A method for calculating the lifting force of a cutter head lifting mechanism of a mower

Abstract

The application discloses a lifting force analysis calculation method of a mower cutter head lifting mechanism, and the method comprises the following steps: establishing a parameterized mechanical model, simplifying the cutter head lifting mechanism into a planar linkage mechanism, and defining the position relationship of each hinged point and the equivalent gravity center of a load; constructing a multi-body dynamics equation set, establishing a geometric constraint equation set based on the vector closed loop principle, and establishing a mechanical balance equation set based on the static force balance principle; numerical iteration solving, setting the rotation angle of the input component as the independent variable, solving the equation set to obtain the input torque under the corresponding pose; and generating a performance curve, drawing the process curve of the lifting force / torque changing with the lifting angle. The application can quickly predict the lifting force characteristics in the forward design stage by replacing the traditional simulation software, solves the problems of low simulation calculation efficiency, high threshold and easy to produce false values in the prior art, and is suitable for the parameterized design and optimization of the cutter head lifting mechanism of the riding mower.

Description

Technical Field

[0001] This application belongs to the interdisciplinary field of lawnmower design and computational mechanics, specifically involving an analytical calculation method for the lifting force of a lawnmower cutter head lifting mechanism based on dynamic static analysis of a planar linkage mechanism, which is particularly applicable to the forward design and performance optimization of the cutter head lifting mechanism of a ride-on lawnmower. Background Technology

[0002] With the rapid development of the ride-on lawnmower market, vehicle models and cutter head widths are becoming increasingly diverse, requiring the arrangement of the cutter head lifting mechanism to adapt to the varied overall vehicle layout. Accurately predicting the cutter head lifting force during the design process is crucial to ensuring ease of operation and mechanism reliability.

[0003] Currently, the industry generally relies on the motion simulation modules of 3D modeling software (such as SolidWorks and ADAMS) for lifting force analysis. This method requires first establishing a complete 3D digital model, setting complex kinematic pair constraints and driving parameters, and repeatedly debugging before results can be obtained. This simulation-based method has the following drawbacks:

[0004] 1. Delayed application stage: It is more suitable for reverse verification after structural qualitative analysis, and it is difficult to support forward development in the early parametric design stage;

[0005] 2. High operational threshold: The simulation process requires setting up complex kinematic pairs, constraints and loads. The steps are complicated and require designers to have high software operation skills. If the constraint definition is omitted or incorrect during the simulation process, it is easy to generate false values ​​that are difficult to identify and mislead the design, affecting the design decision.

[0006] 3. Low efficiency: The simulation needs to be rerun every time the parameters are changed, which results in a long calculation cycle and is not conducive to the rapid comparison and selection of multiple schemes.

[0007] Therefore, there is an urgent need for an analytical calculation method that can quickly and accurately calculate the lifting force of the cutter head at the design stage. Summary of the Invention

[0008] The purpose of this application is to provide an analytical calculation method for the lifting force of the lawnmower blade lifting mechanism, which solves the problems of low efficiency, high threshold and unsuitability for forward design in the existing simulation calculation method. It enables the rapid acquisition of lifting force / torque curves through parametric modeling and supports automatic optimization of mechanism parameters.

[0009] The above-mentioned objective of this application is achieved through the following technical solution:

[0010] A method for analytically calculating the lifting force of a lawnmower blade lifting mechanism, the method comprising:

[0011] S1. Establish a parametric mechanical model. Based on the topology of the cutter head lifting mechanism, simplify it into a planar linkage mechanism and define the positional relationship between each hinge point and the equivalent center of gravity of the load in the planar coordinate system.

[0012] S2, construct a set of multibody dynamic equations, establish a set of geometric constraint equations based on the principle of vector closed loop, and establish a set of mechanical equilibrium equations based on the principle of static equilibrium;

[0013] S3, numerical iterative solution: set the rotation angle of the input component as the independent variable, solve the geometric constraint equations and mechanical equilibrium equations to obtain the input torque under the corresponding pose;

[0014] S4, Generate performance curves, plotting the process curve of lifting force / torque changing with lifting angle based on the obtained input torque data.

[0015] Preferably, in step S1, simplifying the topology of the cutter head lifting mechanism into a planar linkage mechanism and defining the positional relationship between each hinge point and the equivalent center of gravity of the load in a planar coordinate system specifically includes:

[0016] S11, Based on the topology of the cutter head lifting mechanism, the rigid link in three-dimensional space is abstracted into a vector line segment in a two-dimensional plane, and the hinge point is abstracted into a vector endpoint, thus constructing the planar link mechanism;

[0017] S12, the planar linkage mechanism is decomposed into multiple interconnected planar four-bar sub-mechanisms according to the topological connection relationship. The multiple interconnected planar four-bar sub-mechanisms include an input lever arm subsystem, a transmission link subsystem, and a load equivalent subsystem. The input lever arm subsystem is used to receive driving force and generate initial displacement. The transmission link subsystem is used to transmit motion and force. The load equivalent subsystem is used to bear the weight of the cutter head and realize the lifting action.

[0018] S13, define the positional relationship between the hinge points and the equivalent center of gravity of the load in each subsystem in the plane coordinate system, and assign corresponding geometric constraint parameters to each subsystem.

[0019] Preferably, in step S2, the establishment of the geometric constraint equation system based on the vector closed-loop principle specifically includes:

[0020] For each closed kinematic chain in the cutter head lifting mechanism, establish a vector closed-loop equation;

[0021] Projecting the vector closed-loop equation onto a plane coordinate system, it is decomposed into horizontal component equations and vertical component equations, resulting in a system of nonlinear algebraic equations.

[0022] Preferably, in step S2, the establishment of a set of mechanical equilibrium equations based on the principle of static equilibrium specifically includes:

[0023] The load gravity is applied equivalently to the center of gravity of the equivalent load subsystem.

[0024] For the load equivalent subsystem and the transmission linkage subsystem, force balance equations and torque balance equations are established for each subsystem.

[0025] Preferably, in step S3, the rotation angle of the input component is set as the independent variable, and the geometric constraint equations and mechanical equilibrium equations are solved to obtain the input torque under the corresponding pose. Specifically, this includes:

[0026] Set the initial value and step size of the rotation angle of the input component, and enter the loop iteration process;

[0027] In each iteration, the nonlinear algebraic equations are solved using numerical analysis algorithms to obtain the instantaneous pose angles of each member.

[0028] Preferably, in each iteration, the following is also included:

[0029] The instantaneous pose angle is substituted into the mechanical equilibrium equations, and the mechanical equilibrium equations are solved by matrix operations to output the input torque of the input lever arm subsystem under the current pose.

[0030] Preferably, the numerical analysis algorithm is the Newton-Raphson iteration method, the quasi-Newton method, or the bisection method.

[0031] Preferably, after step S4, the method further includes:

[0032] S5, Forward optimization design: Compare the process curve with the preset target force range. If the calculated lifting force value of the process curve exceeds the target force range, adjust the geometric constraint parameters based on sensitivity analysis and return to step S2. Re-execute steps S2 and S3 based on the adjusted geometric constraint parameters to update the process curve until the updated process curve falls into the target force range.

[0033] Preferably, step S4 is followed by a step to verify the feasibility of the movement of the cutter head lifting mechanism:

[0034] The residual value of the nonlinear algebraic equation system is monitored in real time during the iterative solution process. If the residual value exceeds the preset convergence threshold in any iteration step, it is determined that the cutter head lifting mechanism under the current geometric constraint parameters has a motion dead point or assembly interference, and an error prompt message is output.

[0035] Preferably, in step S13, defining the positional relationship between the hinge points and the equivalent center of gravity of the load in each subsystem in the planar coordinate system specifically includes:

[0036] Establish a global absolute coordinate system and a local relative coordinate system;

[0037] The geometric dimensions of the input lever arm subsystem, transmission link subsystem, and load equivalent subsystem are parameterized, and the local vectors of each subsystem are transformed to the global absolute coordinate system through a coordinate transformation matrix to construct a unified mechanical calculation benchmark.

[0038] Compared with the prior art, this application has the following beneficial effects:

[0039] 1. Suitable for forward design: Only geometric parameters need to be input during the conceptual design phase to calculate the lifting force, eliminating the need to build complex 3D models and shortening the development cycle;

[0040] 2. Highly efficient and accurate calculation: Analytical algorithms are used instead of graphical simulation, avoiding complex constraint settings, resulting in fast calculation speed and less spurious values.

[0041] 3. High versatility: As long as the mechanical model of the lifting mechanism is similar (such as a four-bar linkage), the lifting force of different models can be quickly calculated by adjusting the parameters;

[0042] 4. Closed-loop optimization: It integrates calculation, verification and parameter optimization functions, and can automatically find the combination of mechanism parameters that meet the force characteristic requirements. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a flowchart illustrating the analytical calculation method for the lifting force of the lawnmower blade lifting mechanism in one embodiment of this application;

[0045] Figure 2 This is a schematic diagram of the structure of the lawnmower blade lifting mechanism in one embodiment of this application;

[0046] Figure 3 For this application Figure 2 A schematic diagram of the parametric mechanical model of the lawnmower blade lifting mechanism shown;

[0047] Figure 4 This is a schematic diagram of a process curve in one embodiment of this application. Detailed Implementation

[0048] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0049] In the embodiments provided in this application, it should be understood that the disclosed methods and systems can be implemented in other ways. The system embodiments described below are merely illustrative. For example, the division of units and modules is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or modules can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, and can be electrical, mechanical, or other forms.

[0050] In addition, each functional unit in the various embodiments of this application can be integrated into a single processor, or each unit can be a separate device, or two or more units can be integrated into a single device; each functional unit in the various embodiments of this application can be implemented in hardware or in the form of hardware plus software functional units.

[0051] Those skilled in the art will understand that all or part of the steps of the following method embodiments can be implemented by program instructions and related hardware. The aforementioned program instructions can be stored in a computer-readable storage medium. When the program instructions are executed, they perform the steps of the following method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), magnetic disks, or optical disks.

[0052] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "a plurality of" or "several" means two or more, unless otherwise explicitly specified.

[0053] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. It should be noted that the core innovative ideas of this application can be implemented through a variety of specific technical means.

[0054] This application provides an analytical calculation method for the lifting force of a lawnmower blade lifting mechanism. This method replaces traditional three-dimensional simulation with parametric modeling and analytical calculation, which can quickly predict lifting force characteristics and support forward design and parameter optimization.

[0055] like Figure 1-4 As shown, the analytical calculation method for the lifting force of the lawnmower blade lifting mechanism may include the following steps:

[0056] S1. Establish a parametric mechanical model: Based on the topology of the cutter head lifting mechanism, simplify it into a planar linkage mechanism, and define the positional relationship of each hinge point and the equivalent center of gravity of the load in the planar coordinate system.

[0057] Specifically, in this embodiment, the cutter head lifting mechanism is as follows: Figure 2 As shown, the rigid body components in the cutterhead lifting mechanism are abstracted as massless rigid links, and the connection points between the components are abstracted as ideal hinge points. The gravity of the cutterhead is equivalently applied to the midpoint of the line connecting the cutterhead to the connection points of the front and rear lifting shafts. A Cartesian coordinate system is constructed with the center point of the rear lifting shaft as the origin, the direction parallel to the line connecting the centers of the front and rear lifting shafts as the positive X-axis, and the direction perpendicular to this line as the positive Y-axis. The established parametric mechanical model is as follows: Figure 3 As shown, where,

[0058] Point O is the rotation center of the lifting handle (fixed to the upper end of the lifting rocker arm, not shown in the figure), and is a fixed point;

[0059] Point A is the hinge point between the lifting rocker arm and the lifting connecting rod, and is a point of motion;

[0060] Point B is the hinge point of the lifting connecting rod and the rotating arm of the cutter head rear lifting shaft, and is a moving point;

[0061] Point C1 is the center point of the rear lifting shaft of the tool turret, which is a fixed point and also the origin of the defined coordinate system;

[0062] Point C2 is the center point of the front hanger shaft of the cutter head, which is a fixed point;

[0063] Point D1 is the hinge point between the rear hanger shaft of the cutter head and the connecting rod between the front and rear hanger shafts. It is a moving point and also a point collinear with C1B.

[0064] Point D2 is the hinge point of the connecting rod between the front hanger shaft and the front and rear hanger shafts of the cutter head, and it is a moving point;

[0065] Point E1 is the hinge point connecting the rear hanger shaft of the cutter head to the cutter head, and it is a moving point.

[0066] Point E2 is the hinge point connecting the front lifting shaft of the cutter head to the cutter head, and it is a moving point;

[0067] The origin of the plane coordinate system is point C1;

[0068] The X-axis is parallel to the line connecting C1 and C2, with the right side being positive.

[0069] The Y-axis is perpendicular to the line connecting C1 and C2, and the upper edge of the X-axis is positive.

[0070] Specifically, it is known that: the length of OA is L1; the length of AB is L2; ​​the length of BC1 is L3; the length of C1E1 is L4; the length of E1E2 is L5; the length of C2D2 is L6; the distance from point O to point C1 is projected onto the X-axis as L; the distance from point O to point C1 is projected onto the Y-axis as H; and the angles of BC1E1 and D2C2E2 are both α.

[0071] The connection between E1 and E2 can be considered as a connecting rod whose weight is equal to that of the cutter head. The gravity G = m * g, and the cutter head is raised in order to raise E1 and E2.

[0072] Independent variable: the angle of rotation of the rocker arm θ1, the angle between OA and the +Y direction;

[0073] The dependent variable is the lifting torque Me of the rocker arm. The lifting force can be calculated by lifting the design length of the handle. If the handle length is unknown in the early stage, the torque can be calculated first.

[0074] Dependent variable 1, the motion angle θ2 of the lifting link, the angle between AB and the +X direction;

[0075] Dependent variable 2 is the rotation angle θ3 of the rear hanger shaft of the cutter head, which is the angle between C1B and the +Y direction, and also the angle between C2D2 and the +Y direction.

[0076] S2, Construct a set of multibody dynamic equations: establish a set of geometric constraint equations based on the principle of vector closed loop, and establish a set of mechanical equilibrium equations based on the principle of static equilibrium.

[0077] Specifically, a vector closed-loop equation is established for the closed kinematic chain formed by the lifting handle, lifting rocker arm, lifting linkage, cutter head lifting shaft rotating arm, and cutter head body. This vector closed-loop equation is projected onto the X and Y axes of a planar coordinate system and decomposed into two nonlinear algebraic equations. Simultaneously, force balance equations and torque balance equations are established for the equivalent linkage of the cutter head, introducing the weight of the cutter head as an external load and the input torque at the lifting handle as a variable to be determined.

[0078] S3, Numerical Iteration Solution: Set the rotation angle of the input component as the independent variable, solve the geometric constraint equations and the mechanical equilibrium equations to obtain the input torque under the corresponding pose.

[0079] Specifically, the initial value (e.g., -30°), the final value (e.g., 30°), and the step value (e.g., 1°) of the lifting arm rotation angle are set. For each rotation angle value, the geometric constraint equations are first solved numerically to obtain the motion angle of the lifting link and the rotation angle of the rear lifting shaft of the cutter head; then, the obtained motion parameters are substituted into the mechanical equilibrium equations, and the linear equations are solved through matrix operations to obtain the input torque at the current angle.

[0080] S4, Generate Performance Curve: Plot the process curve of lifting force / torque changing with lifting angle based on the obtained input torque data.

[0081] Specifically, such as Figure 4 As shown, a curve is plotted showing the change in lifting torque as a function of the lifting angle, with the lifting arm rotation angle (i.e., lifting angle θ1) as the abscissa and the input torque (i.e., lifting torque Me) as the ordinate. The torque curve can also be converted into an operating lifting force curve based on the design length of the lifting handle to evaluate ease of operation.

[0082] This embodiment simplifies the complex spatial linkage mechanism into a planar linkage mechanism. It describes the geometric constraints between components using the vector closed-loop principle and the force transmission relationships between components using the static equilibrium principle, thus transforming the lifting force calculation problem into a simultaneous solution problem of nonlinear and linear equations. Through numerical iteration, the equations are solved at each discrete position of the lifting stroke to obtain a complete curve of the lifting torque as a function of angle.

[0083] The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism provided in this embodiment can calculate the lifting force during the parameter design stage of the blade lifting mechanism, without the need to establish a three-dimensional solid model or perform complex motion simulation settings. Compared with existing methods that rely on three-dimensional simulation software, the calculation efficiency of this embodiment is significantly improved, and the calculation results have clear physical meaning and traceability, effectively avoiding calculation artifacts and uncertainty caused by nonlinear convergence instability or ambiguity in contact parameter definitions during numerical simulation.

[0084] In one embodiment, step S1 simplifies the cutter head lifting mechanism into a planar linkage mechanism based on its topology, and defines the positional relationship between each hinge point and the equivalent center of gravity of the load in a planar coordinate system, specifically including:

[0085] S11, Constructing a planar linkage mechanism: Based on the topology of the cutter head lifting mechanism, the rigid link in three-dimensional space is abstracted into a vector line segment in a two-dimensional plane, and the hinge point is abstracted into a vector endpoint, thus constructing a planar linkage mechanism.

[0086] Specifically, all rigid body components in the cutter head lifting mechanism (including the lifting handle, lifting rocker arm, lifting linkage, cutter head rear hanger rotating arm, cutter head front hanger rotating arm, front and rear hanger linkages, and cutter head body) are projected onto the main force plane (i.e. the plane of the cutter head lifting motion) according to their spatial connection relationship, forming a topological diagram of the planar linkage mechanism.

[0087] S12, decomposed into multiple sub-mechanisms: The planar linkage mechanism is decomposed into multiple interconnected planar four-bar sub-mechanisms according to the topological connection relationship. The multiple interconnected planar four-bar sub-mechanisms include an input lever arm subsystem, a transmission link subsystem, and a load equivalent subsystem. The input lever arm subsystem is used to receive the driving force and generate the initial displacement, the transmission link subsystem is used to transmit motion and force, and the load equivalent subsystem is used to bear the weight of the cutter head and realize the lifting action.

[0088] Specifically, the input lever arm subsystem receives the driving force and generates the initial displacement, and consists of the lifting handle rotation center and the lifting rocker arm; the transmission linkage subsystem transmits motion and force, and consists of the lifting linkage and the rotating arm of the cutter head rear hanger shaft; the load equivalent subsystem bears the weight of the cutter head and realizes the lifting action, and consists of the cutter head rear hanger shaft, the cutter head front hanger shaft, and the cutter head body. The cutter head lifting mechanism can be decomposed into a first planar four-bar submechanism (input lever arm subsystem and transmission linkage subsystem) and a second planar four-bar submechanism (load equivalent subsystem).

[0089] S13, Define positional relationships: Define the positional relationships of hinge points and equivalent center of gravity of loads in each subsystem in the planar coordinate system, and assign corresponding geometric constraint parameters to each subsystem.

[0090] Specifically, geometric parameters such as the coordinates of the rotation center of the lifting handle, the length of each link, the initial angle between each hinge point, and the offset of the center of gravity of the cutter head relative to the connection point are defined, and these parameters are used as known input quantities.

[0091] This embodiment modularizes the complex cutterhead lifting mechanism according to its function, breaking down the overall mechanism into three functional subsystems: input, transmission, and load. Each subsystem can be independently described geometrically and analyzed mechanically. This modular modeling approach reduces the complexity of mathematical modeling, making the subsequent construction and solution of equations clearer and more efficient.

[0092] This embodiment achieves layered modeling of complex mechanisms by decomposing the cutterhead lifting mechanism into multiple planar four-bar sub-mechanisms. Compared to the overall modeling method, the modeling approach of this embodiment is more in line with the thinking habits of engineering designers, facilitating independent optimization of specific subsystems during the design process. Furthermore, the subsystem division method is universal, applicable to cutterhead lifting mechanisms of different models and layouts; simply adjusting the geometric constraint parameters of each subsystem allows for rapid adaptation to new vehicle models.

[0093] In one embodiment, step S2, establishing a set of geometric constraint equations based on the vector closed-loop principle, specifically includes:

[0094] First, for each closed kinematic chain in the cutter head lifting mechanism, establish the vector closed-loop equation:

[0095]

[0096] in, Let represent the vector length of the i-th link in the closed kinematic chain, and n represent the number of links in the closed kinematic chain.

[0097] Then, the vector closed-loop equation is projected onto a plane coordinate system and decomposed into horizontal component equations and vertical component equations:

[0098]

[0099]

[0100] in, Let represent the angle between the i-th member and the horizontal axis (X-axis) of the plane coordinate system. This represents the length of the i-th member.

[0101] Finally, by combining the two component equations above, we obtain a system of nonlinear algebraic equations:

[0102]

[0103] For the two closed kinematic chains in the cutter head lifting mechanism (i.e., the first planar four-bar sub-mechanism and the second planar four-bar sub-mechanism), the above-mentioned nonlinear equation system is established respectively, so as to determine the functional relationship between the motion parameters of the input component and the motion parameters of each driven component.

[0104] This embodiment utilizes the vector closed-loop principle to describe the geometric constraints of a planar linkage mechanism. In a planar four-bar submechanism, the links are connected end-to-end to form a closed loop, and the sum of their vectors is zero. Decomposing this vector equation into scalar equations along the X and Y axes allows us to establish two nonlinear algebraic equations. Since there are two unknown motion parameters in the mechanism (such as the lifting link's motion angle and the rotation angle of the cutterhead's rear suspension shaft), the two equations form a closed, solvable system of nonlinear equations.

[0105] The method for establishing geometric constraint equations provided in this embodiment can accurately describe the positional changes of the cutterhead lifting mechanism throughout its entire stroke. Compared to kinematic analysis relying on 3D simulation software, the analytical method in this embodiment has the advantages of high computational accuracy, fast computation speed, and traceability of intermediate variables. Furthermore, the method for establishing the nonlinear equation system is universal and applicable to any planar linkage mechanism; the equation form can be adjusted simply based on the number of links and connection relationships of the specific mechanism.

[0106] In one embodiment, step S2 involves establishing a set of mechanical equilibrium equations based on the principle of static equilibrium, specifically including:

[0107] First, the load gravity is applied equivalently to the center of gravity of the equivalent load subsystem.

[0108] Specifically, the mass m of the cutter head is equivalently concentrated at the midpoint of the line connecting the cutter head and the hinge points of the front and rear suspension shafts, and the load gravity vector is expressed as:

[0109]

[0110] Where g is the gravitational acceleration, with a value of 9.8 m / s² or 10 m / s².

[0111] Then, for the load equivalent subsystem and the transmission linkage subsystem, the force balance equations and torque balance equations of each subsystem are established respectively.

[0112] Specifically, for the equivalent link of the cutter head (load equivalent subsystem), the force balance equation is:

[0113]

[0114] The equilibrium equation for the torque is:

[0115]

[0116] For the lifting link (transmission link subsystem), the force balance equation is:

[0117]

[0118] The equilibrium equation for the torque is:

[0119]

[0120] For the combination of the lifting rocker arm and the cutter head lifting shaft rotating arm, the force balance equation is:

[0121]

[0122] The equilibrium equation for the torque is:

[0123]

[0124] For the lifting handle rocker arm (input lever arm subsystem), the torque balance equation is:

[0125]

[0126] in, This represents the resultant force vector acting on the current subsystem. This represents the resultant torque vector acting on the current subsystem. , The goal is to increase the rotational torque of the rocker arm.

[0127] By simultaneously solving the equilibrium equations of all components, a system of linear equations is formed that includes the unknowns of the constraint reactions at each hinge point and the input torque:

[0128]

[0129] Wherein, [A] is the coefficient matrix, [X] is a column vector containing 15 unknowns (components of constraint reaction forces at each hinge point and input torque), and [B] is a column vector of constant terms (including gravity components).

[0130] This embodiment employs the dynamic-static analysis principle of planar linkage mechanisms, treating each linkage component in the cutterhead lifting mechanism as an independent isolated body for analysis. For each component, force balance equations (X and Y directions) and torque balance equations (around the Z-axis perpendicular to the plane of motion) are established. By simultaneously solving the balance equations of all components, a closed linear equation system is formed, with unknowns including constraint reactions and input torques at each hinge point. Since the number of equations is equal to the number of unknowns, this linear equation system has a unique solution.

[0131] The method for establishing the mechanical equilibrium equations provided in this embodiment can accurately describe the force transmission relationship of the cutterhead lifting mechanism under any orientation. By transforming the complex force problem of the mechanism into a problem of solving a linear equation system, the calculation process is stable and reliable. Compared with methods relying on finite element analysis or multibody dynamics simulation, this embodiment has the advantages of low computational load, fast calculation speed, and good numerical stability. At the same time, all intermediate variables (constraint reaction forces at each hinge point) can be output, which facilitates designers to perform strength verification and life assessment of the mechanism.

[0132] In one embodiment, step S3 sets the rotation angle of the input component as the independent variable, solves the geometric constraint equations and the mechanical equilibrium equations to obtain the input torque under the corresponding pose, specifically including:

[0133] First, set the initial value and step size of the rotation angle of the input component, and then enter the loop iteration process.

[0134] Specifically, the initial value θ1 of the lifting rocker arm rotation angle is set. start (e.g., -30°), termination value θ end (e.g., 30°) and step size Δθ (e.g., 1°). Initialize the storage array Me[] to store the input torque corresponding to each angle.

[0135] Then, in each iteration, a numerical analysis algorithm is used to solve the nonlinear algebraic equations to obtain the instantaneous pose angle of each member.

[0136] Specifically, the current value of θ1 is substituted into the geometric constraint equations to establish a system of nonlinear algebraic equations about θ2 and θ3. The Newton-Raphson iterative method is then used to solve this system of nonlinear equations. Initial guesses for θ2 and θ3 are set, and the iterative process is repeated until the convergence condition is met.

[0137] Specifically, in this embodiment, the numerical analysis algorithm is the Newton-Raphson iteration method, the quasi-Newton method, or the bisection method.

[0138] Quasi-Newton methods are used to avoid calculating the inverse of the Jacobian matrix in each iteration.

[0139] The bisection method is applicable to solving single-variable nonlinear equations. For the case where the equation f(x)=0 is monotonic in the interval [a,b], the root of the equation is approximated by continuously bisecting the interval.

[0140] The Newton-Raphson iterative method utilizes a local linear approximation of the objective function and determines the iteration direction through the inverse of the Jacobian matrix, exhibiting a second-order convergence speed. Quasi-Newton methods avoid the overhead of recalculating the Jacobian matrix in each iteration by recursively updating the approximation during the iteration process. The bisection method leverages the monotonicity of the function, gradually approximating the root through interval halving, possessing a linear convergence speed but good stability.

[0141] This embodiment provides a variety of numerical solution algorithms for systems of equations of different sizes and characteristics. For small-scale (≤10 variables) nonlinear equation systems, the Newton-Raphson method achieves the fastest convergence speed; for scenarios where Jacobian matrix computation is costly, the quasi-Newton method significantly reduces the computational overhead of a single iteration; for single-variable nonlinear equations, the bisection method yields the most stable solution. Designers can flexibly choose appropriate algorithm combinations based on specific problems.

[0142] This embodiment employs a "discretization-numerical iteration" strategy, discretizing the continuous motion path into multiple position points, and independently solving the kinematic and dynamic equations at each position point. The kinematic solution uses the Newton-Raphson iterative method to solve the nonlinear equations. This method utilizes a local linear approximation of the objective function, determines the iteration direction through the inverse of the Jacobian matrix, and has a second-order convergence rate, enabling high-precision solutions to be obtained within a small number of iterations.

[0143] The numerical iterative solution method provided in this embodiment can efficiently complete the entire calculation while ensuring computational accuracy. Using the Newton-Raphson iterative method to solve the nonlinear equation system improves computation speed by approximately 5-10 times compared to direct or symbolic solutions. Furthermore, the discretized solution strategy naturally supports parallel computing, further enhancing computational efficiency.

[0144] In one embodiment, each iteration also includes:

[0145] The instantaneous pose angle is substituted into the mechanical equilibrium equations, and the mechanical equilibrium equations are solved by matrix operations to output the input torque of the input lever arm subsystem under the current pose.

[0146] Specifically, the current θ1, θ2, and θ3 are substituted into the coefficient matrix and constant terms of the mechanical equilibrium equations to form a 15×15 linear equation system. The LU decomposition method is used to solve this linear equation system: the coefficient matrix A is decomposed into the product of the lower triangular matrix L and the upper triangular matrix U, i.e., A = L·U. The solution process consists of two steps: forward substitution (L·y = b) and backward substitution (U·x = y), to obtain the input torque Me at the current angle.

[0147] Store each θ1 and its corresponding Me value, and increment θ1 by a step size Δθ, repeating the above steps until θ1 reaches the termination value θ. end .

[0148] The LU decomposition method transforms the solution of a linear system of equations into the solution of two triangular systems of equations by decomposing a matrix into a product of triangular matrices. This method is computationally efficient and numerically stable.

[0149] In solving linear equation systems, the LU decomposition method has better numerical stability and lower computational complexity compared to Gaussian elimination.

[0150] In one embodiment, step S4 is followed by:

[0151] S5, Forward Optimization Design: Compare the process curve with the preset target force range. If the calculated lifting force of the process curve exceeds the target force range, adjust the geometric constraint parameters based on sensitivity analysis and return to step S2. Re-execute steps S2 and S3 based on the adjusted geometric constraint parameters to update the process curve until the updated process curve falls into the target force range.

[0152] Specifically, step S5 includes the following sub-steps:

[0153] S51, Target Range Setting: Set the target range for the operating lifting force according to ergonomic requirements, such as an upper limit of no more than 50N and a lower limit of no less than 10N. Alternatively, set the target torque range according to the performance requirements of the mechanism.

[0154] S52, Curve Comparison: Compare the lifting force process curve generated in step S4 with the target range to identify the angle range and excess amount that exceed the target range.

[0155] S53, Sensitivity Analysis: For angle positions where the lifting force exceeds the target range, calculate the sensitivity coefficient of each geometric constraint parameter relative to the lifting force value at that position.

[0156] Specifically, for angles θ that exceed the target interval exceed Calculate the geometric constraint parameters (Including link lengths L1, L2, L3, hinge point coordinates L, H, included angle α, etc.) the lifting force value relative to this position. Partial derivatives:

[0157]

[0158] in, These are the geometric constraint parameters. To increase force value The sensitivity coefficient, the absolute value of which reflects the degree of influence of the parameter on the lifting force, and the positive or negative sign indicates the direction of the influence.

[0159] S54, Parameter Adjustment: Based on the magnitude of the sensitivity coefficient, determine the geometric constraint parameter with the greatest impact, and adjust this parameter according to the gradient descent direction.

[0160] S55, Iterative Cycle: Substitute the adjusted geometric constraint parameters into step S2 to re-establish the geometric constraint equations and mechanical equilibrium equations. Execute steps S3 and S4 to generate a new process curve. Repeat steps S52 to S54 until the process curve falls completely within the target range.

[0161] S56, Output Results: Outputs the combination of structural parameters that meet the design requirements and the corresponding lifting force process curve, which is used to guide the design of the physical prototype.

[0162] This embodiment constructs a closed-loop design process of "modeling-computation-evaluation-optimization". By comparing the process curve generated in step S4 with the preset target range, the performance of the current design scheme is quantitatively evaluated to determine whether it meets the requirements. If it does not meet the requirements, sensitivity analysis is used to determine the key parameters affecting performance and their adjustment directions. Geometric parameters are automatically or semi-automatically adjusted and recalculated, forming a design iteration cycle. This closed-loop process transforms the traditional "design-simulation-modification" reverse cycle into a "parameter-computation-evaluation" forward cycle, significantly shortening the design cycle.

[0163] The forward optimization design method provided in this embodiment realizes a parameterized design closed loop for the cutterhead lifting mechanism. Compared with the traditional method that relies on design experience for multiple trial-and-error adjustments, this embodiment accurately identifies key parameters through sensitivity analysis and quickly converges to the optimal solution using gradient descent, improving optimization efficiency by approximately 3-5 times. Simultaneously, this closed-loop process can be fully automated, facilitating integration into CAD / CAE systems and achieving seamless design-verification-optimization, significantly improving design quality and efficiency.

[0164] In one embodiment, step S4 is followed by a step to verify the feasibility of the movement of the cutter head lifting mechanism:

[0165] The residual value of the nonlinear algebraic equation system is monitored in real time during the iterative solution process. If the residual value exceeds the preset convergence threshold in any iteration step, it is determined that there is a motion dead point or assembly interference in the cutter head lifting mechanism under the current geometric constraint parameters, and an error message is output.

[0166] Specifically, the feasibility verification of the exercise includes the following sub-steps:

[0167] S61, Residual Monitoring: During the iterative solution process in step S3, the residuals of the nonlinear algebraic equation system are calculated in real time.

[0168] S62, Convergence Judgment: Preset convergence threshold (e.g., 1×10⁻⁶). -6 The maximum number of iterations (e.g., 100) is set. If the current residual value is less than the convergence threshold, it is considered convergent, and subsequent steps are executed; if the current number of iterations is greater than the maximum number of iterations, it is considered non-convergent.

[0169] S63, Dead Point Judgment: When the iteration fails to converge, further analyze the reasons for the non-convergence. If the residual oscillates during the iteration process but cannot decrease, it is determined that the mechanism has a motion dead point, that is, the mechanism is in a self-locking position or a singular configuration at the current input angle.

[0170] S64, Interference Detection: Substitute the obtained instantaneous pose angles into the geometric constraint equations to calculate the actual distance between each hinge point. If the distance between any two non-connected hinge points is less than the preset safety distance, then the mechanism is determined to have assembly interference.

[0171] S65, Error Message: When a dead point or assembly interference is detected, an error message containing the following information is output:

[0172] The location at which non-convergence occurs;

[0173] Possible cause analysis (dead spot or interference);

[0174] Recommended geometric parameters to be adjusted and their adjustment directions.

[0175] This embodiment utilizes the convergence characteristics of the nonlinear equations solution process to determine the kinematic feasibility of the mechanism. In planar linkage mechanisms, if the mechanism has dead points (i.e., singular configurations), the Jacobian matrix of the geometric constraint equations will become a singular matrix, causing the Newton-Raphson iteration method to fail to converge. If the mechanism has assembly interference, the solution to the geometric constraint equations will not exist in the real domain, which will also lead to iteration divergence. Therefore, by monitoring the convergence of the iteration process, kinematic defects in the mechanism design can be effectively identified.

[0176] The kinematic feasibility verification method provided in this embodiment can automatically detect kinematic defects in the cutter head lifting mechanism during the parameter design stage, avoiding the rework risk of discovering problems only in the later stages of design through 3D simulation or physical prototype testing. Compared with traditional methods that require manual inspection or rely on kinematic analysis using simulation software, the verification process in this embodiment is fully automated and can accurately locate the angle and position of the problem and its possible causes, providing designers with clear modification suggestions and significantly reducing the design rework rate.

[0177] In one embodiment, step S13, defining the positional relationship between the hinge points and the equivalent center of gravity of the load in each subsystem in a planar coordinate system, specifically includes:

[0178] First, establish a global absolute coordinate system and a local relative coordinate system.

[0179] Specifically, a global absolute coordinate system is defined, with the center point of the rear hanger shaft of the cutter head as the origin. The X-axis is parallel to the line connecting the center points of the front and rear hanger shafts, and the Y-axis is perpendicular to this line and points upwards. At the same time, a local relative coordinate system is established for each planar four-bar submechanism, with the fixed hinge point of the submechanism as the origin, and coordinate axes defined along the direction of each link.

[0180] Then, the geometric dimensions of the input lever arm subsystem, transmission link subsystem, and load equivalent subsystem are parameterized.

[0181] Specifically, the lengths of each link (L1, L2, L3, L4, L5, L6), the coordinates of each fixed hinge point (L, H), and the fixed included angle (α) between each link are defined as adjustable geometric parameters. By changing the values ​​of these parameters, different models and layouts of cutter head lifting mechanisms can be quickly adapted.

[0182] Finally, the local vectors of each subsystem are transformed to the global absolute coordinate system through the coordinate transformation matrix to construct a unified mechanical calculation benchmark. This allows the geometric constraint parameters and mechanical parameters of all subsystems to be uniformly expressed in the global absolute coordinate system, forming a complete mechanical calculation model.

[0183] This embodiment achieves hierarchical parametric modeling of complex mechanisms by introducing a multi-coordinate system description method that combines a global absolute coordinate system and a local relative coordinate system. The geometric parameters of each subsystem are defined independently in its local coordinate system, facilitating parametric management and independent optimization. A coordinate transformation matrix is ​​used to transform the local vectors of each subsystem to the global coordinate system, ensuring the consistency of the overall mechanism's kinematic and dynamic analysis. This divide-and-conquer modeling strategy reduces the mathematical description difficulty of complex mechanisms.

[0184] The coordinate system establishment and parameterization method provided in this embodiment significantly improves the versatility and maintainability of the model. By parameterizing the geometric dimensions, designers only need to modify the parameter values ​​to quickly adapt to different models of cutterhead lifting mechanisms without having to rebuild the mathematical model. Through the transformation between the local and global coordinate systems, independent design and subsequent assembly of each subsystem are supported, facilitating use in collaborative design environments. This method also facilitates integration with CAD software, allowing optimized parameters to be directly exported to generate 3D models, achieving integrated design-calculation-modeling.

[0185] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0186] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0187] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0188] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for analytically calculating the lifting force of a lawnmower blade lifting mechanism, characterized in that, The method includes: S1. Establish a parametric mechanical model. Based on the topology of the cutter head lifting mechanism, simplify it into a planar linkage mechanism and define the positional relationship between each hinge point and the equivalent center of gravity of the load in the planar coordinate system. S2, construct a set of multibody dynamic equations, establish a set of geometric constraint equations based on the principle of vector closed loop, and establish a set of mechanical equilibrium equations based on the principle of static equilibrium; S3, numerical iterative solution: set the rotation angle of the input component as the independent variable, solve the geometric constraint equations and mechanical equilibrium equations to obtain the input torque under the corresponding pose; S4, Generate performance curves, plotting the process curve of lifting force / torque changing with lifting angle based on the obtained input torque data.

2. The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism according to claim 1, characterized in that, In step S1, simplifying the topology of the cutter head lifting mechanism into a planar linkage mechanism and defining the positional relationship between each hinge point and the equivalent center of gravity of the load in a planar coordinate system specifically includes: S11, Based on the topology of the cutter head lifting mechanism, the rigid link in three-dimensional space is abstracted into a vector line segment in a two-dimensional plane, and the hinge point is abstracted into a vector endpoint, thus constructing the planar link mechanism; S12, the planar linkage mechanism is decomposed into multiple interconnected planar four-bar sub-mechanisms according to the topological connection relationship. The multiple interconnected planar four-bar sub-mechanisms include an input lever arm subsystem, a transmission link subsystem, and a load equivalent subsystem. The input lever arm subsystem is used to receive driving force and generate initial displacement. The transmission link subsystem is used to transmit motion and force. The load equivalent subsystem is used to bear the weight of the cutter head and realize the lifting action. S13, define the positional relationship between the hinge points and the equivalent center of gravity of the load in each subsystem in the plane coordinate system, and assign corresponding geometric constraint parameters to each subsystem.

3. The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism according to claim 2, characterized in that, In step S2, establishing the geometric constraint equation system based on the vector closed-loop principle specifically includes: For each closed kinematic chain in the cutter head lifting mechanism, establish a vector closed-loop equation; Projecting the vector closed-loop equation onto a plane coordinate system, it is decomposed into horizontal component equations and vertical component equations, resulting in a system of nonlinear algebraic equations.

4. The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism according to claim 2, characterized in that, In step S2, establishing a set of mechanical equilibrium equations based on the principle of static equilibrium specifically includes: The load gravity is applied equivalently to the center of gravity of the equivalent load subsystem. For the load equivalent subsystem and the transmission linkage subsystem, force balance equations and torque balance equations are established for each subsystem.

5. The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism according to claim 3, characterized in that, In step S3, the rotation angle of the input component is set as the independent variable, and the geometric constraint equations and mechanical equilibrium equations are solved to obtain the input torque under the corresponding pose. Specifically, this includes: Set the initial value and step size of the rotation angle of the input component, and enter the loop iteration process; In each iteration, the nonlinear algebraic equations are solved using numerical analysis algorithms to obtain the instantaneous pose angles of each member.

6. The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism according to claim 5, characterized in that, Each iteration also includes: The instantaneous pose angle is substituted into the mechanical equilibrium equations, and the mechanical equilibrium equations are solved by matrix operations to output the input torque of the input lever arm subsystem under the current pose.

7. The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism according to claim 5, characterized in that, The numerical analysis algorithm is specifically the Newton-Raphson iteration method, the quasi-Newton method, or the bisection method.

8. The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism according to claim 2, characterized in that, Step S4 is followed by: S5, Forward optimization design: Compare the process curve with the preset target force range. If the calculated lifting force value of the process curve exceeds the target force range, adjust the geometric constraint parameters based on sensitivity analysis and return to step S2. Re-execute steps S2 and S3 based on the adjusted geometric constraint parameters to update the process curve until the updated process curve falls into the target force range.

9. The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism according to claim 3, characterized in that, Step S4 is followed by a step to verify the feasibility of the cutter head lifting mechanism's movement: The residual value of the nonlinear algebraic equation system is monitored in real time during the iterative solution process. If the residual value exceeds the preset convergence threshold in any iteration step, it is determined that the cutter head lifting mechanism under the current geometric constraint parameters has a motion dead point or assembly interference, and an error prompt message is output.

10. The analytical calculation method for the lifting force of the lawnmower blade lifting mechanism according to claim 2, characterized in that, In step S13, defining the positional relationship between the hinge points and the equivalent center of gravity of the load in each subsystem in the planar coordinate system specifically includes: Establish a global absolute coordinate system and a local relative coordinate system; The geometric dimensions of the input lever arm subsystem, transmission link subsystem, and load equivalent subsystem are parameterized, and the local vectors of each subsystem are transformed to the global absolute coordinate system through a coordinate transformation matrix to construct a unified mechanical calculation benchmark.

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