Pseudo-Rigid Body Dynamic Modeling of Compliant Members for Design

Movement in compliant mechanisms is achieved, at least in part, via deformable flexible members, rather than using articulating joints. These flexible members are traditionally modeled using Finite Element Models (FEMs). In this article, an alternative strategy for modeling compliant cantilever beams is developed with the objectives of reducing computational expense, and providing accuracy with respect to design optimization solutions. The method involves approximating the response of a flexible beam with an n-link/m-joint Pseudo-Rigid Body Dynamic Model (PRBDM). Traditionally, PRBDM models have shown an approximation of compliant elements using 2 or 3 revolute joints (2R/3R-PRBDM). In this study, a more general nR-PRBDM model is developed. The first n resonant frequencies of the PRBDM are matched to exact or FEM solutions to approximate the response of the compliant system. These models can be used for co-design studies of flexible structural members, and are capable of modeling higher deflection of compliant elements.