The derivation of a bistable criterion for double V-beam mechanisms

This study presents the theoretical derivation of the discriminant D as a structural and material criterion for determining whether bistability can occur in micromechanically bistable mechanisms. When D < 0, the mechanism displays bistable behavior if an appropriate force is applied to push the bistable mechanism, whereas when D > 0, bistable behavior cannot occur. The proposed V-beam bistable mechanism was successfully fabricated with various beam lengths and tilted angles. The experiments conducted in this study validated the theoretical study of bistability. A comparison of the theoretical solutions and experimental results shows good agreement. Results further show that to design a bistable V-beam mechanism, the tilted angle should be larger for the same beam length, whereas the beam length should be longer for the same tilted angle. The developed discriminant D can be used to predict if a bistable mechanism can achieve bistable behavior based on structural sizes and material properties. Consequently, researchers can reduce trial-and-error experiments when designing a bistable mechanism. A V-beam with a larger tilted angle of up to 5° was successfully fabricated to act as a bistable mechanism, compared to a 3.5° tilted angle in existing studies. Consequently, the proposed method has the advantages of shorter beam lengths and smaller device areas.