全对称四自由度并联机器人机构运动性能分析与多目标优化设计  

Kinematic Performance Analysis and Multi-objective Optimization Design of Fully Symmetric 4-DOF Parallel Robot Mechanism

作　　者：张莉 朱磊[2] 戚继球[2] ZHANG Li;ZHU Lei;QI Jiqiu(Department of Mechanical Engineering,Jiangsu College of Safety Technology,Xuzhou Jiangsu 221000,China;School of Materials and physics,China University of Mining and Technology,Xuzhou Jiangsu 221116,China)

机构地区：[1]江苏安全技术职业学院机械工程系,江苏徐州221000 [2]中国矿业大学材料与物理学院,江苏徐州221116

出　　处：《机械设计与研究》2023年第6期68-74,79,共8页Machine Design And Research

基　　金：江苏省博士后科研资助计划项目(2019K205);国家自然科学基金资助项目(52171091)。

摘　　要：基于方位特征集设计理论和方法,设计了一种完全对称、且具有三平移一转动性质的4-RRPaR并联机器人机构,分析方位特征集、自由度、耦合度等拓扑参数。根据矢量法构建运动学位置方程,推导得到运动学逆解解析式,同时根据算例分析得到位置正解和位置逆解数值解。利用雅可比矩阵计算得到位置正解奇异、位置逆解奇异产生条件,选择极坐标边界搜索法计算工作空间与转动能力等性能指标。分析表明:机构边界光滑且内部存在空洞情况、动平台转动角度范围较小。另外,提出有效转动能力比指标ω概念,结合有效工作空间利用率μ,建立多目标的数学优化模型,采用经典的NSGA-Ⅱ搜索算法对有效转动能力比指标ω与有效工作空间利用率μ进行多目标参数优化,最后通过算例分析得到优化后的工作空间以及转动能力,优化后的工作空间边界圆润且内部不存在空洞情况、转动灵活性较好。可权衡设计需求和实际应用需求来选择最佳的优化参数。A fully symmetric 4-RRPaR parallel robot mechanism with three translational and one rotational properties is designed based on the design theory and method of orientation feature set.The topological parameters such as orientation feature set,degree of freedom and coupling degree are analyzed.The kinematics position equation is constructed according to the vector method,and the analytic expression of the inverse kinematics solution is derived.At the same time,the forward position solution and the numerical solution of the inverse position solution are obtained according to the analysis of an example.The Jacobian matrix is used to calculate the conditions for generating the singularity of forward position solution and inverse position solution,and polar coordinate boundary search method is selected to calculate the performance indices such as workspace and rotation capacity.The analysis shows that the boundary of the mechanism is smooth and there are cavities in it,and the rotational angle range of the moving platform is small.In addition,the concept of effective rotation capacity ratio index is put forward.Combined with the utilization rate of effective workspace,a multi-objective mathematical optimization model is established.The classic NSGA2 search algorithm is used to optimize the effective rotation capacity ratio index and the utilization rate of effective workspace for multi-objective parameters.Finally,the optimized workspace and rotation capacity are obtained through numerical example analysis.The optimized workspace has a smooth boundary,no cavities inside and good rotation flexibility.The best optimization parameters can be selected by balancing the design requirements with the actual application requirements.

关 键 词：3T1R 并联机构 方位特征集 工作空间 奇异位形 NSCA2搜索算法 

分 类 号：TH122[机械工程—机械设计及理论]