On the synthesis of spatial revolute—revolute—spherical—cylindrical motion generators with prescribed coupler loads

Abstract

This work extends the concepts and methodologies of Shen et al. for the synthesis of spherical four-bar motion generators to the synthesis of spatial revolute—revolute—spherical—cylindrical (RRSC) motion generators with applied coupler loads. A constraint that includes coupler loads and driver static torques for the RRSC mechanism is formulated using the principle of virtual work. This constraint is combined with the conventional constraints for the R—R and C—S dyads to form a non-linear optimization problem from which RRSC mechanism solutions are calculated that approximate prescribed coupler poses and satisfy prescribed driver static torques for given coupler loads. The formulated RRSC coupler load and driver static torque constraint are also incorporated in a simplified RRSC motion generation model to form a simplified non-linear optimization problem for calculating RRSC mechanism solutions. This work demonstrates both the conventional and simplified non-linear optimization problems.