Kinematic synthesis of spatial R-R dyads for path following with applications to coupled serial chain mechanisms

The dimensional synthesis of a spatial two revolute jointed dyad for path f ollowing tasks with applications to coupled serial chain mechanisms is pres ented. The precision point synthesis equations obtained using the rotation matrix approach form a rank-deficient linear system in the link-vector comp onents. The nullspace of this rank-deficient linear system is derived analy tically and interpreted geometrically. The nullspace vectors lead to the sp ecification of additional constraints via the so-called auxiliary equations and to the solution of the linear system of equations. The geometry also a llows the derivation of a closed,form solution for the three design positio n problem. Finally, optimal path following by coupled R-R dyads is achieved by optimization over the free choice variables.