Workspace analysis of a 6-RSS parallel robot considering non-ideal spherical joints

This paper gives an analytical description for the ideal and the real workspace of a 6-RSS parallel robot; that is, by considering its geometrical and its mechanical constraints. The ideal workspace is described as a set of inequalities representing a 3D volume that encloses valid attitudes, whose frontier can be plotted as a 3D surface by using Constructive Solid Geometry and an adaptive polygonization method. The real workspace represents a subset of the ideal one, determined by the presence of joint limits at the spherical joints. These ones arise from the fact that these spherical joints are not ideal, but implemented as spherical plain bearings. However, although it is not straight forward to express these joint limits in an analytical way, it was possible to find an analytical expression to describe the real workspace, represented by additional inequalities that must be met by a desired attitude of the platform.