Design of Distributed Compliant Mechanisms

The optimization problem formulations currently used to synthesize compliant mechanism topologies aim to maximize the flexibility for obtaining the desired output motion while maximizing the 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. The current elastic mechanics-based formulations do generate compliant topologies that closely imitate a rigid-body linkage by means of lumped compliance as in flexural pivots. Systematically generating such topology solutions could serve as a creative aid in the conceptual design of mechanisms, especially when the force-deflection specifications are nonintuitive to human designers. However, flexural pivot-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 it to a few pivots. In this article, we discuss why current formulations often lead to lumped compliant designs, put forth a proper quantitative measure for distributed compliance, and present a novel formulation that guarantees distributed compliant topologies. The method is explained in detail and is illustrated with examples.