4-PRP_aR并联机构尺度参数多目标优化

Multi-objective Optimization of Dimensional Parameter for 4-PRP_aR Parallel Mechanism

以三移动一转动4-PRP_aR并联机构为研究对象,采用进化多目标算法求解机构尺度综合问题。应用约束旋量理论分析机构自由度,给出了机构位置逆解解析表达式,为机构性能分析奠定基础。建立机构运动和力传递性能评价指标,给出了规则有效传递工作空间(Regular effective transmission workspace,RETW)及其平均传递指标的定义。以最大化RETW半径及平均传递指标为目标,建立机构尺度参数多目标优化设计模型,并应用快速精英多目标遗传算法和差分进化算法相结合的方法求解该问题。给出了机构尺度参数多目标优化设计实例。结果表明,模型和算法可行有效,可为物理样机研制和实际应用提供理论基础。

Taking a 4-PRP_aR parallel mechanism with three translational and one rotational as the research object,the evolutionary multi-objective algorithm is applied to solve the dimensional synthesis problem of mechanism.The degree of freedom of mechanism is analyzed by means of constraint screw theory,and the analytical expression of the inverse position solution of mechanism is given.These works can be foundations for the mechanism performance analysis.The evaluation indices for motion and force transmission performance of mechanism are established,and the definition of regular effective transmission workspace(RETW)and its average transmission indices are presented.A multi-objective optimization model is constructed to formulate the design problem of dimensional parameters on the maximizing radius of RETW and average transmission indices,and the fast and elitist multi-objective genetic algorithm combined with differential evolution algorithm is used to solve this problem.A real case of multi-objective optimization for dimensional parameters is given,and the result shows that the model and algorithm are feasible and effective.The research results can provide a theoretical basis for the practical application and the development of physical prototype.