A passive variable stiffness joint profile design optimization method based on a preset response curve

Abstract

The application is a passive variable stiffness joint contour design optimization method based on a preset response curve, comprising the following steps: S1, constructing a basic unit; S2, forming a preset response curve; S3, analyzing according to the degree of freedom range and rated torque of the basic unit and the curve requirement of the preset response curve, and obtaining corresponding constraint data; S4, calculating the constraint equation based on the spring according to the stress analysis of the spring in the basic unit, and then determining the coordinates of the contact point to obtain the overall shape of the cam contour curve in the basic unit; S5, optimizing the cam contour curve; S6, determining the optimization parameters of the spring; S7, obtaining the constraint equation about the optimization parameters according to the geometric relationship and stress analysis of the optimized basic unit, and finally calculating the optimized data according to the constraint equation. The application is inversely designed and optimized based on the mechanical response curve of "displacement-force and angle-torque", so that the passive variable stiffness design has a trace to follow, and the overload capacity is excellent.

Description

Technical Field

[0001] This invention relates to the field of robot joint technology, and more specifically, to a method for optimizing the design of passive variable stiffness joint profiles based on preset response curves. Background Technology

[0002] Passive variable stiffness joints are a commonly used type of joint in robot joint technology. They can cope with complex working conditions and provide stiffness requirements in different scenarios.

[0003] However, in practical engineering, complex physical interaction scenarios often require designers to pre-define customized "displacement-force" mechanical response curves based on specific tasks. Existing passive variable stiffness joints lack a systematic reverse design theory that can directly map the "target mechanical response curve" to the "geometric profile of the physical mechanism." Designers typically have to approximate the target performance through repeated trial and error and adjusting spring stiffness, which is not only inefficient but also makes it difficult to guarantee that the final mechanism accurately reproduces the pre-defined nonlinear stiffness characteristics and overload resistance.

[0004] Therefore, there is an urgent need in this field for a passive variable stiffness joint that can pre-determine the nonlinear target response curve from the physical structure. This joint needs to have a matching inverse contour design method that uses the target curve as input energy, while also taking into account the engineering requirements of compact structure and easy optimization and iteration. In this way, without relying on electronic sensing and active control, the safety and environmental adaptability of the robot in complex physical interaction scenarios can be fundamentally improved from the physical body level.

[0005] In order to solve the above problems, people have been seeking an ideal technological solution. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by providing a passive variable stiffness joint profile design optimization method based on a preset response curve, which performs reverse design optimization based on the "displacement-force and angle-torque" mechanical response curve and ensures that the variable stiffness performance of the joint meets the design requirements.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a passive variable stiffness joint profile design optimization method based on a preset response curve, comprising the following steps:

[0008] S1 constructs a basic unit, which includes a joint configuration consisting of a pair of cams and a spring. The pair of cams engage through a cam profile curve, and the spring is used to provide a restoring force for the pair of cams. The profile curve of the cam profile curve follows the requirements of a preset response curve.

[0009] S2 generates a preset response curve. The independent variable of the horizontal axis of the preset curve is the relative rotation angle of the two cams in the cam spring mechanism of the basic unit. When the displacement or angle is small, the curve has high stiffness to ensure static positioning accuracy. After entering the working section, the curve turns to negative stiffness so that the response torque meets the compliance requirements. As the displacement or angle continues to increase, the curve transitions to zero stiffness, providing an overload buffer while maintaining compliance. When the displacement or angle reaches the set threshold, the curve returns to high stiffness, which plays a role in mechanical limiting and preventing bottoming out.

[0010] S3 analyzes the basic unit's degree of freedom range, rated torque, and preset response curve requirements to obtain the maximum force or maximum torque change rate, as well as the maximum energy change rate; based on the force analysis of the spring in the basic unit, the spring data, including maximum length, maximum force, and maximum tensile strength, can be obtained.

[0011] S4 calculates the constraint equation based on the spring in the basic unit by analyzing the force on the spring, and then determines the coordinates of the contact point based on the constraint equation and the motion parameters of the active intervention constraint, and obtains the overall shape of the cam profile curve in the basic unit.

[0012] To make the mechanism more compact and reduce the stiffness requirement of a single spring, the spring fixing point is changed from a single spring or a single set of springs to two or two sets of springs that are offset to both sides by equal distances. Since the position and number of springs have changed, the overall shape of the cam profile curve needs to be optimized based on the geometric conditions after offset.

[0013] S6 determines the optimal parameters of the spring, including: maximum spring length, maximum spring force, and maximum spring extension / retraction.

[0014] Based on the motion characteristics of the basic unit, different correction scaling factors are set for the horizontal and vertical coordinates of the cam profile curve. Then, combined with the offset distance, the relationship between the coordinates of the optimized cam profile curve and the coordinates of the unoptimized cam profile curve is obtained.

[0015] S7 obtains constraint equations for the optimization parameters based on the geometric relationships and force analysis of the optimized basic elements, and finally calculates the optimized data based on these constraint equations.

[0016] This invention pre-sets the necessary constraints for the desired profile to form a pre-response curve, and then optimizes the curve based on the basic profile. Its core design concept lies in the ability to design the profile surface and elastic parameters according to the desired torque. In terms of application, within a small deformation range, it exhibits large or positive stiffness, providing a certain degree of flexible deformation while improving the positioning accuracy of the joint end effector. When the deformation range exceeds a certain limit and reaches the overload region, it provides non-positive stiffness, improving the joint's deformation capacity and achieving overload resistance. As the deformation range increases, it reaches a limit value where the stiffness becomes a large positive value, restricting further joint movement. The effect of the desired joint stiffness variation is used to deduce the corresponding response curve value, and then the required profile curve is calculated based on the response curve value. This reverse derivation method eliminates the need for designers to repeatedly try and adjust spring stiffness to approximate the target performance, improving design efficiency and ensuring that the designed basic unit mechanism can relatively accurately meet the preset response curve stiffness characteristics and overload resistance performance.

[0017] Based on the above, the basic unit is a translational joint unit, in which one cam profile curve is roughly "M" shaped, forming a cam groove track in structure, and the other cam is a rolling element that rolls on the cam groove track. There is only one spring, with the lower end fixed point located directly below the center of the cam groove track, and the upper end of the spring connected to the rolling element.

[0018] The profile curve of the cam groove track is determined by the following method:

[0019] Determine the maximum force based on the constraints of the preset response curve. and maximum energy change ;

[0020] The data for the springs are as follows: Maximum length of the spring assembly Maximum force of spring assembly With maximum stretch The above data can define a standard spring;

[0021] Static force analysis of the basic unit of the pre-designed cam groove mechanism yields the constraint force equation of the spring as follows:

[0022] ,

[0023] Where αi and θi are the angles between the spring force and the vertical direction when the maximum force is obtained in the preset response curve, and the angles between the support force along the normal direction of the contact point and the vertical direction.

[0024] The absolute values ​​of both angles are limited to below π / 3, while also limiting... The safety factor SF is set to 2; the elongation of the spring is calculated. and spring force F s2 Substituting these values ​​into the force balance equations allows us to solve for angles α and θ, thus determining the coordinates of the contact point at this point:

[0025] ,

[0026] The overall shape of the cam groove profile curve can be obtained from this.

[0027] To make the mechanism more compact and reduce the stiffness requirement of a single spring, the spring fixing point was changed from being located directly below the center of the cam groove track in the main body to being offset by an equal distance d to both sides. After the offset, the number of springs doubled. Under the premise that the total stiffness remains unchanged, the stiffness requirement of a single spring is reduced accordingly. The original cam profile designed based on the installation method before the offset can no longer meet the given preset response curve requirements. Therefore, the cam profile needs to be redesigned according to the geometric conditions after the offset.

[0028] The optimization parameters for the basic unit include: maximum spring length. Maximum spring force Maximum spring elongation The horizontal coordinate range of the cam groove curve is the displacement range; therefore, the cam groove profile cannot be scaled proportionally. Accordingly, the optimization parameters of the translational joint are adjusted to correct the vertical coordinate: vertical coordinate reduction. , Vertical axis scaling factor Linear skew term coefficient and coefficients of the second curvature term In summary, the optimized coordinates of the cam profile curve and the cam groove profile curve are as follows:

[0029] ,

[0030] The optimized translational variable stiffness principle is similar to the original structure. Let the left spring be spring A and the right spring be spring B. Perform a force analysis on the contact point between the rolling element and the cam groove track after the movement. The force at the contact point is as follows: the tension F of springs A and B... sA F sB Its specific value can be obtained from the distance from the point to the line and Hooke's law; the pulling force F that causes the slider to move at a constant speed e The supporting force F generated by the cam profile due to the spring tension on the pulley n Let the angles between springs A and B and the vertical direction be α and α, respectively. A2 α B2 Total support F n Decomposing these forces into horizontal and vertical components at an angle θ with the vertical direction, we obtain the following formula:

[0031] , ,

[0032] Where the x-index represents the relevant horizontal component force and the y-index represents the relevant vertical component force, the optimized data is obtained through the above formula.

[0033] When the joint is a translational joint, the logic of the entire derivation is as described in the specific process: first, the pre-response curve is analyzed, then the force is analyzed and reverse deduced in combination with the basic unit structure, and finally the numerical value of the profile curve is obtained.

[0034] Based on the above, the basic unit is a rotary joint unit, which includes an upper cam, a lower cam, and a spring. The meshing surfaces of the upper cam and the lower cam mesh, and the two sides of the upper cam and the lower cam are respectively connected by a centrally located spring to provide a reset force.

[0035] By differentiating and accumulating the results from the preset response curve, the maximum torque change rate can be obtained. and maximum energy change ,in, For instantaneous rotation angle, Assuming instantaneous torque, let the data for the basic unit spring assembly before optimization be: maximum length Maximum force of spring assembly With maximum stretch The above data can define a standard spring;

[0036] Under all operating conditions, the maximum rate of change of torque provided by the spring must be able to meet the maximum rate of change of torque required by the input curve; furthermore, according to Hooke's Law, the maximum energy stored in the spring assembly must satisfy the maximum energy change requirement. In summary, the two constraint equations concerning the spring parameters are as follows:

[0037] ,

[0038] In the formula For safety factor, it is set to 2; through this constraint, the required spring data can be obtained. Then, the spring data and the pre-designed response curve are used as input. By calculating the length of the spring and the size of the lever arm point by point, the required cam profile curve can be obtained.

[0039] To make the mechanism more compact and reduce the stiffness requirement of a single spring, the spring fixing point was changed from along the central axis of the two cams to offset by an equal distance d on both sides in a direction perpendicular to the central axis. After the offset, the number of springs doubled. The original cam profile designed based on the installation method before the offset could no longer meet the given preset response curve requirements. Therefore, the cam profile needs to be redesigned according to the geometric conditions after the offset.

[0040] The optimization parameters for the basic unit include: maximum spring length. Maximum spring force Maximum spring elongation cam profile horizontal coordinate scaling factor , Vertical axis scaling factor And the offset displacement of the spring connection point;

[0041] Optimized cam profile curve coordinates for:

[0042] ,

[0043] in The coordinates of the cam profile curve before optimization;

[0044] The origin is set as the midpoint of the line connecting the two spring pivot points after the lower cam is offset, and the two pivot points of the upper cam are set as pivot point a and pivot point b. The coordinates of the two pivot points can be obtained through geometric relationships.

[0045] ,

[0046] In the formula The length of the left spring is given by the formula. The length of the spring on the right. Let be the rotation angle, and the relationship between the lengths of the two springs is:

[0047] ,

[0048] By combining the energy curve obtained by integrating the input preset response curve and Hooke's law, the length of the spring at this time can be calculated. Therefore, the two pivot points above are known quantities.

[0049] According to geometric relationships, the equation of the straight line representing spring a is: The equation of the straight line representing spring b is: The distances from the contact point to these two straight lines are the lever arms of springs a and b, respectively. Using the formula for the distance from a point to a line, we can obtain... , At this time, the spring forces of springs a and b are respectively , There exists a limiting angle. When the absolute value of the rotation angle is less than the absolute value of the limit angle, the optimized cam profile contact point is located inside the rectangle formed by the four spring contact points. When the rotation angle is at the limit angle, the optimized contact point is located outside the rectangle formed by the four spring contact points. Therefore, when the rotation angle is less than the limit angle, the torque τ of spring a is... aThe torque τb of spring a acts to resist external forces, hence its sign is positive; the torque τb of spring b promotes the action of external forces, hence its sign is negative; when the rotation angle is greater than the limit angle, the torque τb of spring a... a and the torque τ of spring b b They all resist external forces, making all signs positive;

[0050] When the contact point between the upper and lower cams is exactly the midpoint between the two connection points of spring b, the rotation angle is exactly the limit angle. By calculating the rotation angle at this point, the torque constraint for the optimization parameters can be obtained:

[0051]

[0052] The optimized data can be obtained through the aforementioned angle and torque constraints.

[0053] When the joint is a rotational joint, the logic of the entire derivation is as described in the specific process: first, the pre-response curve is analyzed, then the force is analyzed and reverse deduced in combination with the basic unit structure, and finally the numerical value of the profile curve is obtained.

[0054] This invention has outstanding substantive features and significant progress compared to the prior art. Specifically, this invention proposes a method for designing a reverse profile curve by limiting the required passive variable stiffness joint through a preset response curve and then using the preset response curve as the target. This eliminates the need for designers to approximate the target performance through repeated trial and error and adjustment of spring stiffness, thereby improving design efficiency. Furthermore, it ensures that the designed basic unit mechanism can relatively accurately meet the preset response curve stiffness characteristics and overload resistance performance.

[0055] What is particularly noteworthy is that the variable stiffness joint designed by this invention has a large or positive stiffness within a small deformation range, which can improve the positioning accuracy of the joint end while providing a certain degree of flexible deformation; when the deformation range exceeds a certain range and reaches the overload area, it provides non-positive stiffness, improves the joint's deformation capacity, and achieves overload resistance; as the deformation range increases, it will reach a limit value, and the stiffness will be a large positive value, which will limit the joint's continued movement and has excellent overload resistance performance. Attached Figure Description

[0056] Figure 1 It is a curve graph of the preset corresponding curve in Embodiment 1 of the present invention.

[0057] Figure 2 This is a schematic diagram of the basic unit structure of Embodiment 1 of the present invention.

[0058] Figure 3 This is a flowchart illustrating the design of the cam profile curve in the basic unit of Embodiment 1 of the present invention.

[0059] Figure 4 This is a comparison of the structural schematic diagrams of the optimized basic unit in Embodiment 1 of the present invention.

[0060] Figure 5 This is a comparison diagram of the cam profile curves before and after optimization in Embodiment 1 of the present invention.

[0061] Figure 6 This is a flowchart of optimizing the cam profile curve in Embodiment 1 of the present invention.

[0062] Figure 7 It is a curve graph of the preset corresponding curve in Embodiment 2 of the present invention.

[0063] Figure 8 This is a schematic diagram of the basic unit structure of Embodiment 2 of the present invention.

[0064] Figure 9 This is a flowchart illustrating the design of the cam profile curve in the basic unit of Embodiment 2 of the present invention.

[0065] Figure 10 This is a comparison of the structural schematic diagrams of the optimized basic unit in Embodiment 2 of the present invention.

[0066] Figure 11 This is a comparison diagram of the cam profile curves before and after optimization in Embodiment 2 of the present invention.

[0067] Figure 12 This is a flowchart of optimizing the cam profile curve in Embodiment 2 of the present invention. Detailed Implementation

[0068] The technical solution of the present invention will be further described in detail below through specific embodiments.

[0069] A method for optimizing the design of passive variable stiffness joint profiles based on preset response curves includes the following steps:

[0070] S1 constructs a basic unit, which includes a joint configuration consisting of a pair of cams and a spring. The pair of cams engage through a cam profile curve, and the spring is used to provide a restoring force for the pair of cams. The profile curve of the cam profile curve follows the requirements of a preset response curve.

[0071] S2 generates a preset response curve. The independent variable of the horizontal axis of the preset curve is the relative rotation angle of the two cams in the cam spring mechanism of the basic unit. When the displacement or angle is small, the curve has high stiffness to ensure static positioning accuracy. After entering the working section, the curve turns to negative stiffness so that the response torque meets the compliance requirements. As the displacement or angle continues to increase, the curve transitions to zero stiffness, providing an overload buffer while maintaining compliance. When the displacement or angle reaches the set threshold, the curve returns to high stiffness, which plays a role in mechanical limiting and preventing bottoming out.

[0072] S3 analyzes the basic unit's degree of freedom range, rated torque, and preset response curve requirements to obtain the maximum force or maximum torque change rate, as well as the maximum energy change rate; based on the force analysis of the spring in the basic unit, the spring data, including maximum length, maximum force, and maximum tensile strength, can be obtained.

[0073] S4 calculates the constraint equation based on the spring in the basic unit by analyzing the force on the spring, and then determines the coordinates of the contact point based on the constraint equation and the motion parameters of the active intervention constraint, and obtains the overall shape of the cam profile curve in the basic unit.

[0074] To make the mechanism more compact and reduce the stiffness requirement of a single spring, the spring fixing point is changed from a single spring or a single set of springs to two or two sets of springs that are offset to both sides by equal distances. Since the position and number of springs have changed, the overall shape of the cam profile curve needs to be optimized based on the geometric conditions after offset.

[0075] S6 determines the optimal parameters of the spring, including: maximum spring length, maximum spring force, and maximum spring extension / retraction.

[0076] Based on the motion characteristics of the basic unit, different correction scaling factors are set for the horizontal and vertical coordinates of the cam profile curve. Then, combined with the offset distance, the relationship between the coordinates of the optimized cam profile curve and the coordinates of the unoptimized cam profile curve is obtained.

[0077] S7 obtains constraint equations for the optimization parameters based on the geometric relationships and force analysis of the optimized basic elements, and finally calculates the optimized data based on these constraint equations.

[0078] Example 1

[0079] like Figures 1-6 As shown, the basic unit is a translational joint unit, in which one cam profile curve is roughly "M" shaped, forming a cam groove track in structure, and the other cam is a rolling element that rolls on the cam groove track. There is only one spring, with the lower end fixed point located directly below the center of the cam groove track, and the upper end of the spring connected to the rolling element.

[0080] The profile curve of the cam groove track is determined by the following method:

[0081] When the displacement is small, the curve exhibits high stiffness to ensure static positioning accuracy. Upon entering the working section, the curve transitions to negative stiffness to meet compliance requirements for the response torque. As the displacement continues to increase, the curve transitions to zero stiffness, maintaining compliance while providing an overload buffer zone. When the displacement reaches a set threshold, the curve returns to high stiffness, acting as a mechanical limiter and preventing bottoming out. The displacement range for each degree of freedom of the overload-resistant translational variable stiffness joint is (-100mm, +100mm), and the rated torque is set to 1.5 N. By analyzing the preset response curves, the maximum force can be calculated. and maximum energy change Let the data of the basic unit spring assembly before optimization be: maximum length Maximum force of spring assembly With maximum stretch The above data can define a standard spring, such as Figure 1 As shown.

[0082] like Figure 2 As shown, the basic unit of the preset cam groove mechanism is defined, where the cam groove track is approximately "M" shaped. There is only one spring, with its lower fixed point located directly below the center of the cam groove track in the main body. Ignoring the inertial effect under low-speed motion, a quasi-static force analysis is performed on the connection point of the upper spring. If the connection point of the upper spring is subjected to a horizontal external force F... e At this time, the connection point will also be subject to a spring force F pointing downwards towards the fixed connection point. s And the supporting force F along the normal direction of the contact point between the roller and the cam groove track. n The spring force F s The angle between the profile and the vertical direction is α, and the support force F is... n The angle between the upper floating connection point and the vertical direction is θ. The sign of angle α is determined by the position of the upper floating connection point relative to the lower fixed connection point (positive if on the right, negative if on the left). Angle θ is then determined according to F. n The direction of the pointer determines the sign (negative for upward-right, positive for upward-left). Based on geometric relationships, the slope of the theoretical profile at this point is tanθ. Therefore, the force balance equations for the horizontal and vertical directions are:

[0083]

[0084] Solving this equation simultaneously, we can obtain... External force F e Given the required force with preset overload resistance, and based on Hooke's law, the constraint equations for the springs in the basic unit of the translational joint are as follows:

[0085]

[0086] Where α iθ i This refers to the angle at which the maximum force is achieved in the angle-torque curve. For the sake of the mechanism's rationality and compactness, the absolute values ​​of both angles are limited to below π / 3. Further research indicates that... The safety factor SF is set to 2.

[0087] Calculate the elongation of the spring. and spring force F s2 Substituting these values ​​into the force balance equations allows us to solve for angles α and θ, thus determining the coordinates of the contact point at this point.

[0088]

[0089] The overall shape of the cam groove profile curve can be obtained from this, and the process is as follows: Figure 3 As shown.

[0090] To make the mechanism more compact and reduce the stiffness requirement of individual springs, the spring fixing points are changed from along the central axes of the two cams to offset by an equal distance *d* to both sides in a direction perpendicular to the central axes. After offsetting, the number of springs doubles, and the stiffness requirement of individual springs decreases accordingly while maintaining the same total stiffness. However, the original cam profile designed based on the mounting method before offsetting can no longer meet the given angle-torque curve requirements; therefore, the cam profile needs to be redesigned according to the geometry after offsetting. Consequently, due to the increased number of springs providing restoring torque, the dimensions of the new cam profile meeting the same torque requirements will be smaller than the original design.

[0091] The optimized parameters for the basic unit of the translational joint include: maximum spring length. Maximum spring force Maximum spring elongation The horizontal coordinate range of the cam groove curve is the displacement range; therefore, the cam groove profile cannot be scaled proportionally. Accordingly, the optimization parameters of the translational joint are adjusted to correct the vertical coordinate: vertical coordinate reduction. , Vertical axis scaling factor Linear skew term coefficient and coefficients of the second curvature term In summary, the optimized coordinates of the cam profile curve and the cam groove profile curve are as follows:

[0092]

[0093] Comparison of spring arrangement before and after optimization, for example Figure 4 As shown.

[0094] Among them, the reduction of the vertical axis The overall cam groove height is reduced, decreasing the vertical thickness of the mechanism and improving compactness; the vertical axis scaling factor... Adjusting the overall curvature to match the spring elongation with the horizontal force output amplitude; resulting in linear force offset.

[0095] Linear skew term Corrects the slope of the foundation stiffness throughout the entire process, compensates for multiple spring lines, and accurately reproduces the segmented mechanical characteristics against overload.

[0096] Quadratic curvature term : Fitting nonlinear curves in the negative stiffness and zero stiffness ranges;

[0097] , The specific values ​​of these parameters are obtained by using the fminconfim function in MATLAB.

[0098] The optimized translational variable stiffness principle is similar to the original structure. Let the left spring be spring A and the right spring be spring B. When the slider is not subjected to any external force in the horizontal direction, the upper connection point is located on the central axis of the cam groove. At this time, the two springs are symmetrically distributed, and the horizontal component forces cancel each other out to 0, which is the initial state. When the slider is subjected to a horizontal component force and begins to move at a constant speed, the upper connection point also moves accordingly. At this time, the lengths of the two springs change, and their offset directions also change, generating a horizontal component force. This horizontal component force works together with the horizontal component force of the cam groove support force (along the normal direction of the contact point between the cam groove and the upper connection point) to make the total horizontal component force reach the expected change, thereby achieving the purpose of variable stiffness.

[0099] After the fixed connection point below shifts, a force analysis is performed on the contact point between the moved pulley and the cam groove. The force at the contact point is as follows: A, B, and the tension F of the springs. sA F sB Its specific value can be obtained from the distance from the point to the line and Hooke's law; the pulling force F that causes the slider to move at a constant speed e The supporting force F generated by the cam profile due to the spring tension on the pulley n Let the angles between springs a and b and the vertical direction be α and α, respectively. A2 α B2 Total support F n Decomposing these forces into horizontal and vertical components at an angle θ with the vertical direction, we obtain the following formula:

[0100] , ,

[0101] Where the x-index represents the relevant horizontal component force and the y-index represents the relevant vertical component force, the optimized data is obtained through the above formula, and the specific optimization process is as follows: Figure 6 As shown, the contour curves before and after optimization are compared as follows: Figure 5 As shown.

[0102] Example 2

[0103] like Figures 7-12 As shown, the basic unit is a rotary joint unit, which includes an upper cam, a lower cam, and a spring. The meshing surfaces of the upper and lower cams engage. The two sides of the upper and lower cams are connected by a centrally located spring to provide the return force. The specific structure is as follows. Figure 8 As shown.

[0104] The horizontal axis of the preset curve is the relative rotation angle between the two cams in the cam-spring mechanism of the basic unit. When the angle is small, the curve exhibits high stiffness to ensure static positioning accuracy. After entering the working section, the curve becomes negative stiffness to ensure the response torque meets the compliance requirements. As the angle continues to increase, the curve transitions to zero stiffness, providing an overload buffer while maintaining compliance. When the independent variable reaches the set threshold, the curve returns to high stiffness, serving as a mechanical limit and preventing bottoming out. The rotation range of each degree of freedom of the non-fixed-axis two-degree-of-freedom rotary joint is (-55°, +55°), and the rated torque is set to 1.5 N·m; the rotation range of each degree of freedom of the fixed-axis single-degree-of-freedom rotary joint is also (-55°, +55°), and the rated torque is set to 0.75 N·m.

[0105] like Figure 7 As shown, the maximum torque change rate can be obtained by differentiating and accumulating the results from the preset response curve. and maximum energy change ,in, For instantaneous rotation angle, Assuming instantaneous torque, let the data for the basic unit spring assembly before optimization be: maximum length Maximum force of spring assembly With maximum stretch The above data can define a standard spring;

[0106] Under all operating conditions, the maximum rate of change of torque provided by the spring must be able to meet the maximum rate of change of torque required by the input curve; furthermore, according to Hooke's Law, the maximum energy stored in the spring assembly must satisfy the maximum energy change requirement. In summary, the two constraint equations concerning the spring parameters are as follows:

[0107] ,

[0108] In the formula For safety, a factor of 2 is set. This constraint allows us to obtain the required spring data. Then, by simultaneously inputting the spring data and the pre-designed response curve, and calculating the spring length and lever arm point by point, we can obtain the required cam profile curve. The process is as follows: Figure 9 As shown;

[0109] To make the mechanism more compact and reduce the stiffness requirement of a single spring, the spring fixing point was changed from along the central axis of the two cams to offset by an equal distance d on both sides in a direction perpendicular to the central axis. After the offset, the number of springs doubled. The original cam profile designed based on the installation method before the offset could no longer meet the given preset response curve requirements. Therefore, the cam profile needs to be redesigned according to the geometric conditions after the offset.

[0110] The optimization parameters for the basic unit include: maximum spring length. Maximum spring force Maximum spring elongation cam profile horizontal coordinate scaling factor , Vertical axis scaling factor And the offset displacement of the spring connection point;

[0111] in, It is a global scaling factor applied to the cam profile along the horizontal axis. These are global scaling factors in the vertical direction of the cam profile. The two factors can be determined using the fmincon function in MATLAB.

[0112] Optimized cam profile curve coordinates for:

[0113] ,

[0114] in The coordinates of the cam profile curve before optimization;

[0115] The origin is set as the midpoint of the line connecting the two spring pivot points after the lower cam is offset, and the two pivot points of the upper cam are set as pivot point a and pivot point b. The coordinates of the two pivot points can be obtained through geometric relationships.

[0116] ,

[0117] In the formula The length of the left spring is given by the formula. The length of the spring on the right. Let be the rotation angle, and the relationship between the lengths of the two springs is:

[0118] ,

[0119] By combining the energy curve obtained by integrating the input preset response curve and Hooke's law, the length of the spring at this time can be calculated. Therefore, the two pivot points above are known quantities.

[0120] According to geometric relationships, the equation of the straight line representing spring a is: The equation of the straight line representing spring b is: The distances from the contact point to these two straight lines are the lever arms of springs a and b, respectively. Using the formula for the distance from a point to a line, we can obtain... , At this time, the spring forces of springs a and b are respectively , There exists a limiting angle. When the absolute value of the rotation angle is less than the absolute value of the limit angle, the optimized cam profile contact point is located inside the rectangle formed by the four spring contact points. When the rotation angle is at the limit angle, the optimized contact point is located outside the rectangle formed by the four spring contact points. Therefore, when the rotation angle is less than the limit angle, the torque τ of spring a is... a The torque τb of spring a acts to resist external forces, hence its sign is positive; the torque τb of spring b promotes the action of external forces, hence its sign is negative; when the rotation angle is greater than the limit angle, the torque τb of spring a... a and the torque τ of spring b b They all resist external forces, making all signs positive;

[0121] When the contact point between the upper and lower cams is exactly the midpoint between the two connection points of spring b, the rotation angle is exactly the limit angle. By calculating the rotation angle at this point, the torque constraint for the optimization parameters can be obtained:

[0122]

[0123] The optimized data can be obtained by applying the angle and torque constraints described above. The optimization process is as follows: Figure 12 As shown, the contour comparison before and after optimization is as follows: Figure 11 As shown, the structural comparison before and after optimization is as follows: Figure 10 As shown.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can still be made to the specific implementation of the present invention or equivalent substitutions can be made to some technical features without departing from the spirit of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the technical solutions claimed in the present invention.

Claims

1. A method for optimizing the design of passive variable stiffness joint profiles based on a preset response curve, characterized in that, Includes the following steps: S1 constructs a basic unit, which includes a joint configuration consisting of a pair of cams and a spring. The pair of cams engage through a cam profile curve, and the spring is used to provide a restoring force for the pair of cams. The profile curve of the cam profile curve follows the requirements of a preset response curve. S2 generates a preset response curve. The independent variable of the horizontal axis of the preset curve is the relative rotation angle of the two cams in the cam spring mechanism of the basic unit. When the displacement or angle is small, the curve has high stiffness to ensure static positioning accuracy. After entering the working section, the curve turns to negative stiffness so that the response torque meets the compliance requirements. As the displacement or angle continues to increase, the curve transitions to zero stiffness, providing an overload buffer while maintaining compliance. When the displacement or angle reaches the set threshold, the curve returns to high stiffness, which plays a role in mechanical limiting and preventing bottoming out. S3 analyzes the basic unit's degree of freedom range and rated torque, as well as the preset response curve requirements, and can obtain the maximum force or maximum torque change rate, and the maximum energy change rate. Based on the force analysis of the spring in the basic unit, the spring data can be obtained, including the maximum length, maximum force, and maximum tensile strength. S4 calculates the constraint equations based on the spring in the basic unit by analyzing the force on the spring, and then determines the coordinates of the contact point based on the constraint equations and the motion parameters of the active intervention constraint, and obtains the overall shape of the cam profile curve in the basic unit. To make the mechanism more compact and reduce the stiffness requirement of a single spring, the spring fixing point is changed from a single spring or a single set of springs to two or two sets of springs that are offset to both sides by equal distances. Since the position and number of springs have changed, the overall shape of the cam profile curve needs to be optimized based on the geometric conditions after offset. S6 determines the optimal parameters of the spring, including: maximum spring length, maximum spring force, and maximum spring extension / retraction. Based on the motion characteristics of the basic unit, different correction scaling factors are set for the horizontal and vertical coordinates of the cam profile curve. Then, combined with the offset distance, the relationship between the coordinates of the optimized cam profile curve and the coordinates of the unoptimized cam profile curve is obtained. S7 obtains constraint equations for the optimization parameters based on the geometric relationships and force analysis of the optimized basic elements, and finally calculates the optimized data based on these constraint equations.

2. The passive variable stiffness joint profile design optimization method based on a preset response curve according to claim 1, characterized in that, The basic unit is a translational joint unit, in which one cam profile curve is roughly "M" shaped, forming a cam groove track in structure, and the other cam is a rolling element that rolls on the cam groove track. There is only one spring, with the lower end fixed point located directly below the center of the cam groove track, and the upper end of the spring connected to the rolling element. The profile curve of the cam groove track is determined by the following method: Determine the maximum force based on the constraints of the preset response curve. and maximum energy change ; The data for the springs are as follows: Maximum length of the spring assembly Maximum force of spring assembly With maximum stretch The above data can define a standard spring; Static force analysis of the basic unit of the pre-designed cam groove mechanism yields the constraint force equation of the spring as follows: ， Where αi and θi are the angles between the spring force and the vertical direction when the maximum force is obtained in the preset response curve, and the angles between the support force along the normal direction of the contact point and the vertical direction. The absolute values ​​of both angles are limited to below π / 3, while also limiting... The safety factor SF is set to 2; the elongation of the spring is calculated. and spring force F s2 Substituting these values ​​into the force balance equations allows us to solve for angles α and θ, thus determining the coordinates of the contact point at this point: ， The overall shape of the cam groove profile curve can be obtained from this. To make the mechanism more compact and reduce the stiffness requirement of a single spring, the spring fixing point was changed from being located directly below the center of the cam groove track in the main body to being offset by an equal distance d to both sides. After the offset, the number of springs doubled. Under the premise that the total stiffness remains unchanged, the stiffness requirement of a single spring is reduced accordingly. The original cam profile designed based on the installation method before the offset can no longer meet the given preset response curve requirements. Therefore, the cam profile needs to be redesigned according to the geometric conditions after the offset. The optimization parameters for the basic unit include: maximum spring length. Maximum spring force Maximum spring elongation The horizontal coordinate range of the cam groove curve is the displacement range; therefore, the cam groove profile cannot be scaled proportionally. Accordingly, the optimization parameters of the translational joint are adjusted to correct the vertical coordinate: vertical coordinate reduction. , Vertical axis scaling factor Linear skew term coefficient and coefficients of the second curvature term In summary, the optimized coordinates of the cam profile curve and the cam groove profile curve are as follows: ， The optimized translational variable stiffness principle is similar to the original structure. Let the left spring be spring A and the right spring be spring B. Perform a force analysis on the contact point between the rolling element and the cam groove track after the movement. The force at the contact point is as follows: the tension F of springs A and B... sA F sB Its specific value can be obtained from the distance from the point to the line and Hooke's law; the pulling force F that causes the slider to move at a constant speed e The supporting force F generated by the cam profile due to the spring tension on the pulley n Let the angles between springs A and B and the vertical direction be α and α, respectively. A2 α B2 Total support F n Decomposing these forces into horizontal and vertical components at an angle θ with the vertical direction, we obtain the following formula: ， ， Where the x-index represents the relevant horizontal component force and the y-index represents the relevant vertical component force, the optimized data is obtained through the above formula.

3. The passive variable stiffness joint profile design optimization method based on a preset response curve according to claim 1, characterized in that, The basic unit is a rotary joint unit, which includes an upper cam, a lower cam, and a spring. The meshing surfaces of the upper cam and the lower cam mesh, and the two sides of the upper cam and the lower cam are respectively connected by a centrally located spring to provide a reset force. By differentiating and accumulating the results from the preset response curve, the maximum torque change rate can be obtained. and maximum energy change ,in, For instantaneous rotation angle, Assuming instantaneous torque, let the data for the basic unit spring assembly before optimization be: maximum length Maximum force of spring assembly With maximum stretch The above data can define a standard spring; Under all operating conditions, the maximum rate of change of torque provided by the spring must be able to meet the maximum rate of change of torque required by the input curve; furthermore, according to Hooke's Law, the maximum energy stored in the spring assembly must satisfy the maximum energy change requirement. In summary, the two constraint equations concerning the spring parameters are as follows: ， In the formula For safety, the factor is set to 2. This constraint allows us to obtain the required spring data. Then, by using the spring data and the pre-designed response curve as inputs, and calculating the length of the spring and the lever arm point by point, we can obtain the required cam profile curve. To make the mechanism more compact and reduce the stiffness requirement of a single spring, the spring fixing point was changed from along the central axis of the two cams to offset by an equal distance d on each side in a direction perpendicular to the central axis. After the offset, the number of springs doubled. The original cam profile designed based on the installation method before the offset could no longer meet the given preset response curve requirements. Therefore, the cam profile needs to be redesigned according to the geometric conditions after the offset. The optimization parameters for the basic unit include: maximum spring length. Maximum spring force Maximum spring elongation cam profile horizontal coordinate scaling factor , Vertical axis scaling factor And the offset displacement of the spring connection point; Optimized cam profile curve coordinates for: ， in The coordinates of the cam profile curve before optimization; The origin is set as the midpoint of the line connecting the two spring pivot points after the lower cam is offset, and the two pivot points of the upper cam are set as pivot point a and pivot point b. The coordinates of the two pivot points can be obtained through geometric relationships. ， In the formula The length of the left spring is given by the formula. The length of the spring on the right. Let be the rotation angle, and the relationship between the lengths of the two springs is: ， By combining the energy curve obtained by integrating the input preset response curve and Hooke's law, the length of the spring at this time can be calculated. Therefore, the two pivot points above are known quantities. According to geometric relationships, the equation of the straight line representing spring a is: The equation of the straight line representing spring b is: The distances from the contact point to these two straight lines are the lever arms of springs a and b, respectively. Using the formula for the distance from a point to a line, we can obtain... , At this time, the spring forces of springs a and b are respectively , There exists a limiting angle. When the absolute value of the rotation angle is less than the absolute value of the limit angle, the optimized cam profile contact point is located inside the rectangle formed by the four spring contact points. When the rotation angle is at the limit angle, the optimized contact point is located outside the rectangle formed by the four spring contact points. Therefore, when the rotation angle is less than the limit angle, the torque τ of spring a is... a The torque τb of spring a acts to resist external forces, hence its sign is positive; the torque τb of spring b promotes the action of external forces, hence its sign is negative; when the rotation angle is greater than the limit angle, the torque τb of spring a... a and the torque τ of spring b b They all resist external forces, making all signs positive; When the contact point between the upper and lower cams is exactly the midpoint between the two connection points of spring b, the rotation angle is exactly the limit angle. By calculating the rotation angle at this point, the torque constraint for the optimization parameters can be obtained: ， The optimized data can be obtained through the aforementioned angle and torque constraints.

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