Synthesis of RCCC Linkages to Visit Four Given Poses

Abstract

This paper focuses on the problem of synthesis of spatial four-bar linkages of the RCCC type for rigid-body guidance with four given poses, R denoting a revolute, C a cylindrical kinematic pair. While synthesis equations for CC and RC dyads are available in the literature, the synthesis of spatial RCCC four-bar linkages requires special attention, due to its asymmetric topology. We revisit the problem to cope robustly with the asymmetry, namely, the approximate nature of the RC dyad and the infinity of exact solutions of the CC dyad for the number of given poses. Our approach includes a robust formulation of the synthesis of CC dyads, for the determination of axis-congruences. Moreover, we formulate a uniform synthesis equation, which enables us to treat both RC and CC dyads, with properly selected constraints for both cases. Two design examples are included.