Geometric Analysis of Overconstrained Parallel Manipulators with Three and Four Degrees of Freedom

Abstract

This paper investigates the constraint characteristics of parallel manipulators with three and four degrees of freedom. An analytical method of using equivalent screw groups is developed in the study based on the linear independence of screw systems and reciprocal screw systems. A procedure for determining overconstraints in spatial parallel mechanisms with fewer six degrees of freedom is given. With this method, the constraint characteristics of four parallel mechanisms with three or four degrees of freedom, i. e. 3-RRC, 3-CPR, 3-URU/SPS and 4-UPU mechanisms, are revealed. The constraint characteristics of three types of parallelogram linkage unites are then discovered, which gives the corresponding equivalent representations in terms of serial mechanisms. The approach is further applied to the geometric analysis of parallel mechanisms with hybrid limbs including 3-R(4U)_RPP and 3-R(4S)_RRRP mechanisms.