Geometric Approach to Realization of Planar Elastic Behaviors with Mechanisms Having Four Elastic Components
American Society of Mechanical Engineers
Journal of Mechanisms and Robotics
This paper addresses the passive realization of any selected planar elastic behavior with redundant elastic manipulators. The class of manipulators considered are either serial mechanisms having four compliant joints or parallel mechanisms having four springs. Sets of necessary and sufficient conditions for mechanisms in this class to passively realize an elastic behavior are presented. The conditions are interpreted in terms of mechanism geometry. Similar conditions for non-redundant cases are highly restrictive. Redundancy yields a significantly larger space of realizable elastic behaviors. Construction-based synthesis procedures for planar elastic behaviors are also developed. In each, the mechanism geometry and the joint/spring stiffnesses are completely decoupled. The procedures allow the geometry of each elastic component to be selected from a restricted space of acceptable candidates.