新型四自由度并联机构运动性能分析与动力学求解研究  

Analysis of Kinematic Performance and Research of Dynamics Solution of New Type 4-DOF Parallel Mechanism

作　　者：王宗平 赵登峰[1] 李宽 曾国英[1] 李中杨 杨贵洋 Wang Zongping , Zhao Dengfeng , Li Kuan, Zeng Guoying , Li Zhongyang , Yang Guiyang(Key Laboratory of Testing Technology of Manufacturing Process of Ministry of Education, Southwest University of Science and Technology, Mianyang 621010 , China)

机构地区：[1]西南科技大学制造过程测试技术省部共建教育部重点实验室,四川绵阳621010

出　　处：《机械传动》2018年第5期18-25,30,共9页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51375410)

摘　　要：提出一种2UPS-RPS-UPU构型的四自由度并联机构,建立了其运动学反解方程,利用速度投影求解了驱动杆速度变化规律,并推导了机构速度雅可比矩阵;基于非保守系统下的拉格朗日方程,推导了系统的动力学模型;为机构动力学分析奠定了基础。提出一种可快速求解拉格朗日方程的方法,结合方程特点,将2阶偏微分项简化为乘积运算,1阶偏微分项通过类似于差商求导的方法简化求解,并利用Matlab对推导结果进行数值计算,绘制机构运动学、动力学各参数变化曲线以及相互关系;并将三维模型导入ADAMS进行仿真,最后对比ADAMS和Matlab仿真结果,表明两种结果完全吻合;从而验证了该方法的正确性和可行性,为后续研究和求解该类问题提供了方法依据;对该机构的进一步研究,以及相关类型的并联机构设计、控制以及性能分析等具有一定的指导性的意义。A 2UPS-RPS-UPU spatial 4-DOF parallel mechanism is introduced. The inverse kinematics equation of 2UPS-RPS-UPU is presented and the speed variation of the driving rod is solved by velocity projection,and the Jacobi matrix of the mechanism is deduced. The dynamics model of the system is established which based on the Lagrange equations of non-conservative system,which lays the foundation for dynamics analysis. A method to solve Lagrange equation with quickness is presented and combining with the equation characteristics,the part of second-order differential of equation will be simplified to the multiplication,and the first order partial differential will simplified solving through the similar method of differential quotient. The results of the derivation is simulated by using Matlab,and the kinematics and dynamics curves of the mechanism with time and interrelationships are plotted. The 3D model is put into ADAMS for simulation,and finally the ADAMS result is in agreement with the Matlab,which verified the correctness and feasibility of the method and also provides the basis for the further study and solving the similar problem. This study is not only helpful for further study of the mechanism,but also has the certain guiding significance for the design,control and character analysis of related type parallel mechanism.

关 键 词：并联机构 动力学模型 差商求导 拉格朗日方程 

分 类 号：TH112[机械工程—机械设计及理论]