Method for obtaining link mechanism layout of specified motion trail

Abstract

The invention belongs to the field of mechanical structure optimization, and particularly relates to a method for obtaining a connecting rod mechanism layout of a specified motion trail, which comprises the following steps of: 1, establishing a connecting rod structure coordinate system to obtain an initial connecting rod mechanism layout; 2, the rod length, the rod density and the target rod number of each rod are obtained; step 3, determining a function relation between a motion point and a force bearing point; 4, establishing a topology model of the link mechanism layout; 5, performing gradient descent on the Q positions to obtain coordinates of each point; step 6, determining sensitivity; 7, the rod density is obtained through an MMA algorithm; 8, performing cyclic judgment; and step 9, obtaining a link mechanism layout. According to the method, the topology model of the link mechanism layout is provided, and in the model solving process, the gradient descent method and the MMA algorithm are combined, so that the solving process of the model is simplified, and the link structure obtained according to the method has good motion precision and reliability.

Description

Technical Field

[0001] The invention belongs to the field of mechanical structure optimization, and in particular relates to a method for obtaining a connecting rod mechanism layout of a specified motion trajectory. Background Art

[0002] The topological optimization design of the connecting rod mechanism occupies a pivotal position in modern mechanical engineering. Its far-reaching significance is not only reflected in improving the overall performance of the mechanical system, but also in being able to accurately control the specified motion trajectory, which is particularly important for aircraft, a highly complex and precise means of transportation. As a key component for connecting and transmitting motion and force, the connecting rod mechanism plays a vital role in aircraft design. Through reasonable layout and design, they can ensure that the various components of the aircraft move accurately according to the predetermined trajectory and angle, thereby realizing a series of complex actions such as take-off, landing, turning, and climbing of the aircraft. In the flight control system of the aircraft, the application of the connecting rod mechanism is particularly extensive. Taking the deflection control of the aircraft wing as an example, the deflection angle of the wing directly affects the lift, drag and flight stability of the aircraft, and is a key link in flight control. Traditional wing deflection control relies on complex hydraulic systems or electric systems, but these systems often have problems such as heavy weight, high energy consumption, and complex maintenance. The connecting rod mechanism after topological optimization can achieve lightweight structure, reduce energy consumption, and improve system reliability and durability while ensuring the accuracy and stability of wing deflection.

[0003] The topological optimization design of the linkage mechanism is essentially an optimization method that maximizes structural efficiency by adjusting material distribution and structural shape while meeting specific performance requirements. In the design of aircraft wing deflection control, topological optimization can help designers accurately calculate the optimal layout and shape of the linkage mechanism, so that during the wing deflection process, the linkage mechanism can achieve the most accurate deflection angle control with the least material consumption and the lowest energy consumption. This optimization not only improves the accuracy and stability of wing deflection control, but also significantly reduces the overall weight and energy consumption of the aircraft, and improves the flight performance and fuel consumption of the aircraft. In addition, the topological optimization of the linkage mechanism also has broad application prospects in other key components of the aircraft. For example, in the landing gear system of the aircraft, through the reasonable design of the linkage mechanism, the landing gear can be accurately folded and unfolded during takeoff and landing, improving the takeoff and landing efficiency of the aircraft, while reducing the weight and complexity of the landing gear system. In the aircraft's control surface control system, the topological optimization of the linkage mechanism can also achieve accurate deflection control of the control surface, improving the aircraft's handling performance and flight stability.

[0004] The topological optimization design of the connecting rod mechanism is of great significance in aircraft design. Through reasonable connecting rod layout and design, the specified motion trajectory control of each component of the aircraft can be accurately realized, and the flight performance and fuel consumption of the aircraft can be improved. Therefore, the present invention studies a method for obtaining the layout of the connecting rod mechanism with a specified motion trajectory. Based on the dynamic equation and the steepest descent method, the sensitivity of the target to the design variables is derived, and then the layout of the mechanism that can meet the specified trajectory is obtained. This method can be used in the design of realizing the specified displacement to ensure the accuracy of the motion. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a method for obtaining the layout of a linkage mechanism with a specified motion trajectory, so that the linkage mechanism can travel along a specified route. The present invention first plans the target motion curve based on the actual working conditions, and then combines topological optimization to determine the target area, the topological model of the linkage mechanism layout, and the necessary conditions such as design variables. Then, the gradient descent method and the MMA algorithm (Method of Moving Asymptotes) are combined to optimize the linkage mechanism layout, and finally a structure that meets the requirements is obtained.

[0006] To achieve the above object, the present invention discloses a method for obtaining a linkage mechanism layout of a specified motion trajectory, which comprises the following steps:

[0007] Step 1: Establish the linkage structure coordinate system and obtain the initial linkage mechanism layout;

[0008] Determine the region range of the linkage mechanism in the initial state and establish the linkage structure coordinate system; establish a mesh structure within the region range, and each point in the mesh structure is used as the vertex of the rod. There are a total of W points, forming a point set D = {D1, D2, ..., D w}, all points are connected in pairs as the initial linkage layout, which includes N e root pole;

[0009] Step 2: Get the rod length, rod density and target number of rods for each rod;

[0010] Select any two points D from the point set D in step 1 i and D j , the obtained rod length l ij , i≠j; initial rod density ρ ij is the set value, 0.2≤v ij ≤0.5, target number of strokes N is the set value, 2≤N≤N e ;

[0011] Step 3: Determine the functional relationship between the moving point and the force point;

[0012] Step 4: Establish a topological model of the linkage mechanism layout;

[0013] The topological model of the linkage mechanism layout is:

[0014]

[0015] 0≤ρ ij ≤1 (6)

[0016] Among them, q is the position of the force point on the predetermined trajectory, p q目标 is the coordinate of the moving point when the force point is at position q, obtained according to the functional relationship between the moving point and the force point in step 3, p q obj is the coordinate of the moving point when the force point is at position q, obtained according to the determined linkage mechanism; q When q is the position q of the force point on the predetermined trajectory, the change of the rod length is the smallest; W is the number of points in the point set D, ρ ij D i and D j Rod density of the rod between two points, L ij is D obtained according to the current linkage layout i and D j The length of the rod between <j,D i , D j ∈D,l ij is the initial D obtained in step 2 i and D j The length of the rod between; N is the preset target number of rods, ε1 is the set value;

[0017] Step 5: Use the gradient descent method to obtain the coordinates of each point at Q positions;

[0018] Select Q positions on the predetermined trajectory of the force point. For position q, specify the corresponding horizontal or vertical coordinate position of the moving point at this time. Use the inner solution formula to apply the gradient descent method to obtain the coordinates (XY) of the rod vertices when the force point moves to the specified position q. q ;

[0019] Step 6: Determine sensitivity;

[0020] The sensitivity is obtained by differentiating the rod density according to the objective function c;

[0021] Step 7: Use MMA algorithm to obtain the rod density;

[0022] The rod density ρ ij As the design variable of the MMA algorithm, the objective function c obtained according to the coordinates of step 5 is used as the objective function of MMA, and the sensitivity to the rod density ρ ijOptimize, and the second constraint and the third constraint need to be satisfied during the optimization process;

[0023] Step 8: Loop judgment;

[0024] Determine whether the objective function c is less than the predetermined value or the number of loops reaches the maximum value. If so, stop the loop and execute step 9. If neither is satisfied, use the rod density ρ obtained in the current step 7. ij Return to step 5, which now uses the updated rod density ρ ij Start a new cycle;

[0025] Step 9: Get the linkage layout;

[0026] The rod density ρ obtained from the current MMA ij , when the rod density ρ ij ≈1 indicates D i and D j A rod exists between two points when the rod density ρ ij ≈0 means D i and D j There is no rod between the two points, according to the rod density ρ ij Get the linkage layout.

[0027] Preferably, the initial rod density ρ in step 2 is ij Set the value to 0.3.

[0028] Preferably, in step 2, the rod length is obtained according to the following formula:

[0029]

[0030] Among them, l ij D i and D j The length of the rod between i ,y i ) is point D i The coordinates of (x j ,y j ) is point D j 's coordinates, and i≠j.

[0031] Preferably, the functional relationship between the moving point and the force point determined in step 3 is:

[0032]

[0033] Among them, (x 受力 ,y 受力 ) is the coordinate value of the force point, (x 运动 ,y 运动 ) are the corresponding moving point coordinate values; f1() and f2() are obtained by fitting.

[0034] Preferably, in step 5, the inner layer solution formula is:

[0035]

[0036] Among them, obj q When the displacement of the force point to the coordinate position q is based on the rod density ρ ij The obtained rod length difference, W is the number of points in the point set D, ρ ij D i and D j Rod density of the rod between two points, L ij is D determined by gradient descent method i and D j The length of the rod between <j,D i , D j ∈D,l ij is the initial D obtained in step 2 i and D j The length of the rod between them, n is the number of iterations, g n is the gradient at the nth iteration, λ n is the learning rate at the nth iteration, i.e., the step size in the gradient descent method, XY n is the vector consisting of the coordinates of the points in set D after the nth iteration, Initial XY 0 The coordinates in are the coordinates of the point set D in step 1, except that the coordinates of the force point and the moving point are modified to the coordinates after the movement.

[0037] Preferably, the gradient descent method is an adaptive gradient descent algorithm, and the adaptive step size adjustment formula is as follows:

[0038]

[0039] Among them, g n is the gradient at the nth iteration, r n It represents the cumulative sum of all squared gradients at the nth iteration, and ε is a set value to prevent the denominator from being zero.

[0040] Preferably, the sensitivity in step 6 is:

[0041]

[0042] Among them, ρ ij is the density of the rod, there are Ne variables in total, and the sensitivity is and A 1*Ne vector obtained by vector multiplication.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] (1) The present invention proposes a topological model of the linkage mechanism layout, which has the advantages of being simple, universal, and easy to solve.

[0045] (2) In the process of solving the model, the present invention combines the gradient descent method and the MMA algorithm, thereby simplifying the process of solving the model.

[0046] (3) The connecting rod structure obtained by the method established by the present invention ensures that the moving point moves along the prescribed trajectory and has good movement accuracy and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Flowchart of a method for obtaining a linkage layout for a specified motion trajectory

[0048] Figure 2 It is a schematic diagram of the area range and vertices in Example 1;

[0049] Figure 3 is a schematic diagram of the initial structure of the connecting rod structure in Example 1;

[0050] Figure 4 is a schematic diagram of the final structure of the connecting rod structure in Example 1;

[0051] Figure 5 : is the error diagram between the motion trajectory of the connecting rod structure in Example 1 and the target trajectory. DETAILED DESCRIPTION

[0052] The exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.

[0053] The present invention provides a method for obtaining a linkage layout of a specified motion trajectory, such as Figure 1 As shown, it includes the following steps:

[0054] Step 1: Establish the linkage structure coordinate system and obtain the initial linkage mechanism layout.

[0055] Determine the area range of the linkage mechanism in the initial state. The area range is a rectangle. Take one vertex of the area range as the origin, one side passing through this vertex as the X-axis, and the other side as the Y-axis to establish the linkage structure coordinate system.

[0056] In the connecting rod structure coordinate system, points are taken in sequence from the origin on the X-axis and Y-axis within the region with the set minimum length of the rod. When the distance between the point and the edge of the region is less than the set minimum length of the rod, the point taking ends, and the intersection of the region and the axis is taken as the last point. At this time, there are A points on the X-axis including the origin, and B points on the Y-axis including the origin, where A and B are both positive integers. According to the points on the X-axis and the points on the Y-axis, a mesh structure is formed within the region after extending parallel to the X-axis and the Y-axis, which includes W = A × B intersections within the region, recorded as point set D, D = {D1, D2, …, D w}, the coordinates of D1 are (x1, y1), the coordinates of D2 are (x2, y2), ..., D W The coordinates of (x W ,y W ).

[0057] Each point in the mesh structure is regarded as the vertex of the rod, and all points are connected in pairs as the initial linkage mechanism layout. At this time, the initial linkage mechanism layout includes N e Total number of poles .

[0058] Step 2: Get the rod length, rod density and target number of rods for each rod.

[0059] Select any two points D from the point set D in step 1 i and D j , the obtained rod length is:

[0060]

[0061] Among them, l ij D i and D j The length of the rod between i ,y i ) is point D i The coordinates of (x j ,y j ) is point D j 's coordinates, and i≠j.

[0062] Initialize D i and D j The rod density ρ of the rod between two points ij , ρ ij The value represents D i and D j The probability of the existence of a rod between two points is when the rod density ρ ij =1 indicates D i and D j A rod exists between two points when the rod density ρ ij =0 means Di and D j There is no rod between the two points. The rod density ρ of all rods at the beginning is ij are the same and can be set to 0.2≤ρ ij ≤0.5, preferably ρ ij =0.3.

[0063] The total number of rods in the initial linkage layout is N e , so we need to calculate N e The length of each rod is initialized, and the rod density is initialized for each rod. Get the preset target number of rods N, 2≤N≤N e .

[0064] Step 3: Determine the functional relationship between the moving point and the force point.

[0065] According to actual needs, in the initial linkage mechanism layout, select the force point P where the force is applied and the motion point M that moves along the specified trajectory, move the force point P to the specified coordinate position, and obtain the corresponding coordinate position of the force point P. According to the coordinate values ​​of multiple force points P (x 受力 ,y 受力 ) and the corresponding moving point M coordinate value (x 运动 ,y 运动 ), the functional relationship between the coordinates of the force point and the coordinates of the motion point is obtained:

[0066]

[0067] Among them, (x 受力 ,y 受力 ) is the coordinate value of the force point P, (x 运动 ,y 运动 ) is the coordinate value of the corresponding moving point M, and f1() and f2() are obtained by fitting.

[0068] Step 4: Establish a topological model of the linkage mechanism layout.

[0069] The goal of the rod mechanism layout is that when the force point moves along the predetermined trajectory, the obtained moving point also moves along the preset target trajectory. Therefore, by selecting Q positions on the predetermined trajectory of the force point, according to the functional relationship between the moving point and the force point in step 3, the position of the corresponding moving point is obtained as the target position, and the position reached by the actual moving point of the linkage mechanism is compared with the target position as the objective function.

[0070] In order to obtain the layout of the linkage mechanism, three constraints are included: the first is that when the force point moves, the change in rod length is minimal; the second is the limit on the number of rods; and the third is that the rod density can only be between [0, 1].

[0071] According to the objective function and constraints, the topological model of the linkage mechanism layout is obtained as follows:

[0072]

[0073] 0≤ρ ij ≤1 (6)

[0074] Among them, formula (3) is the objective function, formula (4) is the first constraint condition, formula (5) is the second constraint condition, and formula (6) is the third constraint condition; q is a position of the force point on the predetermined trajectory, and a total of Q positions are selected, p q目标 is the coordinate of the moving point when the force point is at position q, obtained according to the functional relationship between the moving point and the force point in step 3, p q obj is the coordinate of the moving point when the force point is at position q, obtained according to the determined linkage mechanism; q When q is the position q of the force point on the predetermined trajectory, the change of the rod length is the smallest; W is the number of points in the point set D, ρ ij D i and D j Rod density of the rod between two points, L ij is D obtained according to the current linkage layout i and D j The length of the rod between <j,D i , D j ∈D,l ij is the initial D obtained in step 2 i and D j The length of the rod between; N is the preset target number of rods, ε1 is the set value. Since the optimization process must be closest to N, a certain range must be given, and ε1 is a set minimum value.

[0075] According to the topological model analysis of the linkage layout, in order to obtain the linkage layout, the overall process is divided into inner layer operation and outer layer optimization. The inner layer operation is obtained by using the gradient descent method. When applying the specified displacement, all current rods and corresponding rod densities are applied to obtain the coordinates of each point after the rod displacement caused by the structure. The outer layer optimization uses the MMA algorithm to achieve the rod density ρ ij Optimization.

[0076] Step 5: Use the gradient descent method to obtain the coordinates of each point at Q positions.

[0077] When the displacement of the force point is specified to position q, the corresponding horizontal or vertical coordinate position of the moving point is specified. It should be noted that the position of the moving point cannot be fixed at this time, and space must be reserved for subsequent optimization. Then, the inner layer solution formula is used to apply the gradient descent method to obtain the coordinates of the rod vertices caused by the current linkage mechanism layout when the displacement of the force point is to the specified position. The inner layer solution formula is:

[0078]

[0079] XY n+1 =XY n -λ n o n (8)

[0080]

[0081] Among them, obj q When the displacement of the force point to the coordinate position q is based on the rod density ρ ij The obtained rod length difference, W is the number of points in the point set D, ρ ij D i and D j Rod density of the rod between two points, L ij is D determined by gradient descent method i and D j The length of the rod between <j,D i , D j ∈D,l ij is the initial D obtained in step 2 i and D j The length of the rod between them, n is the number of iterations, g n is the gradient at the nth iteration, λ n is the learning rate at the nth iteration, i.e., the step size in the gradient descent method, XY n is the vector consisting of the coordinates of the points in set D after the nth iteration, , initial XY 0 The coordinates in are the coordinates of the point set D in step 1, except that the coordinates of the force point and the moving point are modified to the coordinates after the movement.

[0082] The gradient descent method can be preferably an adaptive gradient descent algorithm. The characteristics of the adaptive gradient descent algorithm are that the step size is large in the early stage, which can converge quickly, and the step size is small in the later stage, which can adjust the model parameters more finely. The adaptive step size adjustment formula is selected as follows:

[0083]

[0084] Among them, g n is the gradient at the nth iteration, r n It represents the cumulative sum of all squared gradients at the nth iteration, and ε is a set value, usually a very small number, to prevent the denominator from being zero.

[0085] According to formulas (7)-(9), the gradient descent method is used to obtain obj qThe minimum XY value, using the gradient descent method for Q positions, then there are Q sets of XY values, so the XY value can be (XY) q Indicates that at this time (XY) q The value is obj q The coordinates of each point in the minimum time point set D. Further based on the coordinates of each point and the formula in step 2, we can obtain L at this time ij The value of .

[0086] For Q positions, the gradient descent method is used to obtain the displacement of the force point to the coordinate position q, obj q Minimum (XY) q Value coordinates such that the first constraint is satisfied.

[0087] Step 6: Determine sensitivity.

[0088] The sensitivity is obtained by differentiating the rod density according to the objective function c, but because the objective function c does not directly include the solution quantity ρ ij , so the sensitivity needs to be obtained using the implicit method, and the sensitivity is:

[0089]

[0090] Among them, (XY) q It is a 1*2W vector, that is (XY) q Contains a set of x and y coordinates of W points when the force point is displaced to the coordinate position q, ρ ij is the density of the rods, there are Ne variables in total, so the is a 2W*Ne matrix. Since c is a set of relations containing the XY coordinates of Q positions, It is necessary to convert the qth (XY) q Substitute the value into the solution, that is Then sum the formulas obtained at these Q positions to get The vector size is 1*2W. Therefore, the sensitivity is and A 1*Ne vector obtained by vector multiplication.

[0091] Step 7: Use the MMA algorithm to obtain the rod density.

[0092] The MMA algorithm is used to optimize the rod density. ij As the design variable of the MMA algorithm, the objective function c obtained according to the coordinates of step 5 is used as the objective function of MMA, and the sensitivity to the rod density ρ ij The optimization is performed, and the second and third constraints need to be met during the optimization process. The optimized rod density ρ is obtained by using the existing MMA algorithm ij, because there are N e rods, so the optimized N e Rod density.

[0093] Step 8: Loop judgment.

[0094] Determine whether the objective function c is less than the predetermined value ε2 or the number of loops reaches the maximum value. If so, stop the loop and execute step 9. If neither is satisfied, use the rod density ρ obtained in the current step 7. ij Return to step 5, which now uses the updated rod density ρ ij Start a new cycle and add 1 to the number of loops as the new number of loops. The initial value of the number of loops is 0.

[0095] Step 9: Get the linkage layout.

[0096] The rod density ρ obtained from the current MMA ij , when the rod density ρ ij =1 indicates D i and D j A rod exists between two points when the rod density ρ ij =0 means D i and D j There is no rod between the two points, according to the rod density ρ ij The layout of the linkage mechanism is obtained. However, since the actual optimization process uses the approximation objective function, the rod density ρ ij It is impossible to have only two values ​​of 0 and 1, so in practice, when the rod density ρ ij ≈1 indicates D i and D j A rod exists between two points when the rod density ρ ij ≈0 means D i and D j There is no rod between the two points, according to the rod density ρ ij Get the linkage layout.

[0097] Example 1

[0098] This implementation case is to obtain a linkage mechanism layout that can move in a straight line.

[0099] Step 1: Establish the linkage structure coordinate system and obtain the initial linkage mechanism layout.

[0100] First, determine the initial state of the linkage mechanism as a rectangular area of ​​30cm*20cm. Take a vertex of the region as the origin, one side passing through this vertex as the X-axis, and the other side as the Y-axis to establish the linkage structure coordinate system. The minimum length of the rod is 10cm. Therefore, there are 4 points on the X-axis, including 0, 1, 2, and 3 points, and 3 points on the Y-axis, including 0, 1, and 2 points. Through the points on the X-axis and Y-axis, a mesh structure is formed within the region, including 12 points in total, such as Figure 2 As shown, each point in the mesh structure is taken as the vertex of the rod, and all points are connected in pairs as the initial linkage mechanism layout, as shown in Figure 3 At this time, the initial linkage layout includes a total number of rods

[0101] For the convenience of description in this embodiment, the side length of the area range is set to an integer multiple of the minimum length of the rod. In practice, the area range may be 35cm*23cm, then the coordinate values ​​of the points on the X-axis are 0, 1, 2 and 3.5 respectively, and the coordinate values ​​of the points on the Y-axis are 0, 1 and 2.3 respectively.

[0102] Step 2: Get the rod length, rod density and target number of rods for each rod.

[0103] The total number of rods N obtained from step 1 e The target number N is preset to N = 5. Set the initial density ρ of each rod ij are all 0.3, where ρ ij D i

[0104] and D j The rod density of the rods between two points.

[0105] Step 3: Determine the functional relationship between the moving point and the force point.

[0106] In this embodiment, in the connecting rod structure coordinate system, a point with coordinates (0, 2) is selected, that is, Figure 3 Point 1 in the figure is taken as the force point, and the force point moves downward along the Y axis. The point with coordinates (3, 1) is selected, that is, Figure 3 Point 11 in the figure is used as the moving point, and the moving point moves in a horizontal straight line.

[0107] Therefore, when the force point P is initially located at (0, 2), the moving point M is located at (3, 1). When the force point P moves to (0, 1.5), the moving point M is located at (3.6, 1). When the receiving point P moves to (0, 1) at its maximum, the displacement point is (4.2, 1). The functional relationship between the coordinates of the force point and the coordinates of the moving point is obtained by fitting:

[0108]

[0109] Step 4: Establish a topological model of the linkage mechanism layout.

[0110] The goal of the rod mechanism layout is that when the force point moves along the predetermined trajectory, the obtained moving point also moves along the preset target trajectory. Therefore, by selecting Q positions on the predetermined trajectory of the force point, according to the functional relationship between the moving point and the force point in step 3, the position of the corresponding moving point is obtained as the target position, and the position reached by the actual moving point of the linkage mechanism is compared with the target position as the objective function.

[0111] In order to obtain the layout of the linkage mechanism, three constraints are included: the first is that when the force point moves, the change in rod length is minimal; the second is the limit on the number of rods; and the third is that the rod density can only be between [0, 1].

[0112] In this embodiment, five positions are selected on the predetermined trajectory of the force point, so the topological model of the linkage mechanism layout is obtained according to the objective function and the constraint conditions and is embodied as follows:

[0113]

[0114] 0≤ρ ij ≤1 (6)

[0115] Among them, formula (3) is the objective function, formula (4) is the first constraint condition, formula (5) is the second constraint condition, and formula (6) is the third constraint condition; q is a position of the force point on the predetermined trajectory, and a total of 5 positions are selected, p q目标 is the coordinate of the moving point when the force point is at position q, obtained according to the functional relationship between the moving point and the force point in step 3, p q obj is the coordinate of the moving point when the force point is at position q, obtained according to the determined linkage mechanism; q When q is the position q of the force point on the predetermined trajectory, the rod length changes the least; there are 12 points in the point set D, ρ ij D i and D j Rod density of the rod between two points, L ij is D obtained according to the current linkage layout i and D j The length of the rod between <j,D i , D j ∈D,l ij is the initial D obtained in step 2 i and D j The preset target number of strokes is 5 and ε1 is set to 0.02.

[0116] Step 5: Use the gradient descent method to obtain the coordinates of each point at Q positions.

[0117] When the displacement of the force point is specified to position q, the corresponding horizontal or vertical coordinate position of the moving point is specified. It should be noted that the position of the moving point cannot be fixed at this time, and space must be reserved for subsequent optimization. Then, the inner layer solution formula is used to apply the gradient descent method to obtain the coordinates of the rod vertices when the displacement of the force point is to the specified position and the current linkage mechanism layout is applied. The inner layer solution formula is:

[0118]

[0119] XY n+1 =XY n -λ n g n (8)

[0120]

[0121] According to the coordinates of point set D in step 1, as well as the coordinates of the determined force point and motion point, determine the initial XY 0 =[0,0,0,1,1,1,2,2,2,3,3,3,1,1,0,2,1,0,2,1,0,2,1,0], because in this embodiment, the y value of point 11 is a fixed value, and only one of the coordinate values ​​of the x and y axes of the moving point can be set to a fixed value, so y is selected as the fixed value and x is the original value unchanged. The adaptive gradient descent algorithm is used to obtain the XY value of obj1 when it is the smallest. According to the XY value, L ij When step 5 is executed for the first time, ρ ij The initial value is set to 0.3.

[0122] This method is used for 5 positions respectively, and the displacement of 5 force points to 5 different coordinate positions is obtained respectively. q The minimum XY q Value coordinates such that the first constraint is satisfied.

[0123] Step 6: Determine sensitivity.

[0124] The sensitivity formula is obtained by taking the derivative of the rod density according to the objective function c;

[0125]

[0126] Among them, (XY) q It is a 1*24 vector. In this embodiment, there are 12 points, so there are 24 coordinate values ​​(XY) q , ρ ij is the density of the rods, there are a total of Ne = 66 variables, so the is a 24*66 matrix. Since c is a set of relations containing the XY coordinates of Q positions, It is necessary to convert the qth (XY) q Substitute the value into the solution, that is Then sum the formulas obtained at these Q positions, which is The size of this vector is 1*24. Therefore, the objective function is and The multiplication of the two matrices is a 1*66 vector.

[0127] Step 7: Use the MMA algorithm to obtain the rod density.

[0128] The MMA algorithm is used to optimize the rod density. ij As the design variables of the MMA algorithm, there are 66 rods in total, so there are 66 design variables. The objective function c obtained from the coordinates of step 5 is used as the objective function of MMA. According to the sensitivity to the rod density ρ ij During the optimization process, the second constraint and the third constraint need to be met.

[0129] Step 8: Loop judgment.

[0130] Determine whether the objective function c is less than the predetermined value ε2=10 -3 Or the number of cycles 1000 reaches the set maximum value. If so, stop the cycle and execute step 10. If neither of them is reached, use the rod density ρ obtained by the previous MMA. ij Return to step 5 to continue the loop, and add 1 to the number of loops as the new number of loops. The initial value of the number of loops is 0.

[0131] Step 9: Get the linkage layout.

[0132] The rod density ρ obtained from the current MMA ij , when the rod density ρ ij ≈1 indicates D i and D j A rod exists between two points when the rod density ρ ij ≈0 means D i and D j There is no rod between the two points. According to the rod density ρ ij Get the linkage layout. According to the rod density ρ ij Get the linkage layout, such as Figure 4 shown.

[0133] In this embodiment, the relative error between the motion trajectory of the moving point and the target trajectory is measured according to the obtained linkage mechanism layout. The result is as follows: Figure 5As shown, the horizontal axis is the displacement of the force point on the Y axis, and the relative error h is controlled below 0.1.

[0134] The embodiments described above are only descriptions of the preferred implementation modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for obtaining a linkage layout of a specified motion trajectory, characterized in that: It includes the following steps: Step 1: Establish the linkage structure coordinate system and obtain the initial linkage mechanism layout; Determine the region range of the linkage mechanism in the initial state and establish the linkage structure coordinate system; establish a mesh structure within the region range, and each point in the mesh structure is used as the vertex of the rod. There are a total of W points, forming a point set D = {D1, D2, ..., D w }, all points are connected in pairs as the initial linkage layout, which includes N e root pole; Step 2: Get the rod length, rod density and target number of rods for each rod; Select any two points D from the point set D in step 1 i and D j , the obtained rod length l ij , i≠j; initial rod density ρ ij is the set value, 0.2≤ρ ij ≤0.5, target number of strokes N is the set value, 2≤N≤N e ; Step 3: Determine the functional relationship between the moving point and the force point; Step 4: Establish a topological model of the linkage mechanism layout; The topological model of the linkage mechanism layout is: 0≤ρ ij ≤1 (6) Among them, q is the position of the force point on the predetermined trajectory, p q目标 is the coordinate of the moving point when the force point is at position q, obtained according to the functional relationship between the moving point and the force point in step 3, p q obj is the coordinate of the moving point when the force point is at position q, obtained according to the determined linkage mechanism; q When q is the position q of the force point on the predetermined trajectory, the change of the rod length is the smallest; W is the number of points in the point set D, ρ ij D i and D j Rod density of the rod between two points, L ij is D obtained according to the current linkage layout i and D j The length of the rod between <j,D i , D j ∈D,l ij is the initial D obtained in step 2 i and D j The length of the rod between; N is the preset target number of rods, ε1 is the set value; Step 5: Use the gradient descent method to obtain the coordinates of each point at Q positions; Select Q positions on the predetermined trajectory of the force point. For position q, specify the corresponding horizontal or vertical coordinate position of the moving point at this time. Use the inner solution formula to apply the gradient descent method to obtain the coordinates (XY) of the rod vertices when the force point moves to the specified position q. q ; Step 6: Determine sensitivity; The sensitivity is obtained by differentiating the rod density according to the objective function c; Step 7: Use MMA algorithm to obtain the rod density; The rod density ρ ij As the design variable of the MMA algorithm, the objective function c obtained according to the coordinates of step 5 is used as the objective function of MMA, and the sensitivity to the rod density ρ ij Optimize, and the second constraint and the third constraint need to be satisfied during the optimization process; Step 8: Loop judgment; Determine whether the objective function c is less than the predetermined value or the number of loops reaches the maximum value. If so, stop the loop and execute step 9. If neither is satisfied, use the rod density ρ obtained in the current step 7. ij Return to step 5, which now uses the updated rod density ρ ij Start a new cycle; Step 9: Get the linkage layout; The rod density ρ obtained from the current MMA ij , when the rod density ρ ij ≈1 indicates D i and D j A rod exists between two points when the rod density ρ ij ≈0 means D i and D j There is no rod between the two points, according to the rod density ρ ij Get the linkage layout.

2. The method for obtaining a linkage layout of a specified motion trajectory according to claim 1, characterized in that: In step 2, the initial rod density ρ ij Set the value to 0.

3.

3. The method for obtaining a linkage layout of a specified motion trajectory according to claim 1, characterized in that: In step 2, the rod length is obtained according to the following formula: Among them, l ij D i and D j The length of the rod between i ,y i ) is point D i The coordinates of (x j ,y j ) is point D j 's coordinates, and i≠j.

4. The method for obtaining a linkage layout of a specified motion trajectory according to claim 1, characterized in that: The functional relationship between the moving point and the force point in step 3 is: Among them, (x 受力 ,y 受力 ) is the coordinate value of the force point, (x 运动 ,y 运动 ) are the corresponding moving point coordinate values; f1() and f2() are obtained by fitting.

5. The method for obtaining a linkage layout of a specified motion trajectory according to claim 1, characterized in that: In step 5, the inner solution formula is: Among them, obj q When the displacement of the force point to the coordinate position q is based on the rod density ρ ij The obtained rod length difference, W is the number of points in the point set D, ρ ij D i and D j Rod density of the rod between two points, L ij is D determined by gradient descent method i and D j The length of the rod between <j,D i , D j ∈D,l ij is the initial D obtained in step 2 i and D j The length of the rod between them, n is the number of iterations, g n is the gradient at the nth iteration, λ n is the learning rate at the nth iteration, i.e., the step size in the gradient descent method, XY n is the vector consisting of the coordinates of the points in set D after the nth iteration, Initial XY 0 The coordinates in are the coordinates of the point set D in step 1, except that the coordinates of the force point and the moving point are modified to the coordinates after the movement.

6. The method for obtaining a linkage layout of a specified motion trajectory according to claim 5, characterized in that: The gradient descent method is an adaptive gradient descent algorithm, and the adaptive step size adjustment formula is as follows: where g n is the gradient at the nth iteration, r n It represents the cumulative sum of all squared gradients at the nth iteration, and ε is a set value to prevent the denominator from being zero.

7. The method for obtaining a linkage layout of a specified motion trajectory according to claim 1, characterized in that: The sensitivity in step 6 is: Among them, ρ ij is the density of the rod, there are Ne variables in total, and the sensitivity is and A 1*Ne vector obtained by vector multiplication.

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