Probleme geometrique direct et lieux de singularite des manipulateurs paralleles

Abstract

Cette these presente une contribution a l'etude cinematique des manipulateurs paralleles. Ces manipulateurs sont caracterises par une excellente rigidite et une excellente precision de positionnement. L'interet est porte ici aux manipulateurs paralleles plans a trois degres de liberte, aux manipulateurs paralleles spheriques a trois degres de liberte et aux manipulateurs paralleles spatiaux a six degres de liberte. Nous avons apporte des solutions polynomiales nouvelles au probleme geometrique direct et etabli des expressions analytiques originales decrivant les singularites de ces manipulateurs.

Dans la premiere partie, le probleme geometrique direct est d'abord resolu. Pour chaque classe de manipulateurs etudiee ici, une solution polynomiale minimale est derivee. Des solutions explicites sont egalement derivees pour des architectures particulieres.

Dans la deuxieme partie, des expressions analytiques des lieux de singularite sont derivees et etudiees pour chaque classe de manipulateurs paralleles mentionnee ci-dessus.

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This thesis presents a contribution to the kinematic study of parallel manipulators. These manipulators are characterized by excellent rigidity and excellent positioning precision. The focus here is on planar parallel manipulators with three degrees of freedom, spherical parallel manipulators with three degrees of freedom and spatial parallel manipulators with six degrees of freedom. We have brought new polynomial solutions to the direct geometric problem and established original analytical expressions describing the singularities of these manipulators.

In the first part, the direct geometric problem is first solved. For each class of manipulators studied here, a minimal polynomial solution is derived. Explicit solutions are also derived for particular architectures.

In the second part, analytical expressions of singularity loci are derived and studied for each class of parallel manipulators mentioned above.