Description analytique complète des limites de l'espace de travail pour un manipulateur en série plan

We give a general and analytical description of plan workspace boundaries, i.e. the boundaries of the part of the space that is reached by the extremity of a human or robot arm. The proposed method is decomposed into three independent steps, for which we do not use calculus of derivatives, determinants and eigenvalues, or numerical resolutions of non-linear problems, which are often used in the literature. The first step, already presented in previous works, consists in interpreting geometrically the necessary Jacobian rank deficiency of the position function at the boundary, and an alignment condition of some joints allows us to determine a union of arcs of circle, which contains the boundary. Then, for all arc of circle, the study of the infinitesimal displacement of a point with regard to this circle allows one to eliminate all or a part of arcs of circle, previously defined, which is not on the boundary. Finally, a global course of the arcs of circle allows us to determine the outer boundary and the inner boundary of the possible void that contains the origin.