Singularity Analysis of 3-RPR Parallel Manipulators Using Geometric Algebra

Abstract

This paper presents a new method based on geometric algebra for the singularity analysis of 3-degrees of freedom overconstrained 3-RPR planar parallel manipulators. Constraint wrenches acting on the moving platform are obtained using the outer product and dual operations. After the redundant constraint wrenches are identified and removed, a singular polynomial is derived as the coefficient of the outer product of all the non-redundant constraint wrenches. This polynomial provides an overall perspective of the singularity of the 3-RPR parallel manipulators and enables the drawing of 3-dimensional singularity loci, which are important in trajectory planning and workspace design. The main advantage of using geometric algebra is the compact and geometrically intuitive formulation of the singularity polynomial of the 3-RPR parallel manipulators.