Design method of non-circular gear train dividing and indexing mechanism based on genetic algorithm

Abstract

The application discloses a non-circular gear train split-insertion mechanism design method based on a genetic algorithm, relates to a non-circular gear train mechanism design method, and is based on a genetic algorithm, combines a closed trajectory curve normalization thought, and solves optimal mechanism parameters by using a MATLAB numerical method. First, a 2R open-chain non-circular gear train basic configuration is established, a Bezier curve is used to fit a non-circular gear pitch curve, a conjugate non-circular gear pair mathematical model is established, then a vector method is used to establish a kinematics model of the mechanism, a motion equation of an end of an executing component is derived, a normalized processing is performed on a motion trajectory of the end of the mechanism and a rice transplanting trajectory of a humanoid hand, influences of translation, rotation and scaling are eliminated, an error function is established based on a minimum Euclidean distance to compare errors between trajectories, and a Bezier type value point pitch diameter of the non-circular gear pitch curve is taken as a population to search for optimal mechanism solutions in a solution domain space of the type value point.

Description

Technical Field

[0001] This invention relates to a design method for non-circular gear train mechanisms, specifically a design method for a non-circular gear train insertion mechanism based on a genetic algorithm. Background Technology

[0002] In rice transplanting machinery and other fields, periodic non-uniform gear transmissions are frequently involved. Commonly used non-circular gears include eccentric circular gears and elliptical gears. However, the transmission ratio of these non-circular gear mechanisms is limited by the pitch curve equation, and they can only output a limited end-effector pose. The design concept of using Bezier curve fitting for non-circular gear pitch curves has a long history. Non-circular gears fitted with Bezier curves can output arbitrary transmission ratio curves and arbitrarily complex end-effector poses. However, due to the complexity of the design process and parameter optimization, it is difficult to solve for the optimal mechanism parameters.

[0003] Existing design methods for finding optimal mechanism solutions through human-computer interaction suffer from problems such as blind selection of initial parameters and strong coupling between parameters. They can only find non-dominated solutions after setting tolerances, and cannot manually find the optimal mechanism parameters. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a design method for non-circular gear train insertion mechanisms based on genetic algorithms. Specifically, the invention involves: fitting the non-circular gear pitch curve using Bezier curves and establishing a mathematical model of the conjugate non-circular gear pair; establishing a motion model of the mechanism based on the 2R open chain configuration and the vector method; deriving the motion vector equation and velocity vector equation of the mechanism's end effector; and obtaining the minimum objective function value and the coordinate values ​​of the optimal non-circular sun gear point.

[0005] To solve the above-mentioned technical problems, the technical solution provided by the present invention is as follows:

[0006] Step 1: Establish a 2R non-circular gear train mechanism, including a non-circular sun gear, non-circular planet gears, a planet carrier, and an actuator (planting arm). The pitch curve of the non-circular sun gear is fitted by a closed Bezier curve, and the shape of the pitch curve is controlled by 12 Bezier type value points. The non-circular planet gears and the non-circular sun gear mesh conjugately, and the non-circular sun gear and the planet carrier rotate in the same direction at a differential speed, thereby driving the planting arm to form a complex end pose.

[0007] Step 2: Establish a mathematical model of the 2R non-circular gear train insertion mechanism, wherein the pitch curve of the non-circular sun gear is fitted by a Bezier curve, and its pitch curve equation is as follows:

[0008]

[0009] Among them, (P) xi ,P yi) represents the coordinates of the non-circular sun gear pitch curve type value points, i = 1, 2, 3... 12, t is the step size, (B x (t),B y (t) represents the rectangular coordinates of the pitch curve of the non-circular sun gear. According to the principle of pure rolling of the pitch curve of the conjugate non-circular gear pair, the non-circular sun gear satisfies the following relationship for one revolution:

[0010]

[0011] In equation (2), n is the average transmission ratio, a is the gear center distance, θ is the polar angle of the non-circular sun gear pitch curve, and r1(θ) is the polar coordinate of the non-circular sun gear pitch curve. From this, the polar coordinate equation of the conjugate non-circular gear pitch curve can be derived as follows:

[0012]

[0013] In equation (3), The polar coordinates of the non-circular sun wheel pitch curve are given. Polar coordinates of the non-circular planetary gear pitch curve;

[0014] Step 3: Establish the kinematic model of the 2R open-chain non-circular gear mechanism based on the vector method, derive the motion equation of the end effector, and consider the planet carrier as vector R1, the actuator as vector R2, and the trajectory point as vector F:

[0015]

[0016] R2 = le jβ (5)

[0017] F = R1 + R2 (6)

[0018] Where a is the center distance of the conjugate gears, l is the length of the actuator rod, and j is the imaginary unit. Let β be the rotation angle of the non-circular sun gear and β be the rotation angle of the actuator. Expand equations (4) and (5) according to Euler's formula:

[0019]

[0020] R2=l·cosβ (t) +lj·sinβ (t) (8)

[0021] Since the planet carrier and the non-circular sun gear rotate at different speeds in the same direction, calculate the rotation angles of the planet carrier and the non-circular sun gear respectively:

[0022]

[0023] γ (t) =ω2t (10)

[0024] Where, equation (9) is the planet carrier rotation angle, equation (10) is the non-circular sun gear rotation angle, and t is time, then the rotation angle of the actuator relative to the planet carrier is:

[0025]

[0026] In equation (11), i (θ) The transmission ratio of the non-circular sun gear and the non-circular planet gear is calculated using equations (1) and (3). Given the initial installation angle α of the planting arm, which is the initial assembly angle of the actuator relative to the planet carrier, the absolute rotation angle β of the actuator (planting arm) can be derived. (t) :

[0027]

[0028] Based on equations (6), (11), and (12), the end motion vector function of the actuator (planting arm) can be derived:

[0029]

[0030] Taking the first derivative of equation (13) yields the end-effector velocity vector function of the actuator (planting arm):

[0031]

[0032] Step 4: Using the extreme diameter of the non-circular sun gear pitch curve value point as the optimization population and the anthropomorphic hand rice planting trajectory as the optimization target, normalize the end motion trajectory of the non-circular gear insertion mechanism and the anthropomorphic hand rice planting trajectory in the same way, and extract trajectory features. Use the difference between the two features as the objective function, and perform genetic iteration on the optimization population based on the genetic algorithm to search for the optimal gear configuration parameters in the solution space of the non-circular sun gear pitch curve value point, so as to provide the design basis for the non-circular gear insertion mechanism.

[0033] Specifically, coordinate transformation is performed on the end motion trajectory of the non-circular gear inserting mechanism and the anthropomorphic hand rice planting trajectory to eliminate differences in position, angle, and magnitude:

[0034]

[0035] (16)

[0036]

[0037] In the above formulas, equation (15) is the coordinate translation formula for the trajectory curve, equation (16) is the coordinate rotation formula for the trajectory curve, and equation (17) is the coordinate scaling formula for the trajectory curve. (P 0x P 0yThe original trajectory curve is denoted as (P). The trajectory curve obtained by translating the original trajectory curve is (P). 1x P 1y ), the trajectory curve (P) 1x P 1y The trajectory curve (P) is obtained after rotation. 2x P 2y ), the trajectory curve (P) 2x P 2y After scaling, the trajectory curve (P) is obtained. 3x P 3y ), where |AB| are the two farthest points on the closed trajectory curve, τ is the angle between the line |AB| and the -x axis, and d is the scaling factor.

[0038] Extracting the end trajectory features of the non-circular gear insertion mechanism and the anthropomorphic hand rice planting trajectory, (x i y i (x) represents the feature point of the end trajectory of the mechanism to be optimized. gi y gi Let be the feature points of the target trajectory. The objective function of the genetic algorithm is established using the Euclidean distance function.

[0039]

[0040] Step 5: Repeat steps 2 to 4 using programmable numerical calculation software to obtain the minimum objective function value and the coordinates of the optimal non-circular sun gear pitch curve point with a limited number of iterations.

[0041] In the objective function of equation (18), (x i ,y i (x) represents the set of trajectory points at the end of a non-circular gear inserting mechanism. gi ,y gi The two sets of trajectory points are simulated as human hands transplanting rice seedlings. The two sets of trajectory points are re-interpolated and sorted in polar coordinates. The coordinates of 360 points are taken as features. The sum of the Euclidean distances between the corresponding points is the objective function value. The smaller the objective function value, the higher the overlap between the two trajectories, and the closer the coordinate parameters of the corresponding point are to the optimal mechanism solution. In the iterative optimization process, the non-circular gear space size and the convergence speed of the solution domain space are considered. The optimization interval of the initial population is set to [40, 110], and the number of iterations is 200 generations.

[0042] The beneficial effects of this invention are:

[0043] 1. This invention provides a mathematical model for conjugate non-circular gear pairs based on the Bezier curve principle, enabling the realization of non-circular gear pairs with arbitrary transmission ratio curves throughout the entire cycle.

[0044] 2. This invention uses a 2R non-circular gear train mechanism as the basic configuration, establishes a kinematic model based on the vector method, and derives the kinematic equations of the mechanism's end effector, providing a theoretical basis for the development of mechanism optimization design software.

[0045] 3. This invention optimizes the parameters of a non-circular gear train insertion mechanism based on the genetic algorithm, avoiding blind selection of initial parameters and finding local non-dominated solutions. It can search for the optimal parameters of the non-circular gear insertion mechanism within a finite parameter solution space.

[0046] 4. This invention combines numerical calculation methods and is easy to develop using a visualization platform to display the visual output of the design results of non-circular gear trains, reducing the design difficulty of non-circular gear mechanisms and enabling non-professionals to design non-uniform gear transmissions.

[0047] 5. Based on the idea of ​​genetic algorithm and combined with the closed trajectory curve normalization method, this invention establishes a single-objective optimization function based on the end trajectory of the 2R non-circular wheel train insertion mechanism and the rice planting trajectory characteristics of the anthropomorphic hand. The extreme diameter of the Beizer-type value point that controls the shape of the non-circular sun wheel pitch curve is used as the optimization population. The optimization interval and the number of iterations are set to search for the optimal mechanism solution in a limited solution domain space and number of iterations. Attached Figure Description

[0048] Figure 1 This is a simplified diagram of the 2R open-chain non-circular gear train mechanism in an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram of the kinematic model of the 2R open chain non-circular gear train mechanism in an embodiment of the present invention;

[0050] Figure 3-1 This is a schematic diagram of coordinate transformation for eliminating displacement effects on a closed trajectory curve in an embodiment of the present invention;

[0051] Figure 3-2 This is a schematic diagram of coordinate transformation for eliminating the effects of rotation on a closed trajectory curve in an embodiment of the present invention;

[0052] Figure 3-3 This is a schematic diagram of coordinate transformation for eliminating scaling effects on closed trajectory curves in an embodiment of the present invention;

[0053] Figure 3-4 This is a schematic diagram of the normalized result of the closed trajectory curve in an embodiment of the present invention;

[0054] Figure 4 This is a schematic diagram of the interface for the genetic optimization process of non-circular gear parameters in an embodiment of the present invention;

[0055] Figure 5 This is a schematic diagram of the 2R non-circular gear train insertion mechanism configuration under optimal parameters in an embodiment of the present invention;

[0056] Figure 6 This is a transmission ratio curve of the 2R non-circular gear train insertion mechanism under the optimal parameters in an embodiment of the present invention.

[0057] Figure label:

[0058] 1-Non-circular sun gear; 2-Planet carrier; 3-Non-circular planet gear; 4-Actuator; 5-Mechanism end trajectory; 6-Seedling box; 7-Planting arm end trajectory under optimal intercropping mechanism parameters; 8-Ground. Detailed Implementation

[0059] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0060] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0061] This invention, based on a genetic algorithm and incorporating the idea of ​​closed trajectory curve normalization, utilizes MATLAB numerical methods to solve for optimal mechanism parameters. First, a basic configuration of a 2R open-chain non-circular gear train is established. The non-circular gear pitch curve is fitted with a Bezier curve to establish a mathematical model of the conjugate non-circular gear pair. Then, a vector method is used to establish the kinematic model of the mechanism, deriving the end-effector motion equations. The end-effector motion trajectory and the simulated human hand's rice-planting trajectory are normalized to eliminate the effects of translation, rotation, and scaling. An error function is established based on the minimum Euclidean distance to compare the errors between the two trajectories. Minimizing the error value is the optimization objective. The optimal mechanism solution within the solution domain space of the Bezier type value points of the non-circular gear pitch curve is searched using the polar radius of these points as the population.

[0062] This invention provides a genetic algorithm for parameter optimization of a single pair of non-circular gears. Similarly, it can be used to derive two or three pairs of non-circular gear structures of the same form, requiring only a certain angle to be evenly distributed circumferentially.

[0063] The design method for a 2R non-circular gear train insertion mechanism based on a genetic algorithm includes the following steps:

[0064] Combined with appendix Figure 1As shown, step one is to establish a 2R non-circular gear train mechanism, including a non-circular sun gear 1, a non-circular planetary gear 3, a planetary carrier 2, and an actuator 4, i.e., the planting arm. The pitch curve of the non-circular sun gear 1 is fitted by a closed Bezier curve, and the shape of the pitch curve of the non-circular sun gear is controlled by 12 Bezier type value points. The non-circular planetary gear 3 is conjugately meshed with the non-circular sun gear 1. The non-circular sun gear 1 and the planetary carrier 2 rotate in the same direction at a differential speed, driving the actuator 4, which is fixedly connected to the non-circular planetary gear, to form a complex end pose.

[0065] Combined with appendix Figure 2 As shown, step two involves establishing a mathematical model of the 2R non-circular gear train insertion mechanism. The pitch curve of the non-circular sun gear is fitted by a Bezier curve, and its equation is as follows:

[0066]

[0067] Among them, (P) xi P yi ) represents the coordinates of the non-circular sun gear pitch curve type value points, i = 1, 2, 3...12, t is the step size, (B x (t), B y (t) represents the rectangular coordinates of the pitch curve of the non-circular sun gear. According to the principle of pure rolling of the pitch curve of the conjugate non-circular gear pair, the non-circular sun gear satisfies the following relationship for one revolution:

[0068]

[0069] In equation (2), n is the average transmission ratio, α is the center distance of the non-circular gear, and θ is the polar angle of the non-circular sun gear pitch curve. From this, the polar coordinate equation of the conjugate non-circular gear pitch curve is derived as follows:

[0070]

[0071] In equation (3), The polar coordinates of the non-circular sun wheel pitch curve are given. Polar coordinates of the non-circular planetary gear pitch curve;

[0072] Combined with appendix Figure 2 As shown, step three involves constructing a kinematic model of the 2R open-chain non-circular gear mechanism based on the vector method, deriving the motion equations of the mechanism's end effector, treating the planetary carrier as vector R1, the actuator as vector R2, and the trajectory point as vector F:

[0073]

[0074] R2 = le jβ (5)

[0075] F = R1 + R2 (6)

[0076] Where a is the center distance of the conjugate gears, l is the length of the actuator rod, and j is the imaginary unit. Let β be the rotation angle of the non-circular sun gear and β be the rotation angle of the actuator. Expand equations (4) and (5) according to Euler's formula:

[0077]

[0078] R2=l·cosβ (t) +lj·sinβ (t) (8)

[0079] Since the planet carrier and the non-circular sun gear rotate at different speeds in the same direction, calculate the rotation angles of the planet carrier and the non-circular sun gear respectively:

[0080]

[0081] γ (t) =ω2t (10)

[0082] Where, equation (9) is the planet carrier rotation angle, equation (10) is the non-circular sun gear rotation angle, and t is time, then the rotation angle of the actuator 4 relative to the planet carrier is:

[0083]

[0084] In equation (11), i (θ) The transmission ratio of the non-circular sun gear and the non-circular planet gear is calculated using equations (1) and (3). Given the initial installation angle α of the planting arm, which is the initial assembly angle of the actuator 4 relative to the planet carrier, the absolute rotation angle β of the actuator 4 can be derived. (t) :

[0085]

[0086] Based on equations (6), (11), and (12), the end motion vector function of the actuator 4 can be derived:

[0087]

[0088] Taking the first derivative of equation (13) yields the end velocity vector function of the actuator:

[0089]

[0090] Combined with appendix Figure 3-1 , 3-2 3-3, 3-4 and Figure 4As shown, in step four, using the polar radius of the Bezier-type value point of the non-circular sun gear as the optimization population and the anthropomorphic hand rice planting trajectory as the optimization objective, the end motion trajectory of the non-circular gear insertion mechanism and the anthropomorphic hand rice planting trajectory are normalized in the same way, and trajectory features are extracted. The difference between the two features is used as the objective function. Based on the genetic algorithm, the optimization population is subjected to genetic iteration, thereby searching for the optimal gear configuration parameters in the solution space of the non-circular sun gear pitch curve value point coordinates, so as to provide the design basis for the non-circular gear insertion mechanism.

[0091] Specifically, coordinate transformation is performed on the end motion trajectory of the non-circular gear inserting mechanism and the anthropomorphic hand rice planting trajectory to eliminate differences in position, angle, and magnitude:

[0092]

[0093] (16)

[0094]

[0095] In the above formulas, equation (15) is the coordinate translation formula for the trajectory curve, equation (16) is the coordinate rotation formula for the trajectory curve, and equation (17) is the coordinate scaling formula for the trajectory curve. (P 0x P 0y The original trajectory curve is denoted as (P). The trajectory curve obtained by translating the original trajectory curve is (P). 1x ,P 1y ), the trajectory curve (P) 1x ,P 1y The trajectory curve (P) is obtained after rotation. 2x ,P 2y ), the trajectory curve (P) 2x ,P 2y After scaling, the trajectory curve (P) is obtained. 3x ,P 3y ), where |AB| are the two farthest points on the closed trajectory curve, τ is the angle between the line |AB| and the -x axis, and d is the scaling factor;

[0096] Extracting the end trajectory features of the non-circular gear insertion mechanism and the anthropomorphic hand rice planting trajectory, (x i ,y i (x) represents the feature point of the end trajectory of the mechanism to be optimized. gi y gi Let be the feature points of the target trajectory. The objective function of the genetic algorithm is established using the Euclidean distance function.

[0097]

[0098] In the objective function of equation (18), (x i ,y i(x) represents the set of trajectory points at the end of a non-circular gear inserting mechanism. gi y gi The trajectory point set is a simulation of human hand transplanting rice seedlings. The trajectory point sets of the two are re-interpolated and sorted in polar coordinates. The coordinates of 360 points are taken as features. The sum of the Euclidean distances between the corresponding points of the two is the objective function value. The smaller the objective function value, the higher the overlap between the two trajectories, and the closer the coordinate parameters of the corresponding point are to the optimal mechanism solution. In the iterative optimization process, the non-circular gear space size and the convergence speed of the solution domain space are considered. The optimization interval of the initial population is set to [40, 110], and the number of iterations is 200 generations.

[0099] The optimization results of the embodiments of the present invention are as follows: Figure 5 and Figure 6 As shown, Figure 5 This is a schematic diagram of the 2R non-circular gear train insertion mechanism configuration under optimal parameters in an embodiment of the present invention. Figure 6 This is a transmission ratio curve of the 2R non-circular gear train insertion mechanism under optimal parameters in an embodiment of the present invention. Figure 5 Under the 2R non-circular gear train insertion mechanism configuration shown, the coordinates of the non-circular sun gear pitch curve point are: r0 = 53; θ0 = 0°

[0100] r1 = 56; θ1 = 30°

[0101] r² = 64; θ² = 60°

[0102] r3 = 47; θ3 = 90°

[0103] r4 = 25; θ4 = 120°

[0104] r5 = 105; θ5 = 150°

[0105] r6 = 67; θ6 = 180°

[0106] r7 = 112; θ7 = 210°

[0107] r8 = 92; θ8 = 240°

[0108] r9 = 65°; θ9 = 270°

[0109] r 10 =53; θ 10 =300°

[0110] r 11 =53; θ 11 =330°

[0111] In this embodiment, based on the motion trajectory of a simulated human hand during rice transplanting, the end trajectory of the 2R non-circular gear transplanting mechanism is normalized to the motion trajectory of the simulated human hand during transplanting, eliminating the effects of translation, rotation, and scaling. The objective function is established using Euclidean absolute distance to compare the error between the two closed trajectory curves. The smaller the error value, the higher the overlap between the two trajectories, and the closer the obtained gear parameters are to the optimal solution.

[0112] The method of this invention provides a design theoretical support for non-circular gear pairs with arbitrary transmission ratios, and establishes a parameter optimization algorithm for non-circular gear pairs based on genetic algorithms.

[0113] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0114] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A design method for a non-circular gear train insertion mechanism based on a genetic algorithm, characterized in that, The specific steps are as follows: Step 1: Establish the configuration of the 2R non-circular gear train mechanism, including a non-circular sun gear, non-circular planet gears, a planet carrier, and an actuator. The pitch curve of the non-circular sun gear is fitted by a closed Bezier curve. The shape of the pitch curve of the non-circular sun gear is controlled by 12 Bezier type value points. The non-circular planet gears and the non-circular sun gear mesh conjugately. The non-circular sun gear and the planet carrier rotate in the same direction at a differential speed, driving the actuator, which is fixedly connected to the non-circular planet gears, to form a complex end pose. Step 2: Establish a mathematical model of the 2R non-circular gear train insertion mechanism, wherein the pitch curve of the non-circular sun gear is fitted by a Bezier curve, and its pitch curve equation is as follows: (1) in, The coordinates of the non-circular sun gear pitch curve type value points are: t is the step size. Let be the rectangular coordinates of the pitch curve of the non-circular sun gear. According to the principle of pure rolling of the pitch curve of the conjugate non-circular gear pair, the non-circular sun gear satisfies the following relationship for one revolution: （2) In equation (2), n is the average transmission ratio, and a is the center distance of the non-circular gear pair. Let be the polar angle of the non-circular sun gear pitch curve. From this, the polar coordinate equation of the conjugate non-circular gear pitch curve is derived as follows: (3) In equation (3), , , The polar coordinates of the non-circular sun wheel pitch curve are given. Polar coordinates of the non-circular planetary gear pitch curve; Step 3: Establish the kinematic model of the 2R open-chain non-circular gear train mechanism based on the vector method, derive the equation of motion of the end effector of the mechanism, and use the planet carrier as a vector. The execution component is a vector. The trajectory point is then represented by the vector F: (4) (5) (6) Where a is the center distance of the non-circular gear pair, l is the length of the actuator rod, and j is the imaginary unit. For non-circular solar wheel rotation angle, To calculate the component rotation angle, equations (4) and (5) are expanded according to Euler's formula: (7) (8) Since the planet carrier and the non-circular sun gear rotate at different speeds in the same direction, calculate the rotation angles of the planet carrier and the non-circular sun gear respectively: (9) (10) Where, equation (10) is the planet carrier rotation angle, equation (9) is the non-circular sun gear rotation angle, and t is time, then the rotation angle of the actuator relative to the planet carrier is: (11) In equation (11), The transmission ratio of the non-circular sun gear and the non-circular planet gear is calculated using equations (1) and (3). Given the initial installation angle α of the planting arm, which is the initial assembly angle of the actuator relative to the planet carrier, the absolute rotation angle of the actuator can be derived. : (12) Based on equations (6), (11), and (12), the end motion vector function of the actuator can be derived: (13) Taking the first derivative of equation (13) yields the end-effector velocity vector function of the actuator: Step 4: Using the extreme radius of the Bezier-type value point of the non-circular sun gear as the optimization population and the anthropomorphic hand rice planting trajectory as the optimization target, normalize the end motion trajectory of the non-circular gear train insertion mechanism and the anthropomorphic hand rice planting trajectory in the same way, and extract the trajectory features. Use the difference between the two features as the objective function, and perform genetic iteration on the optimization population based on the genetic algorithm to search for the optimal mechanism parameters in the solution space of the non-circular sun gear pitch curve type value point, so as to provide the design basis for the non-circular gear train insertion mechanism. Specifically, coordinate transformation is performed on the end-effector trajectory of the non-circular gear train and the anthropomorphic hand rice-planting trajectory to eliminate differences in position, angle, and magnitude: (15) (16) (17) In the above formulas, equation (15) is the coordinate translation formula for the trajectory curve, equation (16) is the coordinate rotation formula for the trajectory curve, and equation (17) is the coordinate scaling formula for the trajectory curve. The original trajectory curve is obtained by translating the original trajectory curve. , trajectory curve The trajectory curve is obtained after rotation. , trajectory curve The trajectory curve is obtained after scaling. Where |AB| are the two farthest points on the closed trajectory curve, τ is the angle between the line |AB| and the -x axis, and d is the scaling factor; Extract the end trajectory features of the non-circular gear train transplanting mechanism and the anthropomorphic hand transplanting trajectory features. The feature points of the end trajectory of the mechanism to be optimized. For the feature points of the target trajectory, the objective function of the genetic algorithm is established using the Euclidean distance function: (18) Step 5: Repeating steps 2 to 4 using programmable numerical calculation software can yield the minimum objective function value and the coordinates of the optimal non-circular sun gear point with a limited number of iterations.

2. The design method for a non-circular gear train insertion mechanism based on a genetic algorithm according to claim 1, characterized in that, The 2R non-circular gear train mechanism described in step one has a two-arm or three-arm output configuration, with non-circular planetary gears and actuators of the same size installed at equal angles along the circumference of the non-circular sun gear.

3. The design method for a non-circular gear train insertion mechanism based on a genetic algorithm according to claim 1, characterized in that, In step one, the closed Bezier curve is obtained by setting the coordinates of the first and last non-circular sun gear pitch curve points to coincide.

4. The design method for a non-circular gear train insertion mechanism based on a genetic algorithm according to claim 1, characterized in that, In step two, the coordinates of the non-circular sun gear pitch curve type points are arranged at 30° intervals.

5. The design method for a non-circular gear train insertion mechanism based on a genetic algorithm according to claim 1, characterized in that, In step five, during the optimization process of the objective function of the genetic algorithm, the coordinates of the non-circular sun gear pitch curve value points are used as the optimization population. Considering the limitations of the mechanism's motion space and convergence speed, the initial optimization interval of the non-circular sun gear pitch curve value point coordinates is set to [40, 110], and the number of iterations is set to 200 generations.

6. The design method for a non-circular gear train insertion mechanism based on a genetic algorithm according to claim 1, characterized in that, Step four: The trajectory features are an ordered set of discrete points after interpolation of a closed curve in polar coordinates. The discrete points are spaced 1° apart in polar coordinates, and the set contains a total of 360 discrete points.

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