DETERMINATION OF THE WORKSPACE OF A PARALLEL MANIPULATOR FOR A FIXED ORIENTATION

The workspace of a 6 d.o.f. parallel manipulator is bounded because of the limitations on the links lengths, the mechanical limits on the passive joints and links interference. We consider here a general 6 d.o.f. parallel manipulator with extensible links and assume that the orientation of the end-effector is constant. We propose a geometrical method to determine exactly the boundary of planar cross-sections of the workspace. We assume that the mechanical limits on the passive joints can be described by a pyramid with planar faces which define the border of the volume reachable by the link connected to the joint and that the links are cylinder of known radius. Under this assumption it is shown that the workspace is the intersection of various geometrical objects (circles, polygons, conics) and we show how to compute these intersections. Various examples are provided.