Classifying the Boundaries of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms by Visual Inspection

Abstract

The wrench-closure workspace of parallel cable-driven mechanisms is the set of poses for which any wrench can be produced at the end-effector by a set of non-negative cable tensions. It is already known that the boundary of the constant-orientation wrench-closure workspace of a planar parallel cable-driven mechanism is composed of segments of conic sections. However, the relationship between the geometry of the mechanism and the types of these conic sections is unknown. This technical report proposes a graphical method for determining the types of these conic sections from the mechanism geometry. It is also shown that the proposed method can be applied to find the constant-orientation singularities of a 3-RPR planar parallel robot, since these conic sections correspond to the boundary segment of the analogous three-cable driven planar parallel mechanism.