一种并联机构全关节逆运动学分析方法  

An Approach for Inverse Kinematics Analysis of Full Joint of Parallel Mechanism

作　　者：孙涛[1] 王梁[1] 霍欣明 齐杨 王俊 李祺 Sun Tao;Wang Liang;Huo Xinming;Qi Yang;Wang Jun;Li Qi(Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education,Tianjin University,Tianjin 300350,China;School of Mechanical Engineering,Tianjin University of Technology and Education,Tianjin 300222,China;Tianjin Key Laboratory of Aerospace Intelligent Equipment Technology,Tianjin Institute of Aerospace Mechanical and Electrical Equipment,Tianjin 300301,China)

机构地区：[1]天津大学机构理论与装备设计教育部重点实验室,天津300350 [2]天津职业技术师范大学机械工程学院,天津300222 [3]天津市航天机电装备研究所天津市航天智能装备技术重点实验室,天津300301

出　　处：《天津大学学报（自然科学与工程技术版）》2023年第9期942-952,共11页Journal of Tianjin University：Science and Technology

基　　金：国家自然科学基金资助项目(62027812,51875391,51775367,51905378);天津市科技计划资助项目(20201193,18PTLC-SY00080);天津市自然科学基金资助项目(20JCQNJC00360);天津市技术创新引导专项基金企业科技特派员项目(20YDT-PJC00450);天津市航天智能装备技术重点实验室开放项目(TJYHZN2019KT002);天津大学机构理论与装备设计教育部重点实验室开放基金资助项目。

摘　　要：机器人机构逆运动学分析是开展其性能建模和优化设计的基础.然而,现有并联机构运动学逆解方法主要是针对给定位姿下驱动关节运动变量的求解,而对于非驱动关节运动变量则需基于机构的几何特性,通过反复迭代消元计算获得,因而难以形成代数化求解流程和数字化分析软件.针对上述问题,提出一种基于有限旋量的并联机构全关节位置逆解求解方法并开展其数字化软件研发.首先,提出并联机构全关节位置解求解流程,构造并联机构末端及其支链的初始位姿,利用有限旋量建立运动方程,并通过数值方法对运动方程进行求解.以一类两转动并联机构4RSR-SS为例,计算各支链的全关节位置解,并与仿真结果对比验证解的准确性.然后,在此基础上,建立全关节位置解的数字化算法,基于B/S架构开展并联机构运动学分析软件开发,构建运动学逆解、轨迹仿真和工作空间等功能模块,通过对3-PRS并联机构的全关节逆运动学分析验证软件的有效性.最后,从冗余参数、方程数目等方面与现有方法进行比较.提出的全关节逆运动学分析方法的优点在于:可构建简洁的运动方程并同时求解给定目标位姿下的所有关节变量,避免冗余参数和计算;涉及的所有步骤均可利用代数运算求解,有利于实现并联机器人机构逆运动学分析的数字化.Inverse robotic kinematics is the basis of performance modeling and design.Current methods always focus on the mapping between actuator and manipulator spaces.However,for the passive joint,iterative eliminations are based on geometric characteristics.Therefore,the construction of an algebraic solution process and digital analysis software is difficult.To solve the aforementioned problems,an inverse solving method for full joint displacements of the parallel robotic mechanism is proposed by employing the finite screw and developing its digital software in this study.First,the procedure for obtaining the full joint position solution of the parallel mechanism is presented.The initial poses of the end of the parallel mechanism and its branches are constructed.Equations of motions are first estab-lished in the format of the finite screw and then solved numerically.Taking the 4RSR-SS parallel robot with two rota-tional motions as an example,the full joint displacement variables of each limb are calculated and compared with the simulation results to verify the accuracy of the solutions.Then,the digital algorithm for full joint displacements is established,and the inverse kinematics analysis software for parallel mechanisms is developed based on the B/S ar-chitecture,including inverse kinematics,trajectory simulation,and workspace analysis modules.The software is verified by analyzing the kinematics of the 3-PRS parallel mechanism.Finally,comparisons with the existing meth-ods in terms of redundant parameters and number of equations are made.The advantages of the fully joint inverse kinematics analysis method proposed in this study are as follows:kinematic equations can be expressed in a general and concise manner;full joint variables under the given target pose could be solved by a single step instead of itera-tions;it is conducive to programming,which helps realize the digitalization of inverse kinematics analysis.

关 键 词：逆运动学 并联机构 有限旋量 数字化 运动学分析软件 

分 类 号：TH112[机械工程—机械设计及理论]