Lieux de singularité des manipulateurs parallèles à actionnement redondant

Abstract

L'étude des lieux de singularité des manipulateurs parallèles à actionnement redondant ne peut être effectuée de façon classique. En effet, cela implique le calcul du déterminant de la matrice jacobienne du mécanisme, qui doit être carrée. Cette matrice est rectangulaire dans le cas de redondance.

Deux approches ont été utilisées pour résoudre ce problème: la multiplication de la matrice jacobienne et la méthode des parties. La première démarche permet de dégager une expression, dont le résultat est une matrice carrée qui doit être inversible. On obtient ainsi une équation d'expression assez simple, mais dont il est difficile d'extraire les racines. La deuxième technique consiste à obtenir le lieu de singularité par l'intersection des lieux de singularité de parties du mécanisme. Cette méthode est plus longue à appliquer, mais permet d'obtenir l'expression des lieux de singularité.

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The study of the places of singularity of the parallel manipulators with redundant actuation cannot be carried out in a traditional way. Indeed, this implies the calculation of the determinant of the Jacobian matrix of the mechanism, which must be square. This matrix is ​​rectangular in the case of redundancy.

Two approaches have been used to solve this problem: Jacobian matrix multiplication and the method of parts. The first step makes it possible to identify an expression, the result of which is a square matrix which must be invertible. We thus obtain a fairly simple expression equation, but from which it is difficult to extract the roots. The second technique consists in obtaining the locus of singularity by the intersection of the locus of singularity of parts of the mechanism. This method takes longer to apply, but makes it possible to obtain the expression of the places of singularity.