低耦合PRPaR/2CRR并联机构运动学分析与性能优化  

Kinematics Analysis and Performance Optimization of Low Coupling PRPaR/2CRR Parallel Mechanism

作　　者：张莉 朱磊[2] 徐冬 Zhang Li;Zhu Lei;Xu Dong(Department of Mechanical Engineering,Jiangsu College of Safety Technology,Xuzhou 221011,China;School of Materials and Physics,China University of Mining and Technology,Xuzhou 221116,China)

机构地区：[1]江苏安全技术职业学院机械工程学院,江苏徐州221011 [2]中国矿业大学材料与物理学院,江苏徐州221116

出　　处：《机械传动》2024年第10期83-95,共13页Journal of Mechanical Transmission

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

摘　　要：针对3CRR并联机构性能上的不足,通过增加平行四边形机构的支链改进机构,根据拓扑结构综合方法综合出一批空间三平移并联机构,优选得到一种具有空间三平移PRPaR/2CRR并联机构。首先,基于方位特征集理论对机构的自由度、耦合度等特性展开分析,利用杆长限制约束建立非线性运动学方程组,推导出位置逆解表达式,对位置正、逆解进行算例验证,并对主动副的驱动角位移算例进行了分析;进一步,计算速度雅可比矩阵,研究奇异性并得出位置奇位异形产生的条件,并采用图形法分析了机构的工作空间与灵巧度、可操作度分布情况;然后,建立工作空间体积与全局灵巧度、全局可操作度的综合性能多目标优化模型,利用NSGA-Ⅱ算法得到Pareto最优尺度参数解。结果表明,PRPaR/2CRR并联机构工作空间边界光滑、呈半轮胎形状,局部存在空洞情况的特点;PRPaR/2CRR并联机构和3CRR并联机构相比,工作空间V和全局灵巧度GCI、可操作度μ等性能更好。得到的Pareto曲面能够对实际的机构的灵巧性能以及驱动输入控制起到指导作用,具有较好的工业应用前景。The mechanism is improved by adding support chains to the parallelogram mechanism in response to the performance shortcomings of the 3CRR parallel mechanism.Based on the topological structure synthesis method,a batch of spatial triple translational parallel mechanisms were synthesized,and a PRPaR/2CRR parallel mechanism with spatial triple translational motion was optimized.Characteristics such as degrees of freedom and coupling were analyzed based on the theory of directional feature sets,respectively.The nonlinear kinematics equations were established by using the geometric position relation and the constraint of the rod length,and the expression of the inverse position solution was derived.The forward and inverse position solutions were verified by numerical examples.Then,the velocity Jacobian matrix was calculated,the singularity was studied,and the conditions for generating positional anomalies were obtained.In addition,the working space and dexterity degree distribution of the mechanism were analyzed by the graphic method.What's more,a multi-objective optimization design model was established based on the comprehensive performance of the workspace volume,the global dexterity,and the global operability,and the optimal structural parameter size solution was calculated using the NSGA-Ⅱ algorithm.The research results show that the external boundary of the workspace of the PRPaR/2CRR parallel mechanism is smooth,with a semi tire shaped structure and local cavities.A conclusion can be drawn that compared with the 3CRR parallel mechanism,the PRPaR/2CRR parallel mechanism has better workspace V,global dexterity G_(CI),operability μ,and other performance.Research has shown that PRPaR/2CRR has good industrial application prospects.

关 键 词：并联机构 方位特征集 运动学 工作空间 NSGA-Ⅱ优化算法 

分 类 号：TH112[机械工程—机械设计及理论]