Scale Optimization Design And Trajectory Planning Of 4-RUP_aR Parallel Robot

Compared with a series robot,The parallel robot has the advantages of simple structure,high precision,strong bearing capacity,low manufacturing cost and easy control.Therefore,it is widely used in aerospace,medical equipment,precision equipment,parallel machine tools and many other fields.In recent years,with the joint efforts of many researchers,the parallel robot has made many breakthroughs in aspects of configuration innovation,performance optimization,control technology and so on,and has gained more and more attention in the world,and meantime it has become a research hotspot in the modern manufacturing field.This paper studies the kinematics,working space,scale parameter optimization and trajectory planning of 4-RUP_aR parallel robot.First of all,The topological structure of 4-RUP_aR parallel robot was analyzed by Single open chain(SOC)theory.It mainly includes:the number of degrees of freedom is calculated,and the degree of freedom is determined.2.Select the parallel robot driver pair reasonably;the coupling degree of the parallel robot is solved.The kinematic positive and inverse analytical models of 4-RUP_aR parallel robot are established by using the coordinate rotation matrix.Combining with the constraintCondition of rod length,forward kinematics equations are transformed into one-dimensional transcendental equations,and the numerical example of kinematics are verified by differential evolution(DE)algorithm.The results show that the DE algorithm can gain the high precision results with high efficiency.the solution model of workspace is established by considering the constraint conditions such as the Angle limit of parallel robot and the limit of bar length.The"point set"definition is introduced to describe the working space of 4-rupar parallel robot.Using numerical search method to search all“point sets”satisfying all constraints in workspace.In order to express the size and shape of the workspace more intuitively,the visual processing is performed in the Matlab,and the workspace point cloud is plotted.The image of point cloud shows that there is no hole in the workspace of the parallel robot,and it has good symmetry.The scale parameters affecting the working space are analyzed by using the single variable method.Secondly,the workspace maximization of 4-RUP_aR parallel manipulator is the objective function,and the mechanism scale parameter is the decision variable to establish the scale optimization model.The differential evolution algorithm is used to solve the optimization model.The results show that the workspace obtained by the optimized scale parameters increases significantly.Thirdly,the trajectory planning of 4-RUP_aR parallel robot is carried out.A desired trajectory curve is set in the operating space by using a 3-4-5 polynomial.7 key points are taken on the expected trajectory curve,and the inverse solution of the position corresponding to the 7 key points is solved.And then,the 7 driving angles of each branch are fitted to the 3-4-5-6-7 polynomial curve.Take it as an input to solve the output trajectory curve as well as the displacement,velocity and acceleration of the dynamic platform.The simulation results in Matlab show that the actual trajectory curve of the dynamic platform is not only content with the desired trajectory,but also has good motion performance.