A Novel Formulation for the Design of Distributed Compliant Mechanisms

The optimization problem formulations currently used to synthesize compliant topologies aim to maximize flexibility at the output point for desired motion while maximizing overall stiffness for satisfactorily bearing the applied loads. The best solution to this problem, as posed, is a linkage consisting of rigid members connected together with revolute joints. Current elastic mechanics-based formulations do generate compliant topologies that closely imitate a rigid-body linkage by means of lumped compliance as in flexures. Systematically generating such topology solutions could serve as a creative aide for subsequent modifications, especially when the force-deflection specifications are non-intuitive to human designers. However, flexure-based compliant designs are not useful in most applications when large displacements and/or high strength are desired. Ideally, compliant designs should distribute flexibility uniformly throughout the structure rather than limiting to a few flexures. In this paper we discuss why current formulations often do not provide distributed compliant designs, and present a novel formulation that guarantees distributed compliance. The method is explained in detail and is illustrated with examples.