A Methodology for Determining Static Mode Shapes of a Compliant Mechanism Using the Pseudo-Rigid-Body Model (PRBM) Concept and the Degrees-of-Freedom Analysis

Abstract

Traditionally, the deflected configuration of compliant segments is determined through rigorous mathematical analysis using Newtonian mechanics. Application of these principles in evaluating the deformed configuration of compliant mechanisms, containing a variety of segment types, becomes cumbersome. This paper introduces a methodology to determine the expected deflected configuration(s) of a compliant mechanism, for a given set of load and/or displacement boundary conditions. The method utilizes the principle of minimum total potential energy, in conjunction with the degrees-of-freedom analysis and the pseudo-rigid-body model concept. The static mode shape(s) of compliant segments are integrated in identifying the possible functional configuration(s) of a given compliant mechanism’s structural configuration. The methodology, in turn, also facilitates the in situ determination of the deformed configuration of the constituent compliant segments. It thus assists in the identification of an appropriate pseudo-rigid-body model for design and analysis of a compliant mechanism.