Closed-Form Elliptic Integral Solution of Initially-Straight and Initially-Curved Small-Length Flexural Pivots


Compliant mechanisms gain some or all of their mobility from the deflection of their flexible members. The pseudo-rigidbody model (PRBM) concept allows compliant mechanisms to be modeled using existing knowledge of rigid-body mechanisms, thereby, simplifying the design process. A pseudo-rigid-body model represents a compliant segment with two or more rigid-body segments, connected by pin joints or characteristic pivots. A compliant segment that is small in length, compared to the relatively rigid segments between which it is affixed, is termed a small-length flexural pivot (SLFP). This paper presents closed-form deflection solutions using the elliptic integral method for initially-straight and initially-curved SLFPs. The assumptions made in modeling the small-length flexural pivots in a PRBM are validated by means of the elliptic integral solutions.

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; Integral equations; Mechanisms; Rigid structures; Closed form; Design process; Elliptic integrals; Pin joints; Pseudo rigid bodies; Pseudo-rigid body models; Rigid body; Compliant mechanisms

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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