Uniqueness Domains in the Workspace of Parallel Manipulators

TL;DR

This paper characterizes the uniqueness domains in the workspace of parallel manipulators, introducing characteristic surfaces that divide the workspace into regions with unique inverse kinematic solutions, using a 3-RPR manipulator as illustration.

Contribution

It redefines the notion of aspects for parallel manipulators and introduces characteristic surfaces to identify new uniqueness domains in the workspace.

Findings

Identified characteristic surfaces dividing the workspace into basic regions.

Linked multiple solutions to the forward kinematic problem without encountering singularities.

Used octree models to compute and visualize the workspace and joint space.

Abstract

This work investigates new kinematic features of parallel manipulators. It is well known that parallel manipulators admit generally several direct kinematic solutions for a given set of input joint values. The aim of this paper is to characterize the uniqueness domains in the workspace of parallel manipulators, as well as their image in the joint space. The study focuses on the most usual case of parallel manipulators with only one inverse kinematic solution. The notion of aspect introduced for serial manipulators in [Borrel 86] is redefined for such parallel manipulators. Then, it is shown that it is possible to link several solutions to the forward kinematic problem without meeting a singularity, thus meaning that the aspects are not uniqueness domains. An additional set of surfaces, namely the characteristic surfaces, are characterized which divide the workspace into basic regions and yield new uniqueness domains. This study is illustrated all along the paper with a 3-RPR planar parallel manipulator. An octree model of spaces is used to compute the joint space, the workspace and all other newly defined sets.