Singularities within the workspace of spatial parallel mechanisms with symmetric structures

Abstract

This article addresses the symmetry similarities between the singularity distributions within the reachable workspaces of spatial parallel mechanisms and the mechanism structures. The symmetry similarities between the workspace and the mechanism architecture are also fit for interpreting the relationship between the singularities within the workspace and the architecture. Further, this research reveals that the symmetry group of the workspace must be a subgroup of the symmetry group of the distribution of singularities within the reachable workspace, which is rigorously proved in theory. Mechanism examples also demonstrate these similarities of symmetries between the singularities, the reachable workspace, and the mechanism structure. The novelty of this work in engineering applications is that the searching range for the singularities in the reachable workspace can be reduced greatly.