低耦合度2PaUU-PPaP并联机构的运动学分析与多目标优化  

Kinematic Analysis and Multi-objective Scale Synthesis of Low Coupling 2PaUU-PPaP Parallel Mechanism

作　　者：张发海 李丽红 朱磊[2] ZHANG Fa-hai;LI Li-hong;ZHU Lei(Department of Mechanical Engineering,Jiangsu College of Safety Technology,Jiangsu Xuzhou 221000,China;College of materials and Physics,China University of Mining and Technology,Jiangsu Xuzhou 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：《包装工程》2023年第13期217-226,共10页Packaging Engineering

基　　金：江苏省博士后科研资助计划项目(2019K205);中央高校基本科研业务费项目(2019XKQYMS16)。

摘　　要：目的针对三平移并联机构结构复杂、耦合度高而引起的运动学分析、动力学分析、误差分析等十分烦琐的问题,提出一种低耦合度三平移空间并联机构。方法分析得到机构的自由度、耦合度、方位特征集等拓扑参数,建立运动学位置方程推导正、逆解的解析式并对其进行算例验证。根据计算雅可比矩阵推导出位置正解奇异、位置逆解奇异存在条件。进一步研究机构的操作空间,并得到操作空间三维形状图。此外,建立以运动灵巧度与操作空间体积为目标的数学模型,给定目标函数表达式,选择NSGA–Ⅱ算法完成具有Pareto解的多目标参数优化。结果分析表明,搜索得到工作空间外部边界光滑,呈半球形状结构,内部不连续分布的特点。结论在较为均衡平缓的区域选择参数的设计,能够同时兼顾体积和全局灵巧度的较佳值,以期为该类型机构在分拣、包装等应用领域提供参考。The work aims to propose a low coupling degree three translation spatial parallel mechanism to solve the complicated kinematics analysis,dynamics analysis and error analysis caused by the complex structure and high coupling degree of the three translation parallel mechanism.Topological parameters such as DOF,coupling degree and azimuth feature set of the mechanism were analyzed.The analytic expressions of forward and inverse solutions of the kinematic position equations were established and verified by an example.At the same time,according to the calculation of Jacobian matrix,the existence conditions of the singularity of positive position solution and the singularity of inverse position solution were derived.Furthermore,the operating space of the mechanism was studied and a three-dimensional shape map of the operating space was obtained.In addition,the mathematical model with the goal of motion dexterity and operation space volume was established.The objective function expression was given.The NSGA-Ⅱalgorithm was selected to complete multi-objective parameter optimization with Pareto solutions.The analysis showed that the outer boundary of the workspace was smooth and there was a cavity inside,which was a hemispherical structure.The optimal value of both volume and global dexterity can be taken into account when selecting parameters in a relatively balanced and gentle area,so as to provide reference for this type of mechanism in sorting,packaging and other application fields.

关 键 词：耦合度 并联机构奇异性 工作空间 灵巧度 多目标优化 

分 类 号：TH122[机械工程—机械设计及理论]