无伴随运动2PRU-PRUR并联机构高维多目标优化设计

Many-objective Optimization Design of a 2PRU-PRUR Parallel Mechanism Without Parasitic Motion

设计了一种无伴随运动的面对称一移动两转动2PRU-PRUR并联机构,应用旋量理论分析了机构自由度和运动特性。将末端执行器输出轴设置为偏置形式,可提高姿态能力。采用球面姿态角(方位角和倾摆角)描述该输出轴姿态,并推导出机构逆向位置符号解。以旋量理论为数学工具,给出局部和全域传递性能指标的定义和计算方法。在机构性能评价和工作空间分析的基础上,建立了机构尺度参数昂贵约束高维多目标优化模型,并采用多目标进化算法求解该问题。同时,为提高高维多目标优化算法在解决此模型时的性能,提出了一种矢量角高维多目标差分进化(Vector-angle-based many-objective Differential Evolution,VaDE)算法,可综合平衡个体的收敛性和分布性。应用VaDE求解机构高维多目标优化问题,得到多组Pareto备选解。研究结果可为机构尺度综合和实际应用提供参考。

A novel 2PRU-PRUR parallel mechanism with one translational and two rotational(1T2R)degrees of freedom and without parasitic motion,and its mobility and motion characteristic were analyzed by means of the screw theory.The output axis of the moving platform designed as the deviation type can enhance the orientation capability of the mechanism.The orientation of the end-effector output axis was depicted by using the spherical attitude angles(the azimuth and tilt angles),and the symbolic solutions for the inverse displacement analysis were proposed.The screw theory was used as a mathematical tool to establish the definitions and computing methods for the local and global transmission performances indices of the mechanism.Based on the performance evaluation and workspace analysis,a constrained many-objective optimization model was constructed to formulate the design problem of dimensional parameters,and multi-objective evolutionary algorithms were employed to solve this problem.To enhance the optimization performance of the algorithm for solving the problem,a vector-angle-based many-objective differential evolution(VaDE)algorithm was proposed,which can balance comprehensively the convergence and distribution of the individuals.At the same time,the VaDE was utilized to solve the many-objective optimization problem,and multiple Pareto optimal solutions were obtained.The research results can provide reference for the dimensional synthesis and practical application of the proposed mechanism.