Planar Compliance Realization With Two 3-Joint Serial Mechanisms

Abstract

In this paper, the realization of any specified planar compliance with two 3R serial elastic mechanisms is addressed. Using the concept of dual elastic mechanisms, it is shown that the realization of a compliant behavior with two serial mechanisms connected in parallel is equivalent to its realization with a 6-spring fully parallel mechanism. Since the spring axes of a 6-spring parallel mechanism indicate the geometry of a dual 3R serial mechanism, a new synthesis procedure for the realization of a stiffness matrix with a 6-spring parallel mechanism is first developed. Then, this result is extended to a geometric construction-based synthesis procedure for two 3-joint serial mechanisms.