Decoupling Design And Kinematics Analysis Of 4-CRU Parallel Mechanism

Compared with series robots,parallel robots have the advantages of compact structure,high precision and so on,it can be widely used in the fields of aerospace,medical apparatus and so on.In this paper,based on the existing new 4-CRU parallel mechanism,its structure was analyzed by using the based on the theory of single open chain?SOC?,so that the azimuth feature set,number of degrees of freedom?F=4?and type of the moving platform,the coupling degree of the mechanism??=2?were obtained.So based on the principle for the structure coupling-reducing,structural decoupling design of 4-CRU parallel mechanism is carried out,and a new 2-?CRR?₂R type parallel mechanism with lower coupling degree of?=1 is proposed.The 2-?CRR?₂R parallel mechanism is taken as the research object,and its kinematics,workspace,parameter optimization and trajectory planning are studied.First,kinematics analysis of 2-?CRR?₂R parallel mechanism.The positive and inverse position solution models of 2-?CRR?₂R parallel mechanism are established by using the coordinate transformation law of mechanism and the constraint condition of rod length.Based on the geometry and motion constraints,the one-dimensional search model of the position positive solution is established.In the process of solving,multiple solution intervals of the one-dimensional transcendental equation can be obtained by the one-dimensional search method,and then multiple solution intervals can be iterative searched one by one by the golden section method,so all the high-precision positive-value solutions can be obtained.Numerical examples show that the analytical method has high accuracy,good stability and quick convergence speed.In order to further study the motion performance of the mechanism,establishing the vector relationship of the motion pair and the components by the vector method,and then combined with the constraint condition of rod length,the positive and inverse models of the velocity and acceleration of the mechanism are obtained.Numerical examples are given by MATLAB,the velocity and acceleration curves of the mechanism are drawn.At the same time,the driving function in the numerical example is taken as input,and kinematics simulation is carried out by ADAMS,the velocity and acceleration curves are consistent with MATLAB numerical examples.The results show that the analytical model and method are correct and feasible,it lays a foundation for the subsequent parametric design.Secondly,workspace analysis of 2-?CRR?₂R parallel mechanism.Based on the inverse position solution of mechanism,the mathematical model of the working space of the mechanism is established by combining the constraint conditions of the length of the rod and the rotation angle.The number of"point sets"in the workspace of the mechanism was obtained by using MATLB to numerically search the points satisfying the constraint conditions.At the same time,the three-dimensional point cloud diagram and the projection point cloud diagram of the workspace in all directions are drawn.By the point cloud diagram of the workspace,we know that the workspace of the mechanism has regular shape,no void inside and good symmetry.At the same time,the influence of mechanism parameters on workspace size is studied by using single variable method,it provides basic data for the application of the parallel mechanism.Thirdly,dimensional optimization of 2-?CRR?₂R parallel mechanism.The dimensional optimization model is established with the maximum workspace of the mechanism as the optimization objective.The differential evolution?DE?algorithm is used to solve the optimization problem,the optimal dimensional parameters of the mechanism are obtained.Though the workspace is analyzed with the optimized dimensional parameters,the results show that the range of workspace is larger,the number of"point sets"is about 6 times increase,and the shape is more regular.The results show that the method is correct and effective.Fourth,trajectory planning of 2-?CRR?₂R parallel mechanism.The"door frame"shape motion track of the moving platform is given,the equation of the movement curve is a polynomial of 3⁵ degrees.Twelve key points on the trajectory are selected,based on the inverse solution of mechanism position?driving angle?,the driving function was fitted as a4⁸ degree polynomial function by differential evolution algorithm.Taking it as input,kinematics simulation is carried out by ADAMS,motion path,velocity and acceleration of the moving platform of the mechanism.The results show that the actual trajectory of the moving platform is consistent with the desired trajectory,the velocity and acceleration have no obvious fluctuation,and the impact is small,there is a slight deviation from the expected value at the end position,which meets the general accuracy requirements.