Definition sets for the Direct Kinematics of Parallel Manipulators

TL;DR

This paper characterizes the workspace and joint space of parallel manipulators, redefining aspects to identify multiple solutions without singularities, and introduces new uniqueness domains using octree models, exemplified on a 3-RPR manipulator.

Contribution

It redefines the notion of aspects for parallel manipulators and introduces new methods to identify multiple solutions and uniqueness domains in their workspace.

Findings

Redefinition of aspects for parallel manipulators.

Identification of multiple solutions without encountering singularities.

Introduction of new uniqueness domains using octree models.

Abstract

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 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 direct kinematic problem without meeting a singularity, thus meaning that the aspects are not uniqueness domains. Additional surfaces are characterized in the workspace which yield new uniqueness domains. An octree model of spaces is used to compute the joint space, the workspace and all other newly defined sets. This study is illustrated all along the paper with a 3-RPR planar parallel manipulator.