Synthesis of reactionless spatial 3-DoF and 6-DoF mechanisms without separate counter-rotations

In this paper we present the synthesis of novel reactionless spatial three-degrees-of-freedom (3-DoF) and 6-DoF mechanisms without any separate counter-rotation, using four-bar linkages. Based on the conditions of dynamic balancing of a single planar four-bar linkage developed elsewhere, the spatial problem is shown to be equivalent to ensuring that the inertia tensor of reactionless four-bar linkage(s), which is(are) attached on the moving link of a reactionless four-bar linkage, remains constant while moving. The reactionless conditions for planar four-bar linkages undergoing spatial motion are first given. Then, reactionless spatial 3-DoF mechanisms using four-bar linkages are synthesized. A numerical example of the reactionless spatial 3-DoF mechanism is given and, with the help of the dynamic simulation software ADAMS, it is shown that the mechanism is reactionless for arbitrary trajectories. Finally, this mechanism is used to synthesize reactionless 6-DoF parallel mechanisms.