3-[P(RR-RRR)SR]运动学冗余并联机构动力学分析  

Dynamics analysis of the 3-[P(RR-RRR)SR]kinematically redundant parallel mechanism

作　　者：何其臻 张海峰[1] 陈巧红[2] 叶伟[1] HE Qizhen;ZHANG Haifeng;CHEN Qiaohong;YE Wei(School of Mechanical Engineering,Zhejiang Sci-Tech University,Hangzhou 310018,China;School of Computer Science and Technology,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学机械工程学院,杭州310018 [2]浙江理工大学计算机科学与技术学院,杭州310018

出　　处：《机械传动》2025年第3期24-32,共9页Journal of Mechanical Transmission

基　　金：国家自然科学基金项目(52275036)。

摘　　要：【目的】运动学冗余并联机构相较于常规并联机构,具有姿态工作空间大且能避免奇异位形等优势。但其活动度L大于末端执行器的自由度n,导致机构刚体数目过多,使其动力学建模变得更加困难。因此,基于虚功原理提出一种针对3-[P(RR-RRR)SR]运动学冗余并联机构的动力学建模方法,进一步简化建模的过程。【方法】首先,在机构活动度L对应的高维度广义空间上选取广义变量,推导了机构内各构件的速度、加速度和系统输出速度、加速度之间的运动学传递关系,求解了机构各构件与广义变量的雅可比矩阵;然后,运用虚功原理建立了该并联机构的动力学模型;最后,通过末端执行器的五次多项式轨迹跟踪对模型进行仿真,并与Adams软件的计算结果进行比较。【结果】分析结果表明,各关节的驱动力/力矩的理论值与仿真值之间的最大相对误差仅有1.58%。这证明了该模型的准确性与可靠性,同时也说明此方法能够为该机构动力学特性的深入分析和控制策略的研究提供参考。[Objective]Compared with conventional parallel mechanisms,kinematic redundant parallel mechanisms offer advantages such as a larger orientation workspace and the ability to avoid singular configurations.However,their degree of mo‐bility(L)is greater than the number of degrees of freedom(n)of the end effector,which results in an excessive number of rigid bodies and makes dynamic modeling more difficult.Therefore,a dynamic modeling method based on the principle of virtual work was proposed for the 3-[P(RR-RRR)SR]kinematic redundant parallel mechanism,further simplifying the modeling pro‐cess.[Methods]Firstly,generalized variables were selected in the high-dimensional generalized space corresponding to the de‐gree of mobility(L)of the mechanism.The kinematic transfer relations between the velocity and acceleration of each component within the mechanism and the system output velocity and acceleration were derived,and the Jacobian matrices of each compo‐nent and the generalized variable were solved.Then,the dynamic model of the parallel mechanism was established using the principle of virtual work.Finally,the model was simulated by tracking the quintic polynomial trajectory of the end effector and compared with the calculation results of Adams software.[Results]The analysis results indicate that the maximum relative error between the theoretical and simulated values of the driving force/torque at each joint is only 1.58%.This demonstrates the accu‐racy and reliability of the model,and also suggests that this method can provide reference for in-depth analysis of the dynamic characteristics of the mechanism and research on control strategies.

关 键 词：运动学冗余 并联机构 动力学建模 虚功原理 雅可比矩阵 

分 类 号：TH222[机械工程—机械制造及自动化]