A Methodology for Determining Static Mode Shapes of a Compliant Mechanism using the Pseudo-Rigid-Body Model Concept and the Degrees-Of-Freedom Analysis


Traditionally, the deflected configuration of compliant segments is determined through rigorous mathematical analysis using Newtonian mechanics. Application of this approach in evaluating the deformed configuration of compliant mechanisms, containing a variety of segment types, becomes cumbersome. This paper introduces a methodology to determine the possible deflected configuration(s) of a compliant mechanism, for a given set of load and/or displacement boundary conditions. The methodology utilizes the principle of minimum 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 deflected configuration(s) of a given compliant mechanism. The methodology facilitates the in situ determination of the possible deformed configuration(s) of the compliant mechanism and its constituent segments. This, in turn, assists in the important task of identifying an appropriate pseudo-rigid-body model for the design and analysis of a compliant mechanism. The proposed methodology is illustrated with examples, and supported with experimental validation.


Mechanical and Aerospace Engineering

Keywords and Phrases

Bio-inspired design; Compliant mechanisms; Mechanism degrees-of-freedom; Mechanism design; Mechanism synthesis; Microscale mechanisms and robotics; Mode shapes of compliant mechanisms

International Standard Serial Number (ISSN)

1942-4302; 1942-4310

Document Type

Article - Journal

Document Version


File Type





© 2020 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Apr 2021