Stiffness reduction of flexure pivots using fixed-lever buckled beams

Stiffness reduction of compliant mechanisms through beam buckling has become an important research topic, particularly for achieving specific stiffness profiles, static balancing, or bistability. This paper investigates 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 modeling based on Euler-Bernoulli beam theory shows 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 structure can be monolithically integrated into generic flexure pivots to reduce their angular stiffness. Closed-form expressions are derived to guide the design of flexure pivots with targeted angular stiffness reduction. 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°.