A controlled relative motion system comprising a base support, a pivot holder and a plurality of pivoting links with the pivoting links rotatably coupled to both the base support and to members of the pivot holder to rotate about axes which extend in different directions for each of these rotatable couplings in a link, typically in accord with specific geometrical arrangements, and in different directions from similar axes in another of such links. The foregoing various rotatable couplings are provided by insertable bearings or bushings in the supports and links. The pivoting links have larger portions thereof outside of the interior of the manipulator parts of which can extend outside in different directions. Such systems can incorporate a variety of force imparting members to control movements of various ones of the pivoting links or pivot holder members.