Full-Rotation Singularity-Safe Workspace for Kinematically Redundant Parallel Robots

Abstract

This paper introduces and computes a novel type of workspace for kinematically redundant parallel robots that defines the region in which the end-effector can make full rotations without coming close to singular configurations; it departs from the traditional full-rotation dexterous workspace, which considers full rotations without encountering singularities but does not take into account the performance problems resulting from closeness to these locations. Kinematically redundant architectures have the advantage of being able to be reconfigured without changing the pose of the end-effector, thus being capable of avoiding singularities and being suitable for applications where high dexterity is required. Knowing the workspace of these robots in which the endeffector is able to complete full, smooth rotations is a key design aspect to improve performance; however, since this singularity-safe workspace is generally small, or even non-existent, in most parallel manipulators, its characterisation and calculation have not received attention in the literature. The proposed workspace for kinematically redundant robots is introduced using a planar parallel architecture as a case study; the formulation works by treating the manipulator as two halves, calculating the full-rotation workspace of the end-effector for each half whilst ensuring singularity conditions are not approached or met, and then finding the intersection of both regions. The method is demonstrated on two example robot instances, and a numerical analysis is also carried out as a comparison.