Singularity analysis of planar parallel manipulators based on forward kinematic solutions

An efficient approach for determining the force-unconstrained poses (singularity loci) of planar parallel manipulators (PPMs) is presented. The approach is implemented for the 3-RPR, 3-PRR, and 3-RRR PPMs, where the underline indicates the actuated joint. The force-unconstrained poses are identified based upon concepts of reciprocal screws, kinematics, and elimination methods. The use of screw quantities provides a clear insight as to how the forces are acting on the mechanism. This allows finding conditions of singular configurations that are related to displacements of passive joints. Based on these conditions, the force-unconstrained poses are obtained by solving the forward kinematic analysis of manipulators with the same architecture but different actuation layouts. It is demonstrated that the singularity loci of the 3-RPR, 3-PRR, and 3-RRR PPMs can be described with single-variable polynomials of degrees 2, 2, and 6, respectively.