Avoiding singular configurations in finite position synthesis of spherical 4R linkages

In this paper we consider the generalization of planar rectification theory to spherical 4R linkages. The goal is to ensure that the result of a finite position synthesis is a linkage that does not have a ‘branching problem.’ Branching defects limit the usefulness of a linkage and the ability to remove them in the design process is of fundamental importance. The primary results of planar rectification theory, Filemon’s construction and Waldron’s ‘three circle diagram,’ are found to have direct analogies in spherical 4R synthesis theory. In this case, however, we obtain three quadric cones, not circles, as our ‘spherical version’ of Waldron’s three circle diagram.