown in Figure 3 (3-1), taking point 5 as the coordinate origin, the coordinates of point 2 are (-62.5, 25.9, 100), the distance between point 2 and point 5 is 120.74 mm, the crease rod is connected to the flexible hinge, the length of the crease rod is 100.74 mm, and the cross-sectional radius is 2 mm, as shown in Figure 5 ;

[0108] Repeat step 2.4 to determine the lengths of the remaining crease rods in a basic Miura unit in the origami pattern;

[0109] Step 2.5 Determine the length of the diagonal strut and the cross-sectional dimensions of the diagonal strut;

[0110] In the embodiment, as shown in Figure 3 (3-1), taking point 5 as the coordinate origin, the coordinates of point 1 are (-152.1, -86.3, 100), the distance between point 5 and point 1 is 201.42 mm, the diagonal strut is connected to the sleeve of the diagonal strut, the length of one straight rod of the diagonal strut is 171.42 mm, taking point 5 as the coordinate origin, the coordinates of point 2 are (-62.5, 25.9, 100), the coordinates of point 4 are (-68.9, -86.3, 0), then the distance between point 2 and point 4 is 130.06 mm, the diagonal strut is connected to the flexible hinge, the length of the other straight rod in the diagonal strut is 100.06 mm, and the positional relationship between the two straight rods in the diagonal strut is related to the vector r51 、r 42 The positional relationship between them is consistent, and the cross-sectional radius of the two straight rods in the diagonal brace is 1.5mm. Figure 6 As shown;

[0111] Repeat step 2.5 to determine the length of the remaining diagonal braces of a basic Miura unit in the origami pattern;

[0112] Step 2.6: Assemble the flexible hinge, crease rod and diagonal brace rod according to the origami style, and finally obtain a curved folding structure based on Miura origami and soft hinge;

[0113] In the embodiment, Figure 3 As shown in (3-2), after determining all the flexible hinges, crease rods and diagonal struts involved in a basic Miura unit, they are assembled according to the geometric relationship between the vertices, creases and paper surface in the Miura origami unit. The flexible hinges, crease rods and diagonal struts correspond to the vertices, creases and paper surface diagonals one by one, respectively. The two ends of the crease rod are respectively fastened to the rod sleeves at one end of the corresponding flexible hinge crease rod joint, and the four sections of the diagonal struts are respectively fastened to the rod sleeves at one end of the corresponding flexible hinge diagonal strut joint. The curved surface folding structure corresponding to a basic Miura unit in the origami style is shown as follows: Figure 3 As shown in (3-3);

[0114] Repeat the above process, Figure 2 The curved surface folding structure corresponding to the origami style shown is as follows Figure 7 As shown;

[0115] In the embodiment, the material of the flexible hinge is Hei-Cast 8400 soft glue, which is formed by vacuum casting, and the material of the crease rod and the diagonal support rod is photosensitive resin, which is formed by 3D printing;

[0116] It also includes step three: Figure 8 As shown, the semi-cylindrical curved surface folding structure obtained by the optimization in step 2 is pre-fabricated and assembled on the ground. When not subjected to external force, the natural state of the semi-cylindrical curved surface folding structure is the unfolded state. To fold the semi-cylindrical curved surface folding structure, firstly, all the flexible hinges and the crease rod 801 at the bottom are placed on a horizontal plane, and then vertical downward pressure is applied to all the flexible hinges and the crease rod 802 on the top of the curved surface folding structure. As the pressure increases, the flexible hinges at various locations of the curved surface folding structure will deform, and the crease rods and the diagonal bracing rods fixed to the flexible hinges will undergo rigid body motion, thereby realizing the folding of the curved surface folding structure, as shown in FIG. Figure 9As shown, the deformation modes of the units of the semi-cylindrical surface deployable structure are consistent with those of the Miura origami, saving storage space and being able to be placed in the rocket launch cabin with a small volume. After folding, each flexible hinge of the semi-cylindrical surface deployable structure stores a certain amount of elastic potential energy due to deformation. Place all the flexible hinges and crease bars at the bottom of the semi-cylindrical surface deployable structure on a horizontal plane, and remove the external force applied vertically downward on the top of the surface deployable structure. Then, the elastic potential energy stored in the flexible hinges is released, and the flexible hinges return to their natural state, driving the connected crease bars and diagonal braces to perform rigid body motion, and the semi-cylindrical surface deployable structure returns to the deployed state, realizing self-deployment after successful orbit injection, solving the problem of inconvenient launch of large-scale structures. Moreover, the optimized semi-cylindrical surface deployable structure has been pre-assembled and does not require on-orbit assembly, actively adapting to the harsh working environment after the rocket enters orbit.

[0117] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An optimization method for a curved folding and unfolding structure based on Miura origami and soft hinges, characterized in that: It includes the following steps: Step 1: Obtain a surface folding and unfolding origami pattern by combining an ideal surface with the Miura origami pattern, which specifically includes the following sub-steps: Step 1.1 Determine the directrix of the cylindrical surface, select the control point a on the directrix and the discrete point c outside the directrix; sequentially connect these control points and discrete points to form a broken line segment; Step 1.2 Determine the width t of the paper tape, and determine the positions of the remaining points b and d on the paper tape according to the width t of the paper tape; Step 1.3 Determine the stretching height H, and stretch the points b and d on the paper tape to a predetermined height to obtain a half Miura structure; Step 1.4 For the half Miura structure generated in Step 1.3, mirror it along the horizontal plane to obtain the entire Miura structure; Step 1.5 Determine the number of arrays i, and array the Miura structure generated in Step 1.4 along the height direction to obtain a surface folding and unfolding origami pattern based on Miura origami; Step 2: Construct a surface folding and unfolding structure by combining the surface folding and unfolding origami pattern with soft hinges, which specifically includes the following sub-steps: Step 2.1 Determine the coordinates of each vertex in the surface folding and unfolding origami pattern based on Miura origami obtained in Step 1, as well as the direction vectors formed by adjacent points and opposite points; Step 2.2 Determine the spatial positions of the crease rod joints and strut rod joints in each flexible hinge according to the direction vectors obtained in Step 2.1, and determine the cross-sectional dimensions and lengths of the crease rod joints and strut rod joints; Step 2.3 Determine the dimensions of the crease rod joint sleeves connected to the crease rod joints and the strut rod joint sleeves connected to the strut rod joints, including: the length of the crease rod joint sleeve, the outer diameter of the crease rod joint sleeve, the inner diameter of the crease rod joint sleeve, the depth of the crease rod joint sleeve, the length of the strut rod joint sleeve, the outer diameter of the strut rod joint sleeve, the inner diameter of the strut rod joint sleeve, the depth of the strut rod joint sleeve; Step 2.4 Determine the length and cross-sectional dimensions of the crease rod; Step 2.5 Determine the length and cross-sectional dimensions of the strut rod; Step 2.6 Assemble the flexible hinges, crease rods and strut rods according to the origami pattern to obtain a surface folding and unfolding structure based on Miura origami and soft hinges, that is, optimize the surface folding and unfolding structure based on Miura origami and soft hinges.

2. The optimization method of the curved surface folding and unfolding structure based on Miura origami and soft hinges according to claim 1, characterized in that: It also includes Step 3: According to the surface folding and unfolding structure optimized in Step 2, pre-fabricate and assemble it on the ground and store it in a compressed manner. When launching is required, put it into the rocket launch cabin in a smaller volume, and then unfold it automatically after successfully entering the orbit to solve the problem of inconvenient launch of large-scale structures. And the optimized surface folding and unfolding structure has been pre-assembled and does not require on-orbit assembly, and actively adapts to the harsh working environment after the rocket enters the orbit.

Images