A Method for a More Accurate Calculation of the Stiffness Coefficient in a Pseudo-Rigid-Body Model (PRBM) of a Fixed-Free Beam Subjected to End Forces


The pseudo-rigid-body model (PRBM) concept allows compliant mechanisms to be modeled using existing knowledge of rigid-body mechanisms, thereby considerably simplifying their analysis and design. The PRBMs represent the compliant segments with two or more rigid-body segments, connected using pin joints (characteristic pivots). The beam compliance is modeled using a torsional spring placed at the characteristic pivot, whose spring constant K is evaluated using a pseudo-rigid-body parameter termed as the beam stiffness coefficient. This paper presents a method to more accurately calculate the beam stiffness coefficient for a fixed-free compliant beam subjected to a combination of horizontal and vertical forces. The improved stiffness coefficient (KΘ) expressions are derived as a function of the pseudo-rigid-body angle, Θ and the load factor, n. To exemplify the application of the improved results, the expressions derived are successfully implemented in modeling a fixed-guided beam with an inflection point, allowing it to be modeled as two fixed-free beams pinned at the inflection point.

Meeting Name

ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2014 (2014: Aug. 17-20, Buffalo, NY)


Mechanical and Aerospace Engineering

Keywords and Phrases

Design; Mechanisms; Rigid structures; Stiffness; Torsional stress; Accurate calculations; Compliant beams; Inflection points; Pseudo rigid bodies; Pseudo-rigid-body models; Spring constants; Stiffness coefficients; Torsional springs; Compliant mechanisms

International Standard Book Number (ISBN)


Document Type

Article - Conference proceedings

Document Version


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© 2014 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Aug 2014