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.