A New Mathematical Method to Study the Singularity of 3-RSR Multimode Mobile Parallel Mechanism

Abstract

In the process of parallel mechanism design, it is difficult to avoid the singularity, especially in the mobile parallel mechanism. Therefore, a new mathematical method to study the singularity of multimode mobile parallel mechanism is proposed. In this paper, the singularity of 3-RSR parallel mechanism (PM) is analyzed by using reciprocal screw methods and linear geometry theory from two aspects of fixed mode and all-attitude multiple motion modes. Specifically, the complete Jacobian matrix of the PM is obtained by using the screw theory, and the reciprocal screw of each branch is expressed with algebraic method and geometric drawing method. Furthermore, the singularity of the PM can be obtained by analyzing the reciprocal screw correlation and using the spatial linear geometry theory. Finally, we analyze the singular configuration of the PM under various modes, which provide theoretical guidance for the gait planning of the multimode mobile PM and will be useful for the selection of mechanism drive and time-sharing control.