A topological design optimization method and optimized structure of a connecting rod jumping mechanism

Abstract

The present invention belongs to the technical field of connecting rod jump mechanism design optimization methods, and specifically relates to a topological design optimization method and optimized structure of a connecting rod jump mechanism. Based on the optimization of the connecting rod jump mechanism, the present invention proposes the division of design domain and non-design domain, which can ensure the calculation convergence and high efficiency to design the jump mechanism. At the same time, after obtaining the connecting rod configuration that meets the functional requirements, an optimization method for the connecting rod size parameters and the number of energy storage springs, stiffness value and installation position based on the energy angle is proposed. Compared with the traditional method for optimizing the connecting rod size parameters, the method of the present invention avoids establishing the relationship between the position of each rod and the input angle through formula deduction, but obtains the position of the rod at each moment based on the principle of energy minimization, which can realize the automatic comprehensive optimization of different connecting rod configurations and can effectively improve the calculation efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of connecting rod jumping mechanism design optimization methods, and in particular relates to a topological design optimization method and an optimized structure of a connecting rod jumping mechanism. Background Art

[0002] As a mobile platform, two-wheeled robots have unique movement capabilities and flexibility. Compared with traditional wheeled mobile robots, two-wheeled robots can achieve more stable and efficient movement in complex environments through self-balancing mechanisms. In order to achieve efficient jumping, two-wheeled robots often use connecting rod jumping mechanisms as jumping devices, such as Acento's four-link configuration and Oline's five-link configuration. These connecting rod jumping mechanism configurations generally establish the relationship between the position of each rod and the input angle through formula derivation, which makes it difficult to achieve deeper optimization and has low calculation efficiency. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the defect of low optimization efficiency of the optimization method of the connecting rod jumping mechanism in the prior art, thereby providing a topological design optimization method and an optimization structure of the connecting rod jumping mechanism.

[0004] A topological design optimization method for a connecting rod jumping mechanism comprises the following steps:

[0005] Step S1: Divide the design domain and non-design domain in the connecting rod jump mechanism, take the deformation parameters of the spring and the rigid block as the design variables, take the power transmittance as the objective function, take the tracking trajectory error as the constraint function, and output the topological configuration based on the SBM method;

[0006] Step S2: taking the shape parameters of the rigid block as optimization variables, taking the straightness error of the foot end trajectory as the constraint target, and minimizing the change in the direction of the velocity vector of the foot end trajectory;

[0007] Step S3: Taking the energy storage spring stiffness value as the optimization variable and the peak torque of the driving motor as the constraint target, the spring energy storage is maximized.

[0008] Furthermore, the step S1 includes the following method steps:

[0009] Step S1.1: Divide the design domain and non-design domain in the connecting rod jump mechanism;

[0010] Step S1.2: Interpolate the deformation parameters of the spring using the SIMP method:

[0011] ;

[0012] in, is the penalty coefficient, is the coefficient of variation of the spring, is the maximum stiffness of the spring, is the spring number, Indicates the total amount of connecting springs and anchoring springs;

[0013] Step S1.3: Calculate the deformation parameters of the rigid block:

[0014] ;

[0015] Where x and y represent the position vector of the center of the rigid block in the ground coordinate system, θ is the rotation angle of the rigid block, is the number of the rigid block, is the number of rigid blocks, for the moment;

[0016] Step S1.4: Calculate the virtual input force, end effector output work and average work transfer efficiency of the link jump mechanism;

[0017] ;

[0018] ;

[0019] ;

[0020] in, is the virtual input force, and its direction is opposite to the direction of motion of the output block; Output work for the end effector; is the average work transfer efficiency during the exercise cycle; for The work transfer efficiency at each moment; is the internal energy stored in the spring; For the i-th block in The state quantity at the moment; N is the output block number; for The horizontal coordinate of the ideal trajectory at the moment; for The ordinate of the ideal trajectory at each moment; for The horizontal coordinate of the ideal trajectory at the moment; for The ideal trajectory ordinate at each moment, is the unit force in the opposite direction of the ideal trajectory, T represents the number of divided time nodes, express Moment The status parameter of an output block.

[0021] Furthermore, the step S1.1 includes the following method steps: dividing the connecting rod jumping mechanism into rectangular rigid blocks arranged in a matrix of multiple rows and columns; adjacent corner points of adjacent rigid blocks define connecting springs, and each corner point of each rigid block is connected to an anchoring spring; the area of ​​the rigid block connected to the fuselage is defined as an anchoring area, the design area includes the area of ​​the rigid block where there is a hinge between the connecting rods, that is, the design domain, and the area of ​​the remaining rigid blocks is defined as a non-design domain; the anchoring springs connected to all corner points in the anchoring area are defined as design anchoring springs, and other anchoring springs are defined as non-design anchoring springs; the connecting springs connected to all corner points in the design area are defined as design connecting springs, and other connecting springs are defined as non-design connecting springs; the stiffness values ​​of all non-design anchoring springs are defined as zero; the rigid blocks connected by all non-design connecting springs are defined as being fixed to each other to form a rigid body.

[0022] Furthermore, step S2 includes the following method steps:

[0023] Step S2.1: Establish the calculation formula for minimizing the change in the direction of the foot-end trajectory velocity vector of the connecting rod jumping mechanism:

[0024] ;

[0025] in, is the number of steps, is the velocity direction change of the terminal trajectory, is the velocity direction of the terminal trajectory at time k, is the velocity direction of the terminal trajectory at time k+1;

[0026] ;

[0027] ;

[0028] in, and is the corresponding coordinate of the terminal trajectory, and its subscript indicates the corresponding time;

[0029] Step S2.2: Establish the calculation formula of the foot end trajectory straightness error:

[0030] 。

[0031] Furthermore, step S3 includes the following method steps:

[0032] Step S3.1: Establish the spring energy storage calculation formula of the connecting rod jumping mechanism:

[0033] ;

[0034] in, is the number of steps; for The stiffness value of the coil spring at the hinge point; for The travel angle of the coil spring at the hinge point; m is the total number of hinge points; represents the energy storage of the i-th energy storage spring; The torque value required for the driving motor at the t moment;

[0035] Step S3.2: Establish a calculation formula for the peak torque of the drive motor:

[0036] 。

[0037] A topological design optimization structure of a connecting rod jumping mechanism is formed by design optimization using any of the above methods.

[0038] Furthermore, the topological design optimized structure is a six-link jumping mechanism, including a first rod, a second rod, a third rod, a fourth rod, a fifth rod, a hip joint motor, an energy storage spring and a wheel-side motor; the first end of the fifth rod is hinged to the fuselage and is driven to rotate by the hip joint motor; the first end of the first rod is hinged to the fuselage, and the second end is hinged to the first end of the second rod; the second end of the second rod is hinged to the second end of the third rod, and the third end is hinged to the first end of the fourth rod; the first end of the third rod is hinged to the fuselage; the fourth rod is hinged to the fifth rod, and a wheel is installed on the second end, and the wheel-side motor is used to drive the wheel.

[0039] Beneficial effects: The present invention proposes the division of design domain and non-design domain based on the optimization of the connecting rod jumping mechanism, which can ensure the calculation convergence and high efficiency to design the jumping mechanism. At the same time, after obtaining the connecting rod configuration that meets the functional requirements, an optimization method for the connecting rod size parameters and the number of energy storage springs, stiffness value and installation position based on the energy angle is proposed. Compared with the traditional method of optimizing the connecting rod size parameters, the method of the present invention avoids establishing the relationship between the position of each rod and the input angle through formula deduction, but obtains the position of the rod at each moment based on the principle of energy minimization, which can realize the automatic comprehensive optimization of different connecting rod configurations and can effectively improve the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0041] Figure 1It is a schematic block diagram of the overall process of the present invention;

[0042] Figure 2 It is a schematic diagram of the jump structure of the present invention;

[0043] Figure 3 It is a schematic diagram of the rigid block of the present invention. DETAILED DESCRIPTION

[0044] In order to make the above-mentioned purpose, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth so as to fully understand the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present application, so the present application is not limited by the specific embodiments disclosed below. In the description of the present application, it is necessary to understand that the orientation or positional relationship indicated by the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", "axial", "radial", "circumferential" etc. is based on the orientation or positional relationship shown in the accompanying drawings, only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present application.

[0045] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0046] In this application, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0047] In the present application, unless otherwise clearly specified and limited, a first feature being “above” or “below” a second feature may mean that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. Moreover, a first feature being “above”, “above”, and “above” a second feature may mean that the first feature is directly above or obliquely above the second feature, or simply means that the first feature is higher in level than the second feature. A first feature being “below”, “below”, and “below” a second feature may mean that the first feature is directly below or obliquely below the second feature, or simply means that the first feature is lower in level than the second feature.

[0048] It should be noted that when an element is referred to as being "fixed to" or "disposed on" another element, it may be directly on the other element or there may be a central element. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be a central element at the same time. The terms "vertical", "horizontal", "upper", "lower", "left", "right" and similar expressions used herein are for illustrative purposes only and are not intended to be the only implementation method.

[0049] The present invention discloses a topological design optimization method for a connecting rod jumping mechanism, comprising the following method steps:

[0050] Step S1: Divide the design domain and non-design domain in the connecting rod jump mechanism, take the deformation parameters of the spring and rigid block as the design variables, take the power transmittance as the objective function, take the tracking trajectory error as the constraint function, and output the topological configuration based on the SBM method; the SBM method draws on the core idea of ​​variable density topology optimization (SIMP) in structural design. In this method, the structural unit that can be deformed and bear the load is regarded as a rigid unit cell in the connecting rod design area. At the same time, the density parameter of each structural unit is converted into the spring stiffness parameter connecting the rigid unit cell. The minimum energy consumption target of the structural topology optimization corresponds to the minimization of the internal energy of the spring in the SBM model. By representing the combination of kinematic pairs such as fixed pairs and rotating pairs through different combinations of spring stiffness, the heuristic design of the connecting rod mechanism "from scratch" is realized.

[0051] Step S1.1: Divide the design domain and non-design domain in the connecting rod jump mechanism;

[0052] Step S1.2: Interpolate the deformation parameters of the spring using the SIMP method:

[0053] ;

[0054] in, is the penalty coefficient, is the coefficient of variation of the spring, is the maximum stiffness of the spring, is the spring number, Indicates the total amount of connecting springs and anchoring springs;

[0055] Step S1.3: Calculate the state parameters of the rigid block:

[0056] ;

[0057] Where x and y represent the position vector of the center of the rigid block in the ground coordinate system, θ is the rotation angle of the rigid block, is the number of the rigid block, is the number of rigid blocks, for the moment;

[0058] Step S1.4: Calculate the virtual input force, end effector output work and average work transfer efficiency of the link jump mechanism;

[0059] ;

[0060] ;

[0061] ;

[0062] in, is the virtual input force, and its direction is opposite to the direction of motion of the output block; Output work for the end effector; is the average work transfer efficiency during the exercise cycle; for The work transfer efficiency at each moment; is the internal energy stored in the spring; For the i-th block in The state quantity at the moment; N is the output block number; for The horizontal coordinate of the ideal trajectory at the moment; for The ordinate of the ideal trajectory at each moment; for The horizontal coordinate of the ideal trajectory at the moment; for The ideal trajectory ordinate at each moment, is the unit force in the opposite direction of the ideal trajectory, T represents the number of divided time nodes, which is 37 in this embodiment, express Moment The state parameters of the output blocks, the others Same reason.

[0063] Step S2: taking the shape parameters of the rigid block as optimization variables, taking the straightness error of the foot end trajectory as the constraint target, and minimizing the change in the direction of the velocity vector of the foot end trajectory;

[0064] Step S2.1: Establish the calculation formula for minimizing the change in the direction of the foot-end trajectory velocity vector of the connecting rod jumping mechanism:

[0065] ;

[0066] in, is the number of steps, is the velocity direction change of the terminal trajectory, is the velocity direction of the terminal trajectory at time k, is the velocity direction of the terminal trajectory at time k+1;

[0067] ;

[0068] ;

[0069] in, and is the corresponding coordinate of the terminal trajectory, and its subscript indicates the corresponding time;

[0070] Step S2.2: Establish the calculation formula of the foot end trajectory straightness error:

[0071] 。

[0072] Step S3: Taking the energy storage spring stiffness value as the optimization variable and the peak torque of the driving motor as the constraint target, the spring energy storage is maximized.

[0073] Step S3.1: Establish the spring energy storage calculation formula of the connecting rod jumping mechanism:

[0074] ;

[0075] in, is the number of steps; for The stiffness value of the coil spring at the hinge point; for The travel angle of the coil spring at the hinge point; m is the total number of hinge points; represents the energy storage of the i-th energy storage spring; The torque value required for the driving motor at the t moment;

[0076] Step S3.2: Establish a calculation formula for the peak torque of the drive motor:

[0077] 。

[0078] The present invention proposes the division of design domain and non-design domain based on the optimization of the connecting rod jumping mechanism, which can ensure the calculation convergence and high efficiency to design the jumping mechanism. At the same time, after obtaining the connecting rod configuration that meets the functional requirements, an energy-based optimization method for the connecting rod size parameters and the number of energy storage springs, stiffness value and installation position is proposed. Compared with the traditional method for optimizing the connecting rod size parameters, the method of the present invention avoids establishing the relationship between the position of each rod and the input angle through formula deduction, but obtains the position of the rod at each moment based on the principle of energy minimization, which can realize the automatic comprehensive optimization of different connecting rod configurations and effectively improve the calculation efficiency.

[0079] Embodiment 1

[0080] Reference Figure 1~Figure 3 As shown, this embodiment discloses a topological design method of a six-link jumping mechanism, wherein the six-link jumping mechanism includes a first rod, a second rod, a third rod, a fourth rod, a fifth rod, a hip joint motor, an energy storage spring and a wheel-side motor; the first end of the fifth rod is hinged to the fuselage at point G and is driven to rotate by the hip joint motor; the first end of the first rod is hinged to the fuselage at point A, and the second end is hinged to the first end of the second rod at point B; the second end of the second rod is hinged to the second end of the third rod at point D, and the third end is hinged to the first end of the fourth rod at point F; the first end of the third rod is hinged to the fuselage at point C; the fourth rod is hinged to the fifth rod at point E, and the second end is equipped with a wheel at point H, and the wheel-side motor is used to drive the wheel.

[0081] A topological design method for a six-link jumping mechanism includes the following steps:

[0082] Step S1: Divide the design domain and non-design domain in the connecting rod jump mechanism, take the deformation parameters of the spring and the rigid block as the design variables, take the power transmittance as the objective function, take the tracking trajectory error as the constraint function, and output the topological configuration based on the SBM method;

[0083] Step S1.1: Divide the design domain and non-design domain in the connecting rod jump mechanism;

[0084] Specifically, the connecting rod jumping mechanism is divided into eighteen rectangular rigid blocks with six horizontal rows and three vertical columns, and the initial position state of each rigid block is defined as follows:

[0085] ;

[0086] Where I is the number of the rigid block, They are the horizontal coordinate, vertical coordinate and rotation angle of the center coordinate of rigid block I. Define the input block, output block, rotation excitation and foot-end output point in the rigid block; define the iterative rotation angle of the rotation excitation and the number of iterations; define the target trajectory of the foot-end output point and divide it into multiple nodes;

[0087] Specifically, the eighteen rigid blocks are divided into the first column, the second column and the third column from left to right. The first column is numbered 1 to 6 rigid blocks from top to bottom, the second column is numbered 7 to 12 rigid blocks from top to bottom, and the third column is numbered 13 to 18 rigid blocks from top to bottom.

[0088] The rigid block No. 2 is defined as an input block, its upper left corner point is the first end of the fifth rod, and is defined as a rotational excitation; the rigid block No. 6 is defined as an output block, its lower left corner point is the second end of the fourth rod, and is defined as a foot-end output point.

[0089] Adjacent corner points of adjacent rigid blocks are defined with connecting springs, and each corner point of each rigid block is connected to an anchor spring. Define the anchoring area, design area, and rigid body area; the anchoring area is the body area of ​​the jumping robot, including rigid blocks No. 1, No. 7, and the upper left and upper right corner points of rigid blocks No. 2, the upper left and upper right corner points of rigid blocks No. 8, the upper left and lower left corner points of rigid blocks No. 13, and the upper left corner point of rigid blocks No. 14. The design area includes rigid blocks No. 1, No. 2, No. 3, No. 7, No. 8, No. 9, No. 13, No. 14, No. 15, the upper left and upper right corner points of rigid blocks No. 4, the upper left and upper right corner points of rigid blocks No. 10, and the upper left and upper right corner points of rigid blocks No. 16. The rigid body area includes rigid block No. 5, rigid block No. 6, rigid block No. 11, rigid block No. 12, rigid block No. 17, rigid block No. 18, the lower left corner point and the lower right corner point of rigid block No. 4, the lower left corner point and the lower right corner point of rigid block No. 10, and the lower left corner point and the lower right corner point of rigid block No. 16.

[0090] The anchor springs connected at all corner points in the anchor area are defined as design anchor springs, and other anchor springs are defined as non-design anchor springs; the connection springs connected at all corner points in the design area are defined as design connection springs, and other connection springs are defined as non-design connection springs. The stiffness values ​​of all non-design anchor springs are defined as zero. The rigid blocks connected by all non-design connection springs are defined as being fixed to each other to form a rigid body.

[0091] Define the stiffness coefficient of the spring :

[0092] ;

[0093] in, is the spring stiffness, is the spring stiffness coefficient, and its value range is between 0 and 1; is the penalty coefficient, which is 3 in this embodiment; Indicates the total amount of connecting springs and anchoring springs; ; = .

[0094] Define the shape coefficient of the rigid block , represents the horizontal position of node j, represents the vertical position of node j, and 0.5 represents its origin. Therefore, the coordinates of the center of rigid block j at time 0 can be obtained from the shape parameter It is expressed as:

[0095] ;

[0096] in, Indicates the corresponding position of the node in the ground coordinate system at time 0 when the shape parameters have not changed; represents the rigid block length; Indicates the rigid block width.

[0097] The local coordinates of node j with respect to the rigid block can be expressed as:

[0098] ;

[0099] in, and Represents the coordinates of the center of the rigid block.

[0100] The spring length formula is derived from the coordinates of the center position of the moving rigid block, the angle of the rigid block, and the relative coordinate transformation of the nodes:

[0101] The spring length is:

[0102] ;

[0103] in, is the coordinate of the center position of the rigid block, subscript The numbers of the connecting springs are: is the number of the anchor spring; is the coordinate of the corresponding node in the local coordinate system of its rigid block; is the transformation matrix from the center coordinates of the rigid block to the local coordinates of the spring node, Indicates the rotation angle of the rigid block center at this moment relative to the initial moment (counterclockwise is positive);

[0104] The internal energy of the spring is:

[0105] ;

[0106] in, is the spring stiffness value of the ith connection, is the jth anchor spring stiffness value.

[0107] The sum of the internal energy of the spring is:

[0108] ;

[0109] Thus, the internal energy of the entire discrete domain is obtained. The connecting rod position is considered to be the optimal position at that moment that satisfies the static equilibrium equation, that is, the sum of the internal forces of the system is equal to the force exerted by the system on the outside world.

[0110] ;

[0111] in, are the horizontal coordinate, vertical coordinate and rotation angle of each rigid block center point in sequence; is the internal force of the system, is the external work done by the end effector of the system from time 0 to the current time, which is:

[0112] ;

[0113] in, It represents the external work done by the end effector of the system from time 0 to the current time. Indicates that the end effector is t The path of time, is the output force of the end effector:

[0114] ;

[0115] in, is the unit force in the opposite direction of the target path; is the target path point, and the target path is the ideal trajectory.

[0116] By solving the quasi-static equilibrium equation by Newton's method, we can obtain the Distribution of block positions at time As the input block rotates counterclockwise by a certain angle, the position state of the rigid block at all times can be obtained. .

[0117] In order to ensure the continuity, complete rotation and non-singularity of the link jump mechanism during the entire motion process, it is believed that the energy has two destinations: one is the increase of the internal energy, and the other is the output work of the end effector. When the mechanism does not meet the required characteristics, the internal energy of the system will increase abnormally. Therefore, the optimal link mechanism is obtained by minimizing the ratio of the internal energy of the link jump mechanism to the output work of the end effector. The final optimization problem is expressed as:

[0118] ;

[0119] in, is the average transmittance, which is the ratio of output power to input power; Ψ is the Euclidean distance between the actual and ideal paths, for Output the actual position of the end of the block at any moment, for Output the ideal position of the end of the block at any moment, is the number of node steps.

[0120] ;

[0121] in, Represents the Nth rigid block (i.e. output block) at time t state variables, Represents the transformation matrix from the local coordinate system of the rigid block to the global coordinate system, Represents the relative position of the output point to the center of the Nth rigid block.

[0122] The input work can be expressed as:

[0123] ;

[0124] The target accuracy point Add constraints to the optimization problem so that the path error is within a specified minimum value. Within , MMA (Method of Moving Asymptote) is used for iterative optimization.

[0125] Perform objective function sensitivity analysis:

[0126] ;

[0127] Perform constraint function sensitivity analysis:

[0128] ;

[0129] ;

[0130] Among them, for The state quantity of each rigid block at the moment , where the partial derivatives and differentials can be obtained by differentiating the function.

[0131] In order to ensure the stable balance of the connecting rod jumping mechanism during the energy storage process, the optimization goal is to minimize the change in the direction of the foot end trajectory velocity vector (i.e., the cumulative straightness error), the constraint target is the foot end trajectory straightness error ±5mm, and the design variable is the rigid block shape parameter :

[0132] ;

[0133] in, is the number of node steps, is the velocity change of the terminal trajectory, is the velocity of the terminal trajectory, For the The foot end output horizontal coordinate when walking, For the The foot end output ordinate when walking:

[0134] ;

[0135] Perform objective function sensitivity analysis:

[0136] ;

[0137] ;

[0138] ;

[0139]

[0140] Among them, the partial derivatives and differentials in the formula can be obtained by differentiating the function.

[0141] Perform constraint function sensitivity analysis:

[0142] in, , The solution of is given in the above method, and the remaining differentials can be obtained by differentiating the function.

[0143] Optimization design of energy storage spring stiffness;

[0144] The force analysis is performed on each rod, and the moment is taken for each hinge. Based on the ISBM, the block position distribution at each moment is obtained, and the relative position of each hinge and the relative change angle of the hinge can be obtained, and then the spring energy storage is obtained, and the force condition of each rod at each moment is obtained.

[0145] Under the condition of ensuring the peak torque of the driving motor, the jumping robot can obtain the maximum jumping height by configuring different spring stiffness values ​​at the hinge point. The optimization goal is to maximize the spring energy storage, and the constraint goal is the peak torque of the driving motor 35 , the design variable is the stiffness of the coil spring at the hinge point:

[0146] ;

[0147] in, is the number of node steps; for The stiffness value of the coil spring at the hinge point; For the To Within the time range Helical spring travel angle at hinge point; Represents the total number of energy storage springs installed. This configuration selects hinge points B, D, E, and F as the optimal hinge point locations; For the The torque value needs to be provided to drive the motor at all times.

[0148] Perform objective function sensitivity analysis:

[0149] ;

[0150] Perform constraint function sensitivity analysis:

[0151] ;

[0152] Step S1.2: Interpolate the deformation parameters of the spring using the SIMP method:

[0153] ;

[0154] in, is the penalty coefficient, is the coefficient of variation of the spring;

[0155] Step S1.3: Calculate the state parameters of the rigid block:

[0156] ;

[0157] Where x and y represent the position vector of the center of the rigid block in the ground coordinate system, and θ is the rotation angle of the rigid block;

[0158] Step S1.4: Calculate the virtual input force, end effector output work and average work transfer efficiency of the link jump mechanism;

[0159] ;

[0160] ;

[0161] ;

[0162] in, is the virtual input force, and its direction is opposite to the direction of motion of the output block; Output work for the end effector; is the average work transfer efficiency during the exercise cycle; is the internal energy stored in the spring; For the i-th block in The state quantity at the moment; N is the output block number; for The horizontal coordinate of the ideal trajectory at the moment; for The vertical coordinate of the ideal trajectory at each moment.

[0163] Step S2: taking the shape parameters of the rigid block as optimization variables, taking the straightness error of the foot end trajectory as the constraint target, and minimizing the change in the direction of the velocity vector of the foot end trajectory;

[0164] Step S2.1: Establish the calculation formula for minimizing the change in the direction of the foot-end trajectory velocity vector of the connecting rod jumping mechanism:

[0165] ;

[0166] in, For the number of steps, is the velocity change of the terminal trajectory, is the velocity of the terminal trajectory;

[0167] ;

[0168] ;

[0169] in, and is the corresponding coordinate of the terminal trajectory, and its subscript indicates the corresponding time;

[0170] Step S2.2: Establish the calculation formula of the foot end trajectory straightness error:

[0171] .

[0172] Step S3: Taking the energy storage spring stiffness value as the optimization variable and the peak torque of the driving motor as the constraint target, the spring energy storage is maximized.

[0173] Step S3.1: Establish the spring energy storage calculation formula of the connecting rod jumping mechanism:

[0174] ;

[0175] in, is the number of steps; for The stiffness value of the coil spring at the hinge point; for The travel angle of the coil spring at the hinge point; m is the total number of hinge points; represents the energy storage of the i-th energy storage spring; The torque value required for the driving motor at the t moment;

[0176] Step S3.2: Establish a calculation formula for the peak torque of the drive motor:

[0177] .

[0178] Specifically, refer to Figure 2 As shown:

[0179] ;

[0180] ;

[0181] ;

[0182] ;

[0183] ;

[0184] ;

[0185] The above formula is written in matrix form .in:

[0186] ;

[0187] Based on ISBM, the position distribution of each moment block is obtained, and the relative position of each hinge point and the relative change angle of the hinge point can be obtained, and then the spring energy storage can be obtained to obtain the A and B matrices.

[0188] ;

[0189] Therefore, based on the above, the stress condition of each rod at each moment can be obtained.

[0190] Under the condition of ensuring the peak torque of the driving motor, the jumping robot can obtain the maximum jumping height by configuring different spring stiffness values ​​at the hinge point. The optimization goal is to maximize the spring energy storage, and the constraint goal is the peak torque of the driving motor 35 , the design variable is the stiffness of the coil spring at the hinge point, as shown below:

[0191] ;

[0192] In the formula, is the number of node steps; for The stiffness value of the coil spring at the hinge point; For the To Within the time range Helical spring travel angle at hinge point; Represents the total number of energy storage springs installed. This configuration selects hinge points B, D, E, and F as the optimal hinge point locations; For the The torque value needs to be provided to drive the motor at all times.

[0193] Objective function sensitivity analysis:

[0194] ;

[0195] Constraint function sensitivity analysis:

[0196] .

[0197] Embodiment 2:

[0198] The second embodiment discloses a topological design optimization structure of a connecting rod jumping mechanism, which is designed and optimized by any method of the first embodiment.

[0199] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0200] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be construed as limiting the scope of the patent application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent application shall be subject to the attached claims.

Claims

1. A topological design optimization method for a connecting rod jumping mechanism, characterized in that: The method comprises the following steps: Step S1: Divide the design domain and non-design domain in the connecting rod jump mechanism, take the deformation parameters of the spring and the rigid block as the design variables, take the power transmittance as the objective function, take the tracking trajectory error as the constraint function, and output the topological configuration based on the SBM method; Step S2: taking the shape parameters of the rigid block as optimization variables, taking the straightness error of the foot end trajectory as the constraint target, and minimizing the change in the direction of the velocity vector of the foot end trajectory; Step S3: taking the energy storage spring stiffness value as the optimization variable and the peak torque of the driving motor as the constraint target to maximize the spring energy storage; The step S1 comprises the following method steps: Step S1.1: Divide the design domain and non-design domain in the connecting rod jump mechanism; Step S1.2: Interpolate the deformation parameters of the spring using the SIMP method: ； in, is the penalty coefficient, is the coefficient of variation of the spring, is the maximum stiffness of the spring, is the spring number, Indicates the total amount of connecting springs and anchoring springs; Step S1.3: Calculate the state parameters of the rigid block: ； Where x and y represent the position vector of the center of the rigid block in the ground coordinate system, θ is the rotation angle of the rigid block, is the number of the rigid block, is the number of rigid blocks, for the moment; Step S1.4: Calculate the virtual input force, end effector output work and average work transfer efficiency of the link jump mechanism; ； ； ； in, is the virtual input force, and its direction is opposite to the direction of motion of the output block; Output work for the end effector; is the average work transfer efficiency during the exercise cycle; for The work transfer efficiency at each moment; is the internal energy stored in the spring; For the i-th block in The state quantity at the moment; N is the output block number; for The horizontal coordinate of the ideal trajectory at the moment; for The ordinate of the ideal trajectory at each moment; for The horizontal coordinate of the ideal trajectory at the moment; for The ideal trajectory ordinate at each moment, is the unit force in the opposite direction of the ideal trajectory, T represents the number of divided time nodes, express Moment The status parameter of an output block.

2. The topological design optimization method of a connecting rod jumping mechanism according to claim 1, characterized in that: The step S1.1 includes the following method steps: dividing the connecting rod jumping mechanism into rectangular rigid blocks arranged in a matrix of multiple rows and columns; adjacent corner points of adjacent rigid blocks define connecting springs, and each corner point of each rigid block is connected to an anchoring spring; the area of ​​the rigid block connected to the fuselage is defined as an anchoring area, the design area includes the area of ​​the rigid block where there is a hinge between the connecting rods, that is, the design domain, and the area of ​​the remaining rigid blocks is defined as a non-design domain; the anchoring springs connected to all corner points in the anchoring area are defined as design anchoring springs, and other anchoring springs are defined as non-design anchoring springs; the connecting springs connected to all corner points in the design area are defined as design connecting springs, and other connecting springs are defined as non-design connecting springs; the stiffness values ​​of all non-design anchoring springs are defined as zero; the rigid blocks connected by all non-design connecting springs are defined as being fixed to each other to form a rigid body.

3. The topological design optimization method of a connecting rod jumping mechanism according to claim 1, characterized in that: The step S2 comprises the following method steps: Step S2.1: Establish the calculation formula for minimizing the change in the direction of the foot-end trajectory velocity vector of the connecting rod jumping mechanism: ； in, is the number of steps, is the velocity direction change of the terminal trajectory, is the velocity direction of the terminal trajectory at time k, is the velocity direction of the terminal trajectory at time k+1; ； ； in, and is the corresponding coordinate of the terminal trajectory, and its subscript indicates the corresponding time; Step S2.2: Establish the calculation formula of the foot end trajectory straightness error: 。 4. The topological design optimization method of a connecting rod jumping mechanism according to claim 1, characterized in that: The step S3 comprises the following method steps: Step S3.1: Establish the spring energy storage calculation formula of the connecting rod jumping mechanism: ； in, is the number of steps; for Coil spring at the hinge point; for The travel angle of the coil spring at the hinge point; m is the total number of hinge points; The torque value required for the driving motor at the t moment; Step S3.2: Establish a calculation formula for the peak torque of the drive motor: 。 5. A topological design optimization structure of a connecting rod jumping mechanism, characterized in that: The method described in any one of claims 1 to 4 is used to design and optimize the formation.

6. The topological design optimization structure of the connecting rod jumping mechanism according to claim 5, characterized in that: The topological design optimized structure is a six-link jumping mechanism, including a first rod, a second rod, a third rod, a fourth rod, a fifth rod, a hip joint motor, an energy storage spring and a wheel-side motor; the first end of the fifth rod is hinged to the fuselage and driven to rotate by the hip joint motor; the first end of the first rod is hinged to the fuselage, and the second end is hinged to the first end of the second rod; the second end of the second rod is hinged to the second end of the third rod, and the third end is hinged to the first end of the fourth rod; the first end of the third rod is hinged to the fuselage; the fourth rod is hinged to the fifth rod, and a wheel is installed on the second end, and the wheel-side motor is used to drive the wheel.

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