On the Synthesis of Reactionless Spatial 3-DOF Mechanisms Using Planar 4-Bar Linkages

This paper presents the synthesis of a novel reactionless spatial 3-DOF mechanism using four-bar linkages without any counter-rotation. Based on the conditions of static and dynamic balancing of a single planar four-bar linkage developed elsewhere, the spatial problem is shown to be equivalent to verifying if the inertia tensor of reactionless four-bar linkages can be kept constant when the planar mechanism(s) is(are) moving. The reactionless conditions for planar four-bar linkages in space are first given. Then, reactionless spatial 3-DOF mechanisms using four-bar linkages are synthesized. A numerical example of the reactionless spatial 3-DOF mechanisms is given and, with the help of the dynamic simulation software ADAMS, it is shown that the mechanisms are reactionless for any trajectory and can be used to synthesize 6-DOF reactionless mechanisms.