Position, Velocity, and Acceleration Synthesis of the RRSS Spatial Path-Generating Mechanism Using the Selective Precision Synthesis Method

Abstract

The inclusion of velocity and acceleration constraints is a crucial step in the coupling of the dynamics with the kinematics of spatial mechanisms. In this paper, an optimum synthesis technique is presented which allows an arbitrary combination of positions, velocities, and accelerations to be specified along with appropriate tolerances at one or more of the prescribed path points. The method of Selective Precision Synthesis is used to formulate nonlinear constraint equations which are then solved by the generalized reduced gradient method of optimization. This is significant since it paves the way for the coupling of mechanism dynamics with the kinematics of spatial mechanisms. The technique developed herein is general to all spatial mechanisms and is exemplified by the RRSS path-generating spatial mechanism.