Singularity analysis of a 2-UPR-RPU parallel mechanism

Abstract

The 3-DOF parallel mechanism (PM) with one translational and two rotational (1T2R) DOFs is an important category of the lower-mobility PM. The 1T2R 3-DOF PM can be classified into four categories based on the geometry between the two axes of rotations, P*U*-equivalent, UP-equivalent, PU-equivalent, RPR-equivalent PM. The singularity analysis mainly focuses on P*U*-equivalent and UP-equivalent PM, while there is few research on the PU-equivalent and PRP-equivalent PM. A singularity investigation of a 2-UPR-RPU PM belonging to the PRP-equivalent PM of 1T2R is presented. The mobility of a 2-UPR-RPU PM is analyzed by using screw theory. Forward and inverse position relations are established. The Jacobian of the 2-UPR-RPU PM is obtained. Based on the analysis of the Jacobian matrix, three kinds of kinematic singularities of the 2-UPR-RPU PM are identified. The constraint singularity of this PM is analyzed. The 2-UPR-RPU PM has no inverse, forward and constraint singularity and has two kind of combined singularities.