零耦合度部分运动解耦三平移并联机构刚度建模与分析

(RPa∥3R)2R+RPa机构是基于方位特征(POC)方程并联机构拓扑综合理论的一种非对称并联机构,其耦合度为零,且具有部分运动解耦性。本文对该机构进行刚度建模和特性分析。首先,对该机构进行拓扑结构描述,基于虚拟弹簧法对机构支链进行刚度建模,给出支链的静力学方程,并求解机构的刚度矩阵;其次,给出机构在工作空间中的整体刚度分布,并分别对x、y、z轴方向的扭转、线性刚度进行分析;进一步对机构进行有限元分析,并与虚拟弹簧法所得的机构变形结果进行对比,验证刚度结果的正确性;最后,对比非对称的(RPa∥3R)2R+RPa机构与对称Delta机构在不同截面下的刚度特性,结果表明,(RPa∥3R)2R+RPa机构的刚度大于Delta机构。

Stiffness Analysis of Three-translation Parallel Mechanism with Zero Coupling Degree and Partial Motion Decoupling

The(RPa∥3R)2R+RPa mechanism is an asymmetric 3-DOF translational parallel mechanism(PM)designed by the author’s team based on the POC equation of the topological structure design theory.This parallel manipulator has zero coupling degree and partial motion decoupling is also easy to be manufactured.The stiffness model and performance of the PM were studied.Firstly,the stiffness model of the limb was established by using the virtual spring method,and the static equation of the limb was given.Then the overall stiffness distribution of the PM in the working space was given,and the torsion and linear stiffness of the x,y and z axes were analyzed respectively.Furthermore,finite element analysis method was used to analyze the deformation of the PM,and the deformation results of the PM were compared with those obtained by the virtual spring method,the correctness of stiffness results was verified.Finally,the stiffness characteristics of(RPa∥3R)2R+RPa mechanism and Delta mechanism were compared with different sections,which indicated that the stiffness value of(RPa∥3R)2R+RPa PM was greater than that of the Delta PM.The research result laid a foundation for the structural design of the parallel manipulator,and also provided a systematic theoretical framework to evaluate the kinematic properties of such PMs as a basis for future dimensional optimization,prototype development and dynamics analysis.