De la simplification et la résolution du modèle géométrique direct des robots parallèles

Abstract

A parallel manipulator is made of two bodies, a platform and a base, connected by articulated and motorized kinematic chains that enable one to move with respect to the other. The forward kinematic problem for six degrees of freedom parallel manipulators is fundamental, This problem is to find the position and the orientatíon of the platform with respect to a reference frame when the control variables are known. An equivalent statement is to place a given solid onto six spheres with fixed centers and radii. This problem may be considered either from a geometric point of view or an algebric one, calling for the use of various methods. The forward kinematic problem has at most forty solutions over the complex field. We use extra sensors to simplify and solve this problem, as well as, many symbolic and sometimes numerical methods. The results we obtain lead to the design of robot architectures with a minimum number of solutions to the foward kinematic problem, and sometimes even with explicit or unique solutions.