A metric to evaluate and synthesize distributed compliant mechanisms

It is widely accepted that compliant mechanisms with stresses distributed evenly throughout its geometry have better load bearing ability and larger range of motion than mechanisms with compliance and stresses lumped at flexural hinges. In this paper, we present a metric to quantify how uniformly stresses and thus strain energy is distributed throughout the mechanism topology. The resulting metric is used to optimize the cross-sections of conceptual compliant topologies leading to designs with maximal distribution of stresses. This optimization framework is demonstrated for both single point mechanisms and single-input singleoutput mechanisms. It is observed that the optimized designs have a larger range of motion and perform more output work or store more strain energy before failure than their non-optimized counterparts. Furthermore, the nondimensional nature of the metric coupled with the physical insight enables an objective comparison of various topologies and actuation schemes based on how evenly stresses are distributed in the constituent members.