摘要
运用李群理论对1R3T(R——转动自由度;T——移动自由度)并联机构自由度分岔特性进行分析。简要介绍李群理论应用于并联机构自由度分析所需理论基础,对2-xPyRyRxRxR/yPxRxRyRyR并联机构和2-xPyRuPxRxR/yPxRvPyRyR并联机构进行自由度分析,通过对分支运动链产生的位移流形及所有分支位移流形的交集分析,证明这两种并联机构具有自由度分岔特性,其动平台的位移集合为{X(x)}∪{X(y)},进而得到具有自由度分岔特性的1R3T并联机构的分支位移流形为{G(x)}{G(y)}或{X(x)}{R(N,y)},同时给出机构的结构几何条件。当动平台平行于定平台时,该类机构处于奇异位形,此时动平台具有5瞬时自由度,机构的自由度分岔通过这一奇异位形实现,需要5个驱动器实现动平台运动的完全可控。
Mobility bifurcation of 1R3T （R-rotational, T-translational） parallel mechanisms is studied by applying Lie group theory. Some theoretical fundamentals necessary for application of Lie group theory to mobility analysis of parallel mechanisms are briefly reviewed. Mobility analysis of the 2-^xP^yR^yR^xR^xR/^yP^xR^xR^yR^yR and 2-^xP^yR^uP^xR^xR/^yP^xR^vP^yR^yR parallel mechanisms is performed. It is proved that the two parallel mechanisms have mobility bifurcation with displacement set of the moving platform being {X（x）}∪{X（y）}. Further, it is obtained that the limb displacement manifold of the 1R3T parallel mechanism with mobility bifurcation is {G（x）}{G（y）} or {X（x）}{R（N, y）}. The structural geometrical conditions of the 1R3T parallel mechanism with mobility bifurcation are also presented. When the moving platform is parallel to the base, the parallel mechanism is in a singular configuration and the moving platform has five instantaneous degrees of freedom. The mobility bifurcation happening in this singular configuration requires five actuators to control the motion of the moving platform.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2010年第1期55-61,共7页
Journal of Mechanical Engineering
基金
国家自然科学基金资助项目(50605055)
关键词
并联机构
李群
自由度
Parallel mechanism Lie group Mobility I~ mr1
