3-RRR平面并联机构的刚度特性分析

Stiffness Analysis and Stiffness Mapping of 3-RRR Planar Parallel Mechanism Based on CCT Stiffness Matrix

导出了3-RRR平面并联机构基于守恒协调转换刚度矩阵机构刚度结构位形部分的解析表达式和外力作用影响部分的不完全解析表达式.给出了求机构刚度映射的一般方法,求出了不同参数下3-RRR平面并联机构的刚度映射曲线,并对机构的刚度特性进行了分析和讨论.研究发现,3-RRR平面并联机构的刚度是机构构型的函数,并与驱动力和关节刚度成比例;动平台中心趋于工作空间边界刚度增大,在工作空间的边界附近形成一个刚度较强的环状区域,而在工作空间的内部形成一个刚度较弱的区域.

The analytical stiffness equations of the part concerning joint stiffness and configuration and the uncompleted analytical stiffness equations of the part affected by external forces of 3-RRR planar parallel mechanism were all deduced, based on the conservative congruence transformation （CCT） stiffness matrix. The method of stiffness mappings was given, and the maps of the mechanism were presented to illustrate the properties of the stiffness of the mechanism. The stiffness characteristics of the mechanism were analyzed and discussed. It was revealed that the stiffness of the mechanism are configuration dependent and proportional to the actuating forces and joint stiffness. The stiffness becomes higher towards the boundaries of working space and vise versa, which forms a stronger stiffness ＂ring＂ area near the boundaries, and a weaker stiffneas ＂zone＂ near the center of working space.