Modeling and Design of Compliant Bistable Mechanisms: A Brief Review with A Case Study on Variable Constant Force Mechanism

Compliant Bistable Beam Mechanisms (CBBMs), a subclass of Compliant Mechanisms (CMs), have become increasingly prominent in micro-scale and precision engineering applications due to their intrinsic bistability, monolithic fabrication compatibility, and zero-power holding capability. These features make them ideal candidates for integration in MEMS devices, sensors, actuators, and energy harvesting systems. However, the accurate modeling of CBBMs remains a formidable challenge due to the strong nonlinearities associated with post-buckling deformation and snap-through instability. This paper presents a comprehensive review of the current modeling approaches for CBBMs, including analytical, reduced-order, and numerical methods. Particular emphasis is placed on negative-stiffness parametric formulations, which enable efficient design and optimization workflows. Furthermore, a case study is introduced in which a Variable Constant Force Mechanism (VCFM) is designed by combining a Positive Stiffness Structure (PSS) with a Bistable Beam Structure (BSB). A novel FEA-based optimization method is proposed that leverages parametric negative-stiffness expressions to tune bistable characteristics. The method demonstrates fast convergence and accurate control over the force–displacement response, outperforming traditional black-box optimization strategies. A full topology optimization is also conducted to maximize stroke and force flatness.