• CN: 11-2187/TH
  • ISSN: 0577-6686

›› 2010, Vol. 46 ›› Issue (1): 55-61.

• Article • Previous Articles     Next Articles

Mobility Bifurcation of Two 1R3T Parallel Mechanisms Based on Lie Group

CHEN Qiaohong;LI Qinchuan;WU Chuanyu;HU Xudong   

  1. Provincial Key Laboratory of Modern Textile Machinery, Zhejiang Sci-Tech University
  • Published:2010-01-05

Abstract: 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-xPyRyRxRxR/yPxRxRyRyR and 2-xPyRuPxRxR/yPxRvPyRyR 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.

Key words: Lie group, Mobility, Parallel mechanism

CLC Number: