Stiffness Reduction of Flexure Pivots using Fixed-Lever Buckled Beams

Abstract

Stiffness reduction of compliant mechanisms has become an important research topic. Although numerous strategies have been proposed for flexure-based linear stages, design methods exploiting beam buckling to reduce the angular stiffness of flexure pivots remain scarce. This paper introduces a buckling-based mechanism consisting of two beams clamped at one end and attached to a rotating lever at the other. We refer to this support condition as fixed-lever, distinguishing it from the conventional fixed- pinned configuration. Analytical and numerical investigations show that a single fixed- lever buckled beam exhibits highly nonlinear and hysteretic behavior under rotational actuation. However, pairing two such beams and enforcing symmetric buckling yields a nearly constant negative angular stiffness near the neutral position. This negative- stiffness structure can be monolithically integrated into generic flexure pivots to reduce their angular stiffness. Closed-form analytical formulas are derived to guide the design of targeted stiffness-reduction profiles. The concept and analytical model are validated through finite element simulations and experiments on metal and additively manufactured polymer prototypes. Finally, microscale silicon pivots preloaded through thermal oxidation achieve a measured stiffness reduction of 96% over an operating range of ±4.5 deg.