2-PUR-PSR并联机构尺度综合多目标优化

针对由外副驱动的三自由度两转一移并联机构运动学性能优化问题，提出一种尺度综合多目标优化设计方法。首先，运用螺旋理论分析机构的运动学性能；其次，将可达工作空间离散为n层，采用极坐标方法计算每层高度的最大内切圆，通过数值方法计算由每层最大内切圆构成的规则圆台工作空间体积；然后，以规则工作空间体积和全局运动/力传递指标为目标函数，以驱动限制和关节转角限制为约束条件，以机构参数为设计变量；最后，采用多目标粒子群优化算法得到目标函数的Pareto最优解集。结果显示，两个目标函数之间存在相互冲突，Pareto前沿的全局运动/力传递性能(GTI)最优值比优化前提高了57.57%，规则工作空间体积（Vr）最优值比优化前提高了37.59%，证明了优化方法的有效性。

Multi-objective Optimization of Dimensional Synthesis for 2-PUR-PSR Parallel Manipulator

Aiming at the problem of kinematic performance optimization of three degree of freedom (3-DOF) two rotations and one translations parallel mechanism driven by outer pair, a multi-objective optimization design method of the dimension synthesis was proposed. The Screw theory was used to analyze the kinematics performance and obtain the inverse solution of the position for the parallel mechanism. The reachable workspace was divided into n layers, the polar coordinate method was used to calculate the maximum inscribed circle at each layer, and the numerical method was adopted to calculate the volume of the regular workspace of the frustum of a cone formed by the maximum inscribed circle of each layer. Considering the volume of the regular workspace and global motion/force transmission index as the objective functions, driving range and rotation angle of joints as the constraint conditions, and the mechanism parameters as the design variables, the multi-objective particle swarm optimization algorithm was used to find the Pareto optimal front of the objective functions, the results showed that the two objective functions conflicted with each other. The optimal value of GTI at the front of Pareto was increased by 57.57% compared with that before optimization, and the optimal value of Vr was increased by 37.59% compared with that before optimization. The comparison results before and after optimization showed effectiveness of the optimization algorithm.