A reverse design method for a two-dimensional elastic rope

Abstract

The invention discloses a reverse design method for a two-dimensional elastic rope, comprising the following steps: setting an external force combination F and a target shape of the elastic rope, fixing one end of the elastic rope as a fixed end, and the other end as a free end; setting a total length L of the elastic rope, dividing the elastic rope into n equal sections #imgabs0#, wherein the section closest to the fixed end is taken as l1, and the sections are increased in sequence until the lth section closest to the free end is taken as nth section. n ; Then, select the two segments l adjacent to the free end n and l n‑1 , solve for the angle θ between the two segments n Then, consider the first n‑2 segment, solve for l n‑1 , l n‑2 Angle between segments θ n‑1 ; Finally, increase the number of segments in sequence to solve until all segments of the elastic rope are solved, all θ values are solved, and all angle values are obtained #imgabs1# Combined with the length of each segment, the shape before deformation is solved.

Description

Technical Field

[0001] The present invention relates to the field of reverse design, and particularly to a reverse design method for a two-dimensional elastic rope. Technical Background

[0002] Elastic rope structures are very common in nature and engineering, such as ropes, telephone lines, the hair and tails of characters in games and animations, etc. The shapes they present in the real world are usually deformed shapes caused by stretching, bending, and twisting under external forces or constraints, such as gravity. This deformation process can be achieved through experiments or mechanical simulations.

[0003] However, since the solution from the deformed structure of the elastic rope to the undeformed structure is a strongly non-linear problem, it is very difficult to directly solve using traditional mechanical methods. Therefore, how to solve the undeformed elastic rope structure so that after production, it can deform into the shape required by the user under the action of gravity or other external forces is still a thorny problem.

[0004] Currently, for this problem, there are mainly two types of methods. One type attempts to obtain the undeformed structure by solving a system of differential equations, but this method has a complex implementation process and strict mathematical continuity requirements for the target shape. The other type of method is to use global search algorithms in machine learning algorithms, such as simulated annealing (SA), genetic algorithm (GA), and particle swarm optimization (PSO), etc. However, these algorithms have a long search time, and since in this reverse search process, the error does not monotonically decrease as the number of unknowns decreases, they often fall into local minima and cannot find a reverse design solution that meets the requirements. Summary of the Invention

[0005] The purpose of the present invention is to provide a reverse design method for an elastic rope with a simple implementation process and low requirements for mathematical continuity.

[0006] The present invention discloses a reverse design method for a two-dimensional elastic rope, including the following steps:

[0007] Step 1: Set the combination of external forces F acting on the elastic rope and the target shape, fix one end of the elastic rope as the fixed end, and the other end as the free end; assume the total length of the elastic rope is L, and divide the elastic rope into n equal segments Among them, the segment closest to the fixed end is taken as l 1 , increasing sequentially until l n closest to the free end;

[0008] Step 2: Select two adjacent segments l n and l n-1 near the free end, and solve the included angle θ n between the two segments;

[0009] Step 3: Add and consider the l near the free endn-2 Segment, solve for l n-1 , l n-2 The included angle θ between segments n-1 ;

[0010] Step 4: Solve by increasing the number of segments in sequence until all segments are elastic ropes, solve for all θ values, and obtain all included angle values Combined with the length of each segment, solve for the shape before deformation under no force.

[0011] Further, in the second step, the included angle θ between the two segments n Solve using a traversal search algorithm, and the search range, step size, and allowable error are determined by the user according to the accuracy requirements and the solving speed.

[0012] Further, the traversal search algorithm specifically includes: Fix the l n-1 segments, select a rotation angle at a certain angle as the preset value, input the two segments l n and l n-1 and the rotation angle into the simulation environment, obtain their shapes under the corresponding force, compare with the target shape and calculate the error; change the angle, traverse within a certain range, select the step increment Δ, calculate the error values for each angle respectively, and select the rotation angle corresponding to the minimum error value as the rotation angle between l n and l n-1 .

[0013] Further, the calculation method for the calculation error is:

[0014] Among them, the total length of the elastic rope is L, the elastic rope is equally divided into n segments, (x i , y i ) is the position coordinate of the elastic rope node in the simulation environment, is the position coordinate of the corresponding node on the target curve.

[0015] Further, The coordinates are determined by the length of each segment and the rotation angle between the two ends,

[0016] The calculation formula is as follows:

[0017] Among them, l i is the length of each segment of the elastic rope, is the included angle between the i-th elastic rope and the horizontal axis,

[0018] Further, the value range of the rotation angle Δθ can be initially taken as

[0019] Further, the step increment Δ is 0.001.

[0020] Furthermore, the elastic rope is a planar structure, and all external forces on the elastic rope are in the same plane as the elastic rope.

[0021] The beneficial effects of the present invention are as follows:

[0022] 1. The method disclosed in the present invention is to discretize the target design shape and then solve it segment by segment from the free end to the fixed end. Each time, a rotation angle value is solved. After the solution is completed, all the rotation angles and side lengths can be converted into an undeformed elastic rope structure. Compared with the existing methods, this method does not require a complex material model and can be applied to a variety of material scenarios, with higher versatility. This method starts calculating from the free end, which can avoid the error accumulation effect to a certain extent, that is, the rotation angles solved in subsequent calculations will not affect the previous rotation angles.

[0023] 2. The present invention uses a search algorithm, which can effectively avoid the problem that the error does not monotonically decrease as the number of unknowns decreases. This method does not require solving complex static equations, and the amount of calculation for solving is greatly reduced. Description of the Drawings

[0024] Figure 1 is a flowchart of the method of the present invention;

[0025] Figure 2 is the method for solving the rotation angle in the present invention;

[0026] Figure 3 is the method for solving the example of the present invention. Detailed Embodiments

[0027] The present invention will be further described below with reference to the drawings:

[0028] As Figure 1-2 shown, the present invention discloses a reverse design method for a two-dimensional elastic rope, including the following steps:

[0029] S1: Set one end of the target elastic rope as the fixed end A 1 , and the other end as the free end A 2 . Determine the target shape according to the actual application situation, the total length L of the elastic rope, and discretize the elastic rope into n segments of equal length Then the length of each segment is Fix a small segment of elastic rope l 1 connected to the fixed end A 1 . Thus, only by solving the angle between each segment of the elastic rope and the upper segment of the elastic rope can the shape of the target elastic rope before deformation be solved.

[0030] S2: Starting from the free end A 2 , solve by the method of gradually equivalent force and moment. First, take out the two segments of elastic rope l n, l n-1 , and fix l n-1 , solve for l n , l n-1 The included angle Δθ between n-1 .

[0031] S3: Determine the included angle Δθ according to the actual situation n-1 The value range is [-θ max , θ max ; Determine the step increment Δ according to the required accuracy in actual needs.

[0032] Among them, the value range of the included angle Δθ can be initially taken as The step increment Δ can be initially taken as 0.001, and then the value is further optimized according to the calculation results. Among them, the angle value range is determined by the target shape and can be further optimized according to the calculation results. Since the continuity and flexibility of the elastic rope need to be ensured, the included angle is generally not too large.

[0033] S4: In the simulation environment, traverse in [-θ max , θ max with an increment of Δ, and calculate the error e between the simulated shape and the actual shape corresponding to each value, search for the minimum error e min , compare it with e a to obtain the corresponding included angle which is the included angle θ to be solved n-1 .

[0034] Specifically, compare e min with e a . If e min > e a , then further reduce the value of Δ and re-traverse and solve; if e min < e a , then the corresponding included angle is the included angle θ to be solved n-1 .

[0035] Specifically, the error calculation formula where (x i , y i ) is the position coordinate of the elastic rope node in the simulation environment, is the position coordinate of the corresponding node on the target curve. The xy coordinates are determined by the length of each segment and the included angle between the two ends, and the calculation formula is as follows: where l i is the length of each rigid body segment, is the included angle between the rigid body and the horizontal axis,

[0036] S5: Add and fix the elastic rope l n-2, repeat S3 - S4 to solve for

[0037] S6: Each time, add one segment and fix it. Repeat S3 - S5 to solve for the rotation angles between all segments Then it can be determined by and together as the shape of the elastic rope before deformation.

[0038] Specific Example 1

[0039] As Figure 3 shown, divide the elastic rope into 31 segments equally. Then there are 32 nodes and 30 rotation angles. Starting from the fixed end and counting, it is the 1st segment, and the free end is the 31st segment. The rotation angle between the 1st and 2nd segments is θ 1 , and so on. The rotation angle between the 30th and 31st segments is θ 30 .

[0040] Step 1: First, start solving from the free end. Select the 30th and 31st segments and fix the 30th segment. θ 30 is traversed at intervals of 0.001 within the range of . Each value is used as a condition and input into the simulation environment. The shape after force application is compared with the target shape, and the error is calculated according to the error calculation formula. Select the value of θ 30 with the minimum error value;

[0041] Step 2: Then add and fix the 29th segment. The 30th and 31st segments are connected with a rotation angle of θ 30 . θ 29 is traversed at intervals of 0.001 within the range of . Each value is used as a condition and input into the simulation environment. The shape after force application is compared with the target shape, and the error is calculated according to the error calculation formula. According to the error calculation formula, select the value of θ 29 with the minimum error value;

[0042] Steps 3 - 30: And so on. Each time add one segment until adding to the 1st segment. At this time, all the values of θ can be solved All the values;

[0043] Starting from the origin, with a length of l 1 , rotate by θ 1 ; then at the end of l 1 , with a length of l 1 , rotate by θ 2 , and so on, until the shape before deformation without force is drawn by combining the length of each segment.

[0044] The present invention discloses a reverse design method for a two-dimensional elastic rope, which can reversely calculate the structure of the elastic rope before deformation according to the given target shape of the elastic rope after deformation, external force conditions, and material and geometric parameters. The method includes the following steps: the user specifies the material type, target shape, and a set of external forces; based on the target shape, the entire elastic rope is discretized into several segments of equal length, each segment of the elastic rope is treated as a rigid body, and adjacent segments are connected by nodes; the position of each segment of the rope is characterized by the length of each segment of the rope and the rotation angle between this segment and the previous segment; one end of the elastic rope structure is fixed and the other end is free. Starting from the free end, the rotation angle values corresponding to the undeformed structure are calculated segment by segment until the rotation angle calculation of the fixed end is completed; when calculating the rotation angle value, by uniformly searching within a set range, each assumed rotation angle to be solved and the known rotation angle are converted into an undeformed elastic rope structure, which is input into the mechanical simulation model, and then the deformed shape output by the model is compared with the target design shape of the current part. The rotation angle value with the minimum shape error is the required value. This method can solve the problem of reverse design of elastic ropes that cannot be directly solved by traditional mechanical methods, help users design elastic rope structure products with various different shapes, materials, and geometric parameters, and can be applied to fields such as 4D printing and soft robot manufacturing.

[0045] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. An inverse design method for a two-dimensional elastic rope, characterized in that, it comprises the following steps: Step 1. Set the external force combination F applied to the elastic cord and the target shape. Fix one end of the elastic cord as the fixed end, and the other end is the free end. Assume the total length of the elastic cord is L, and divide the elastic cord into n equal segments Among them, the segment closest to the fixed end is taken as l 1 , increasing sequentially until the l closest to the free end n ; Step 2: Select two segments \(l\) adjacent to the free end n and \(l\) n-1 , and solve for the included angle \(\theta\) n ; Step 3. Add the consideration of the l-th segment near the free end, and solve for the included angle θ between the l-th segment and the l'-th segment; n-2 n-1 n-2 n-1 ​​​​ Step 4: Solve by sequentially increasing the number of segments until all segments of the elastic rope are processed, obtaining all θ values and thus all included angle values. Combined with the length of each segment, solve for the shape before deformation under no force. In the second step, the included angle θ between the two segments n The solution uses a traversal search algorithm, and the search range, step size, and allowable error are determined by the user according to the accuracy requirements and the solution speed; The traversal search algorithm specifically includes: fixing the l n-1 section, selecting a turning angle at a certain angle as a preset value, and inputting the two l n and l n-1 and the turning angle into the simulation environment to obtain their shapes under corresponding forces, comparing with the target shape and calculating the error; changing the angle, traversing within a certain range, selecting a step increment Δ, calculating the error values of each angle respectively, and selecting the turning angle corresponding to the minimum error value as the turning angle between l n and l n-1 ; The calculation error calculation method is as follows: Among them, the total length of the elastic rope is L. The elastic rope is equally divided into n segments. (x i , y i ) is the position coordinate of the elastic rope node in the simulation environment, is the position coordinate of the corresponding node on the target curve; The coordinates are determined by the length of each segment and the rotation angle between the two ends. The calculation formula is as follows: where l i is the length of each elastic cord segment, is the angle between the i-th elastic cord and the horizontal axis, 2. The inverse design method for a two-dimensional elastic rope according to claim 1, characterized in that, The value range of the corner Δθ can be initially taken as 3. The inverse design method for a two-dimensional elastic rope according to any one of claims 1-2, characterized in that, the elastic rope is a planar structure, and all external forces on the elastic rope are in the same plane as the elastic rope.

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