A global parameter optimization method based on a parallel four-bar linkage bouncing mechanism

Abstract

The present application relates to parallel four-bar linkage springing mechanism parameter optimization technical field, especially in kind based on parallel four-bar linkage springing mechanism global parameter optimization method, including: step 1, according to the characteristics of parallel four-bar linkage springing mechanism, the motion relationship of each part is established Calculation formula;Step 2, by analyzing the motion characteristics of parallel four-bar linkage springing mechanism, the energy loss of parallel four-bar linkage springing mechanism in the jumping process is calculated;Step 3, taking the jumping height as the optimization object, the function relationship between each optimization parameter is constructed, and the optimization objective function is established;Step 4, the constraint condition of optimization variable is set, the optimization objective function is used for optimization calculation, and the theoretical optimal parameter of parallel four-bar linkage springing mechanism is obtained;Step 5, taking the theoretical optimal parameter as the benchmark, the actual optimal parameter is selected by iterative calculation mode.The present application effectively increases the jumping height of four-bar linkage springing driving mechanism, and improves the overall jumping motion performance.

Description

Technical Field

[0001] This invention relates to the field of parameter optimization technology for parallel four-bar linkage bouncing mechanisms, and particularly to a global parameter optimization method based on parallel four-bar linkage bouncing mechanisms. Background Technology

[0002] Jumping, a widespread form of locomotion in nature, is used by many organisms to adapt to complex environments. Researchers have designed various types of jumping structures to achieve this locomotion, with the parallel four-bar linkage being a fundamental and widely used mechanism. For example, drones use parallel four-bar linkages for catapult takeoff and landing cushioning; in multimodal robot design, parallel four-bar linkages are frequently used to perform jumping motions, especially for multimodal robots that include gliding motions. The parallel four-bar linkage can function as both a leg structure for jumping and a wing structure for gliding, with the two locomotion modes coupled, greatly improving the system's integration.

[0003] Current optimization methods only consider parameter optimization under static conditions, without addressing energy losses in different parts under dynamic conditions. Furthermore, they require setting some parameters as known quantities before optimization calculations and only optimize individual link lengths or spring parameters, without performing overall optimization calculations, thus failing to obtain a globally optimal result. Summary of the Invention

[0004] To address the aforementioned technical problems in existing technologies, this invention proposes a global parameter optimization method based on a parallel four-bar linkage jumping mechanism. This method can effectively improve the jumping height of the mechanism and can be used in the design process of jumping mechanisms for vehicles such as robots and drones that require jumping. The specific technical solution is as follows:

[0005] A global optimization method for a parallel four-bar linkage bouncing mechanism includes the following steps:

[0006] Step 1: Based on the characteristics of the parallel four-bar linkage mechanism, establish the kinematic relationships for each part, which includes three objects: the linkage, the load, and the spring.

[0007] Step 2: Analyze the motion characteristics of the parallel four-bar linkage jumping mechanism and calculate the energy loss of the parallel four-bar linkage jumping mechanism during the jumping process;

[0008] Step 3: Taking the jump height as the optimization object, construct the functional relationship between each optimization parameter and establish the optimization objective function;

[0009] Step 4: Set the constraints for the optimization variables, use the optimization objective function to perform optimization calculations, and obtain the theoretical optimal parameters of the parallel four-bar linkage jumping mechanism;

[0010] Step 5: Using the theoretically optimal parameters as a benchmark, select the actual optimal parameters through iterative calculation.

[0011] Furthermore, step 1 specifically involves establishing the following kinematic equation based on the structural relationship of the parallel four-bar linkage:

[0012]

[0013] Where y1 is the longitudinal displacement of the spring end, x1 is the lateral displacement of the spring end, and y2 is the longitudinal displacement of the load end. This represents the longitudinal displacement of the upper connecting rod's center of mass. This refers to the lateral displacement of the center of mass of the upper connecting rod. This represents the longitudinal displacement of the center of mass of the lower connecting rod. Let θ be the lateral displacement of the lower connecting rod's center of mass, and θ be the angle between the connecting rod and the ground. The longitudinal velocity of the spring end. The longitudinal velocity at the load end. The lateral velocity of the spring end. The lateral velocity of the lower connecting rod's center of mass. The lateral velocity of the upper connecting rod's center of mass. The longitudinal velocity of the center of mass of the upper connecting rod. This represents the longitudinal velocity of the center of mass of the lower connecting rod.

[0014] Furthermore, the energy loss in step 2 includes: the increase in gravitational potential energy E of the load and linkage components from the lowest point of compression to the critical point of takeoff. l The increase in gravitational potential energy E of a spring from its lowest point of compression to its highest point of bounce. s The energy loss E generated by the spring and connecting rod when the spring returns to its original length. loss The takeoff critical point of the bouncing mechanism is when the spring returns to its original length.

[0015] Furthermore, the increase in gravitational potential energy E of the load and linkage components from the lowest point of compression to the critical point of takeoff l The expression is:

[0016]

[0017] Where m load For the quality of the load, Let the mass of the upper two links of the four-bar linkage be... Let h be the mass of the two lower links in the four-bar linkage. Similarly, h is the variable. load Indicates the height of load change. This indicates the height at which the center of gravity of the upper two links of the four-bar linkage changes. This indicates the height at which the center of gravity of the lower two links of the four-bar linkage changes; the diameter of the linkage is D. l The density of the connecting rod is ρl L g Let be the length of the link, and α be the minimum angle between the link and the ground. m link Let the mass of the four links be [mass]; from the proportional relationship of the four links, we can obtain:

[0018] h load =2L h -2L g sinα

[0019]

[0020]

[0021] definition: Substituting into the above equation and rearranging, we get:

[0022] E l =(2m) load g+m link g)(L h -L g sinα).

[0023] Furthermore, the increase in gravitational potential energy E corresponding to the spring's movement from its lowest compression point to its highest bounce point... s The expression is:

[0024]

[0025] in This refers to the change in spring height of the bouncing mechanism from its lowest compression point to its critical takeoff point. Let m be the change in height of the spring in the jumping mechanism from the takeoff critical point to the highest point of the jump. s The bouncing energy E of the bouncing mechanism jump For scenarios with high resistance, then... Compensation calculations were performed, and the results are as follows:

[0026]

[0027]

[0028] spring mass ρ s Let L be the spring density, L be the unfolded length of the spring, L = πD(n1 + 2), and n1 be the effective number of coils of the spring. After sorting, we can obtain:

[0029]

[0030] Among them, the number of springs n, the mean diameter of the spring D, the wire diameter of the spring d, and the original length of the spring L0, m t For the load and the mass of the connecting rod.

[0031] Furthermore, the energy loss E generated by the spring and connecting rod when the spring returns to its original length loss The expression is:

[0032]

[0033] Where, θ off This refers to the takeoff angle of the bouncing mechanism.

[0034] Furthermore, the optimization objective function E in step 3... jump The energy stored in the spring minus the energy loss:

[0035] E jump =(1-η)(E0-E l -E s ),

[0036] Where E0 is the total energy stored in the spring, and η is the energy lost by the spring and connecting rod, E loss With energy E jump and E loss The ratio of the sums;

[0037] Then the objective function E will be further optimized. jump Represented as:

[0038]

[0039] In the above formula:

[0040] G is the spring shear modulus, K w S is the stress concentration factor of the spring. ys L is the torsional yield strength of the spring. d This refers to the spring installation distance;

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Furthermore, step 4 specifically involves setting constraints to limit the upper limit of power output as follows: Or the energy storage constraint is: The spring processing condition constraint is: 4≤D / d≤12; the four-bar linkage spring mechanism's starting constraint is: The optimized parameters and link length constraints are as follows:

[0048] 1≤n≤n max ,

[0049] d min ≤d≤d max ,

[0050] D min ≤D≤D max ,

[0051]

[0052]

[0053]

[0054] in, The maximum torque of the power source; r power It serves as an equivalent force arm for the power source; The upper limit of the power source output is the equivalent vertical pressure; E0 is the target energy stored; m load The mass of the load; k is the spring constant; Δx max This represents the maximum deformation of the spring;

[0055] Further constrain the specific load mass m load The minimum angle α between the connecting rod and the ground;

[0056] Then optimize the objective function E jump The optimization calculations are performed with constraints to finally obtain the objective function E. jump A set of parameters with the largest absolute value.

[0057] Furthermore, step 5 specifically involves: using the theoretically optimal parameters as a benchmark, approximating the number of springs n according to industrial production standards, and then maintaining the remaining parameters including the spring mean diameter D, spring wire diameter d, spring original length L0, and spring installation distance L. d If the approximate values ​​remain unchanged, they are set as constants and substituted into the optimization objective function to update the remaining parameters. Among them, depending on the minimum span of each parameter, the order of the iterated parameters is: number of springs, spring mean diameter and spring wire diameter, original spring length, and spring installation distance.

[0058] Advantages of this invention:

[0059] This invention fully integrates the parameters that affect the bounce height, preventing local optima caused by optimizing only some parameters. It solves the problem that existing methods cannot be applied to situations where the power source output is at its upper limit, effectively increasing the bounce height of the four-bar linkage bounce drive mechanism and thus improving the overall bounce performance. Attached Figure Description

[0060] Figure 1 A schematic diagram of the structural parameters of a parallel four-bar linkage bouncing mechanism;

[0061] Figure 2 This is a schematic diagram showing the height variation of a parallel four-bar linkage.

[0062] Figure 3 This is a flowchart of the iterative calculation method;

[0063] Figure 4 A graph showing the relationship between the bounce height h and the mean diameter D and the wire diameter d of the spring.

[0064] Figure 5 The bounce height h is related to the original length of the spring L0 and the spring mounting distance L. d Relationship diagram;

[0065] Figure 6 The graph shows the relationship between the bounce height h and the number of springs n. Detailed Implementation

[0066] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, and to make the above-mentioned objectives, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be further described below.

[0067] This invention provides a global parameter optimization method based on a parallel four-bar linkage spring mechanism. The optimization involves optimizing the following parameters: given a fixed upper limit for the power source output, the number of springs n, spring mean diameter D, spring wire diameter d, spring original length L0, and spring mounting distance L are optimized. d The parameters are optimized to enable the bouncing mechanism to achieve the maximum bouncing height.

[0068] Specifically, the global optimization method includes the following steps:

[0069] Step 1: Based on the characteristics of the parallel four-bar linkage mechanism, establish the kinematic relationships for calculating each part;

[0070] Specifically, such as Figure 1 As shown, based on the structural relationship of the parallel four-bar linkage, the following kinematic equations for the mechanism are established:

[0071]

[0072] Where y1 is the longitudinal displacement of the spring end, x1 is the lateral displacement of the spring end, and y2 is the longitudinal displacement of the load end. This represents the longitudinal displacement of the upper connecting rod's center of mass. This refers to the lateral displacement of the center of mass of the upper connecting rod. This represents the longitudinal displacement of the center of mass of the lower connecting rod. Let θ be the lateral displacement of the lower connecting rod's center of mass, and θ be the angle between the connecting rod and the ground. The longitudinal velocity of the spring end. The longitudinal velocity at the load end. The lateral velocity of the spring end. The lateral velocity of the lower connecting rod's center of mass. The lateral velocity of the upper connecting rod's center of mass. The longitudinal velocity of the center of mass of the upper connecting rod. This represents the longitudinal velocity of the center of mass of the lower connecting rod.

[0073] Step 2: By analyzing the motion characteristics of the parallel four-bar linkage jumping mechanism, calculate the energy loss of each part of the mechanism during the jump, specifically including:

[0074] (2.1)E l The corresponding energy loss is the change in gravitational potential energy of the load and connecting rod from the lowest point of compression to the critical point of takeoff (when the spring returns to its original length), E. l The expression is:

[0075]

[0076] Where m load For the quality of the load, Let the mass of the upper two links of the four-bar linkage be... Let h be the mass of the two lower links in the four-bar linkage. Similarly, h is the variable. load Indicates the height of load change. This indicates the height at which the center of gravity of the upper two links of the four-bar linkage changes. This indicates the height at which the center of gravity of the lower two links of the four-bar linkage changes; the diameter of the linkage is D. l The density of the connecting rod is ρ l L g Let be the length of the link, and α be the minimum angle between the link and the ground. m link Let the mass of the four links be [mass]; from the proportional relationship of the four links, we can obtain:

[0077] h load =2L h -2L g sinα

[0078]

[0079]

[0080] definition: Substituting into the above equation and rearranging, we get:

[0081] E l =(2m) load g+m link g)(L h -L g sinα);

[0082] (2.2)E s The corresponding energy loss is the change in gravitational potential energy of the spring from its lowest compression point to its highest bounce point, and the mass of the spring is expressed as m. s E s The expression is:

[0083]

[0084] in This represents the change in spring height from the lowest point of compression to the critical point of takeoff. The change in spring height from the takeoff critical point to the highest point of the jump is represented by, for example: Figure 2 As shown; the following calculations assume that the effect of drag on the bounce height is approximately negligible. For scenarios with greater drag, the effect will be different. Compensation calculations were performed, and the results are as follows:

[0085]

[0086]

[0087] spring mass ρ s Let L be the spring density, L be the unfolded length of the spring, L = πD(n1 + 2), and n1 be the effective number of coils of the spring. After sorting, we can obtain:

[0088]

[0089] (2.3) The energy loss ratio η is the energy loss E of the spring and connecting rod. loss With jumping energy E jump and E loss The ratio of the sums, E loss This includes the kinetic energy lost due to the collision when the spring returns to its original length, the horizontal kinetic energy lost by the connecting rod, and the rotational kinetic energy lost by the connecting rod. From the motion relationship of the four links in step 1, the energy loss generated by the spring and connecting rod when the spring returns to its original length, i.e., the energy loss E, can be obtained. loss The expression is:

[0090]

[0091] Where, θ off Takeoff angle;

[0092] Then the energy loss ratio η is the energy loss E of the spring and connecting rod. loss With jumping energy E jump and E loss The ratio of the sums, therefore we can further obtain:

[0093]

[0094] Step 3: Taking the jump height as the optimization object, construct the functional relationship between each optimization parameter and establish the optimization objective function;

[0095] Specifically, optimize the objective function E jump The energy stored in the spring minus the energy loss:

[0096] E jump =(1-η)(E0-E l -E s ),

[0097] Where E0 is the total energy stored in the spring;

[0098] Then, the objective function E will be optimized. jump Represented as:

[0099]

[0100] In the above formula:

[0101] G is the spring shear modulus, K w S is the stress concentration factor of the spring. ys The spring's torsional yield strength.

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] Step 4: Set the constraints for the optimization variables to obtain the theoretical optimal parameters of the parallel four-bar linkage jumping mechanism;

[0109] Specifically, set constraints to limit the upper limit of power output: Or energy storage constraints: Spring processing constraints: 4≤D / d≤12; Four-bar linkage spring mechanism launch constraints: Optimization parameters and link length constraints:

[0110] 1≤n≤n max ,

[0111] d min ≤d≤d max ,

[0112] D min ≤D≤D max ,

[0113]

[0114]

[0115]

[0116] in, The maximum torque of the power source; r power It serves as an equivalent force arm for the power source; The upper limit of the power source output is the equivalent vertical pressure; E0 is the target energy stored; m load The mass of the load; k is the spring constant; Δx max This represents the maximum deformation of the spring;

[0117] Next, determine two structural parameters: load mass m load And the minimum angle α that the link can achieve with the ground, and then optimize the objective function E. jump By performing optimization calculations with relevant constraints, we can finally obtain the objective function E. jump A set of parameters with the largest absolute value.

[0118] Step 5: Using the theoretically optimal parameters as a benchmark, select the practically achievable optimal parameters through iterative calculation. After obtaining the theoretically optimal parameters in Step 4, approximate the number of springs n according to industrial production standards, keeping other parameters unchanged. Substitute this approximate value as a constant into the optimization objective function to update the remaining parameters. Steps 2-4 are based on the same principle as Step 1. Considering the different minimum spans of each parameter under actual conditions, the parameter iteration order is set as n, D and d, L0, L0. d The iterative calculation process is as follows: Figure 3 As shown.

[0119] Example:

[0120] The present invention provides an optimization method for a parallel four-bar linkage bouncing mechanism. Specifically, in the design scheme, the maximum vertical pressure generated by the power source on the parallel four-bar linkage is optimized. The mass of the load m load =10g, the minimum angle α that the connecting rod can form with the ground is 10°; the spring material is A229 spring steel, ρ s =7.86g / cm 3 G = 79.3 GPa, A = 0.6, tensile strength S ut =1.831d -0.1833 GPa, spring torsional yield strength S ys =1.098d -0.1833 GPa; the connecting rod material is a carbon fiber rod, ρ l =1.6g / cm 3 D l =2mm.

[0121] The constraints are set as follows: The maximum thrust of the four-bar linkage is 4 ≤ D / d ≤ 12. 1≤n≤4, 0.25mm≤d≤1mm, 2mm≤D≤10mm, 10mm≤L d ≤100mm.

[0122] After optimization calculations, a set of theoretically optimal parameters can be obtained, as shown in Table 1 below:

[0123]

[0124] Table 1: Instance optimization results.

[0125] As described in step 5, the spring quantity n, spring mean diameter D, spring wire diameter d, spring original length L0, and spring installation distance L are sequentially adjusted. d Approximate estimation was performed, keeping the non-estimated parameters constant, and optimization calculations were conducted to obtain a set of actual optimal parameters, as shown in Table 1. Then, different changes were applied to the obtained optimized parameters to conduct a bounce experiment, and the experimental results are as follows: Figures 4-6 As shown in the figure. The experimental results show that the actual optimal parameters obtained by this optimization algorithm can effectively improve the jump height of the bouncing mechanism.

[0126] Existing methods can only optimize certain parameters individually, such as link length or spring parameters, to obtain a locally optimal result. However, the method of this invention analyzes the influence of link and spring parameters on the bounce height, thereby obtaining a globally optimized structural parameter design result. Furthermore, this invention uses the maximum output torque of the power source as the initial condition for optimization. While maintaining compatibility with mainstream methods that use system energy storage as a known variable, it relaxes the initial condition and expands its applicability. Under a fixed power source output, this invention effectively increases the bounce height of the four-bar linkage bounce drive mechanism, thereby improving the overall bounce performance.

[0127] The embodiments of the present invention have been described in detail above, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations made to these embodiments without departing from the principles and spirit of the present invention are all within the protection scope of the present invention.

Claims

1. A global parameter optimization method based on a parallel four-bar linkage bouncing mechanism, characterized in that, Includes the following steps: Step 1: Based on the characteristics of the parallel four-bar linkage mechanism, establish the kinematic relationships for calculating each part; Step 2: Analyze the motion characteristics of the parallel four-bar linkage jumping mechanism and calculate the energy loss of the parallel four-bar linkage jumping mechanism during the jumping process; Step 3: Taking the jump height as the optimization object, construct the functional relationship between each optimization parameter and establish the optimization objective function; Step 4: Set the constraints for the optimization variables, use the optimization objective function to perform optimization calculations, and obtain the theoretical optimal parameters of the parallel four-bar linkage jumping mechanism; Step 5: Using the theoretically optimal parameters as a benchmark, select the actual optimal parameters through iterative calculation. Step 4 specifically involves setting constraints to limit the upper limit of power output as follows: Or, the energy storage constraint is: The spring processing conditions are constrained as follows: The jumping constraint of the four-bar linkage is: The optimized parameters and link length constraints are as follows: ， ， ， ， ， ， in, This represents the maximum torque of the power source. It serves as an equivalent force arm for the power source; The upper limit of the power source output is the equivalent vertical pressure. The target energy to be stored; For the mass of the load; The spring constant; This represents the maximum deformation of the spring; The length of the link; Further constrain specific load quality The minimum angle between the connecting rod and the ground ; Then optimize the objective function The optimization calculations are performed based on the constraints, and finally, the objective function is obtained. A set of parameters for absolute value; Step 5 specifically involves: using the theoretically optimal parameters as a benchmark, and determining the number of springs according to industrial production standards. Approximate the parameters, then keep the remaining parameters, including the spring mean diameter, unchanged. Spring wire diameter spring original length Spring installation distance If the approximate values ​​remain unchanged, they are set as constants and substituted into the optimization objective function to update the remaining parameters. Among them, depending on the minimum span of each parameter, the order of the iterated parameters is: number of springs, spring mean diameter and spring wire diameter, original spring length, and spring installation distance.

2. The global parameter optimization method based on a parallel four-bar linkage bouncing mechanism as described in claim 1, characterized in that, Step 1 specifically involves establishing the following kinematic equation based on the structural relationship of the parallel four-bar linkage: ， in, This represents the longitudinal displacement of the spring end. For the lateral displacement of the spring end, For the longitudinal displacement of the load end, This represents the longitudinal displacement of the upper connecting rod's center of mass. This refers to the lateral displacement of the center of mass of the upper connecting rod. This represents the longitudinal displacement of the center of mass of the lower connecting rod. This refers to the lateral displacement of the center of mass of the lower connecting rod. Let be the angle between the connecting rod and the ground. The longitudinal velocity of the spring end. The longitudinal velocity at the load end. The lateral velocity of the spring end. The lateral velocity of the lower connecting rod's center of mass. The lateral velocity of the upper connecting rod's center of mass. The longitudinal velocity of the center of mass of the upper connecting rod. This represents the longitudinal velocity of the center of mass of the lower connecting rod.

3. The global parameter optimization method based on a parallel four-bar linkage bouncing mechanism as described in claim 2, characterized in that, The energy loss in step 2 includes: the increase in gravitational potential energy of the load and connecting rod components from the lowest point of compression to the critical point of takeoff. The increase in gravitational potential energy of a spring from its lowest point of compression to its highest point of bounce. Energy loss generated by the spring and connecting rod when the spring returns to its original length The takeoff critical point of the bouncing mechanism is when the spring returns to its original length.

4. The global parameter optimization method based on a parallel four-bar linkage bouncing mechanism as described in claim 3, characterized in that, The increase in gravitational potential energy of the load and linkage components from the lowest point of compression to the critical point of takeoff. The expression is: ， in For the quality of the load, Let the mass of the upper two links of the four-bar linkage be... Let the mass of the lower two links of the four-bar linkage be denoted as . The same applies to variables. Indicates the height of load change. This indicates the height at which the center of gravity of the upper two links of the four-bar linkage changes. This indicates the height at which the center of gravity of the lower two links of the four-bar linkage changes; the diameter of the link is... The connecting rod density is , The length of the link. The minimum angle between the connecting rod and the ground. , Let the mass of the four links be [mass]; from the proportional relationship of the four links, we can obtain: ， definition: Substituting into the above equation and rearranging, we get: 。 5. The global parameter optimization method based on a parallel four-bar linkage bouncing mechanism as described in claim 4, characterized in that, The increase in gravitational potential energy of the spring from its lowest point of compression to its highest point of bounce. The expression is: ； in This refers to the change in spring height of the bouncing mechanism from its lowest compression point to its critical takeoff point. The change in height of the spring in the jumping mechanism from the takeoff critical point to the highest point of the jump is expressed as: The mass of the spring is denoted as: The bouncing energy of the bouncing mechanism For scenarios with high resistance, then... Compensation calculations were performed, and the results are as follows: ； spring mass , For the spring density, The spring's unfolded length, , The effective number of coils of the spring. After sorting, we get: ； Among them, the number of springs Spring mean diameter Spring wire diameter spring original length , For the load and the mass of the connecting rod.

6. The global parameter optimization method based on a parallel four-bar linkage bouncing mechanism as described in claim 5, characterized in that, The energy loss generated by the spring and connecting rod when the spring returns to its original length The expression is: ， in, This refers to the takeoff angle of the bouncing mechanism.

7. The global parameter optimization method based on a parallel four-bar linkage bouncing mechanism as described in claim 6, characterized in that, The optimization objective function in step 3 The energy stored in the spring minus the energy loss: ， in, The total energy stored in the spring. Energy lost by the spring and connecting rod With energy and The ratio of the sums; Then the objective function will be further optimized. Represented as: In the above formula: G is the spring shear modulus. The stress concentration factor of the spring. The spring's torsional yield strength. This refers to the spring installation distance; ； ； ； ； ； 。

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