Analytical modeling and experimental validation of rotationally actuated pinned–pinned and fixed–pinned buckled beam bistable mechanisms

Buckled beams have become key building blocks in compliant mechanisms to achieve nonlinear behaviors, such as bistability, constant-force and stiffness tuning. However, designing and modeling such components is challenging due to their highly nonlinear characteristics and existing models typically lack accuracy or rely on numerical computations. This paper aims at giving closed-form formulas to efficiently characterize the snap through behavior and facilitate the design process of rotationally actuated pinned–pinned and fixed–pinned bistable buckled beams. A new generic analytical model for precompressed beams based on Euler–Bernoulli beam theory is first established and then applied to these two configurations. Finite element and experimental validations are performed, showing excellent agreement with the model. The results show that the angular input at the pinned beam extremity is significantly decoupled from the angular or moment output at the other extremity, until snap-through. Additionally, we show that the stable output values can be controlled by adjusting the precompression displacement of the buckled beam. Finally, we demonstrate the practicality of the studied building blocks and their modeling on a novel bistable gripper design.