S\'eparation des Solutions aux Mod\`eles G\'eom\'etriques Direct et Inverse pour les Manipulateurs Pleinement Parall\`eles

TL;DR

This paper introduces a formalism for managing solutions of direct and inverse kinematic models of fully parallel manipulators, using concepts like working modes, aspects, characteristic surfaces, and uniqueness domains to improve design and trajectory planning.

Contribution

It presents a novel formalism that separates and characterizes solutions of kinematic models for parallel manipulators, aiding in design and trajectory planning.

Findings

Defined working modes and aspects for manipulators.

Introduced characteristic surfaces for solution separation.

Identified uniqueness domains for solution unicity.

Abstract

This article provides a formalism making it possible to manage the solutions of the direct and inverse kinematic models of the fully parallel manipulators. We introduce the concept of working modes to separate the solutions from the opposite geometrical model. Then, we define, for each working mode, the aspects of these manipulators. To separate the solutions from the direct kinematics model, we introduce the concept of characteristic surfaces. Then, we define the uniqueness domains, as being the greatest domains of the workspace in which there is unicity of solutions. The principal applications of this work are the design, the trajectory planning.