Parameter Optimization And Trajectory Planning Of 3P-Delta Parallel Mechanism

Parallel mechanism has been widely used in aerospace,medical rehabilitation,danger disposal and rescue and other fields because of its good kinematics and dynamics performance.3P-Delta parallel mechanism is a spatial three degree of freedom translational parallel mechanism which has the advantages of simple structure and easy to control.It can be used in sorting,handling,packaging and other automatic production lines.In this paper,taking the 3P-Delta parallel mechanism as the research object,the kinematics,parameter optimization,motion simulation and trajectory planning of the mechanism are studied.First of all,the degree of freedom of the 3P-Delta parallel mechanism is calculated.The motion forms of the mechanism are determined as three dimensional translational motions.The kinematic equations of the mechanism are derived using closed-loop vector method.The forward position and the inverse position problems of the mechanism are formulated.The first order Taylor expansion of the kinematic equation of the mechanism is carried out to obtain the Jacobian matrix expressions of the mechanism.The singular positions of the mechanism are obtained based on the Jacobian matrices.Secondly,based on the inverse position solution of the mechanism,the workspace of the mechanism is solved using numerical search method.The workspace diagrams of the mechanism are obtained using Matlab software.The 3D model of the mechanism is established using SolidWorks software.The movement of the mechanism is simulated.The workspace boundary curves of the mechanism are obtained.Comparing with the workspace obtained by using Matlab software,the sizes and shapes of the workspaces obtained by the two methods are basically the same.The correctness of the workspaces is verified.Based on the differential thinking,the workspace of 3P-Delta parallel mechanism is divided into a lot of micro subspace to calculate the volume of the workspace.The Jacobian condition number at each point in the workspace is analyzed using the Jacobian matrix,and the global Jacobian condition number of 3P-Delta parallel mechanism.The structural parameters of the mechanism are optimized using genetic algorithm.The influence of various structural parameters on the volume of the workspace and the global Jacobian condition number is analyzed.Taking the maximum volume of workspace and the minimum global Jacobian condition number as the optimization objective,respectively,the appropriate optimized parameters are selected to optimize the mechanism.Then,the virtual prototype model of the mechanism is established using ADAMS software to simulate the mechanism on the position inverse solution,velocity and acceleration and the motion curves of the mechanism are obtained.Comparing the obtained curves by simulation with the curves obtained by theoretical analysis,the curves obtained by the two methods are basically coincident and the correctness of the theoretical results is verified.Finally,the five polynomial programming and trapezoidal velocity curve planning are performed for the 3P-Delta parallel mechanism.The experimental prototype is constructed.The trajectory of the experimental prototype is planning by selecting trapezoidal velocity curve.Through the trajectory planning,the moving platform can be given a good kinematics performance through a given path.The feasibility of trajectory planning is verified by experiments.