一种新型三平移并联机构的运动学分析与多目标尺度综合

Kinematics Analysis and Multi-objective Scale Synthesis of a New Three Translation Parallel Mechanism

根据方位特征(POC)方程的并联机构拓扑设计理论和方法,设计了一种结构简单且对称的三平移的并联机构,通过方位特征方程分别计算了机构的方位特征集、自由度、耦合度等拓扑特性,验证机构能实现三平移的运动特性;建立机构运动学方程,推导得到机构的正逆解的解析式,以及机构的奇异性、工作空间、灵巧度等运动性能指标。最后,建立多目标优化设计模型,采用带有精英保留策略的快速非支配多目标优化算法(NSGA-Ⅱ)进行结构参数的尺度综合,优化得到一组Pareto最优解(Pareto optimal solutions)。结果表明,不能同时最大化工作空间体积和全局灵巧度,可以根据实际的需求选择Pareto最优解,以满足两个目标的需求。

A simple and symmetrical parallel mechanism with three translations is designed according to the theory and method of topological design of parallel mechanism based on Position and Orientation Characteristic(POC)equation.The topological characteristics of mechanism,such as position and orientation characteristic set,degree of freedom and coupling degree,are calculated respectively by POC equation to verify the kinematics characteristics of the mechanism with three translations.The kinematics equation of the mechanism is established,and the analytical expression of positive and inverse kinematics solution of the mechanism are derived,the singularity,workspace and dexterity of the mechanism are studied.Finally,a multi-objective optimization design model is established,with elite retention strategy of rapid and dominate the multi-objective optimization algorithm(NSGA-Ⅱ),the scale synthesis of the structural parameters is carried out,a set of Pareto optimal solutions are obtained by optimization.The results show that the workspace volume and global dexterity can’t be maximized at the same time.Pareto optimal solution can be selected according to the actual needs to meet the needs of the two goals.