半对称2SPU-2RPC并联机器人机构设计与运动学分析

Mechanism Design and Kinematics Analysis of Semi Symmetric 2SPU-2RPC Parallel Robot

设计一种可实现三平移一转动的空间并联机器人机构。利用方位特征集理论分析机构的自由度和方位特征集。根据向量的外积和矢量法推导得到运动学逆解方程,同时根据Newton-Raphson方法计算机构的运动学正解,选择一组数值解进行正逆解互相验证。计算运动学的雅克比矩阵,分析运动学的奇异性。分析机构的可达工作空间和定姿态工作空间,研究参数对工作空间大小的影响。建立工作空间体积最大化数学优化模型,选择鲸鱼优化算法完成参数的最优化设计。结果表明:L_(2)、r越大,机构的操作空间越大,L_(1)、R越大,机构的操作空间越小;最优R、r、L_(1)、L_(2)分别为1、0.9992、0.3、1.5 mm。

A spatial parallel robot mechanism with three translations and one rotation was designed.The degree of freedom and orientation feature set of the mechanism were analyzed by using the theory of orientation feature set.The inverse kinematics equation was derived according to the vector product and vector method,the forward kinematics solution of the mechanism was calculated by using Newton-Raphson method,and a group of numerical solution was selected to verify each other.The Jacobian matrix of kinematics was calculated and the singularity of kinematics was analyzed.The reachable workspace and fixed attitude workspace of the mechanism were analyzed,and the influences of parameters on the volume of workspace were analyzed.The mathematical optimization model of workspace volume maximization was established,and the whale optimization algorithm was used to complete the optimization design of parameters.The results show that the larger the L_(2) and r are,the larger the operating space of the mechanism is,and the larger the parameter value L_(1) and R are,the smaller the operating space range of the mechanism is;the optimal values of R,r,L_(1),L_(2) are 1 mm,0.9992 mm,0.3 mm and 1.5 mm respectively.