  Double-clamped bistable buckled beams, as the most elegant bistable
mechanisms, demonstrate great versatility in various fields, such as robotics,
energy harvesting, and MEMS. However, their design is always hindered by
time-consuming and expensive computations. In this work, we present a method to
easily and rapidly design bistable buckled beams subjected to a transverse
point force. Based on the Euler-Bernoulli beam theory, we establish a
theoretical model of bistable buckled beams to characterize their snap-through
properties. This model is verified against the results from an FEA model, with
discrepancy less than 7 %. By analyzing and simplifying our theoretical model,
we derive explicit analytical expressions for critical behavioral values on the
force-displacement curve of the beam. These behavioral values include critical
force, critical displacement, and travel, which are generally sufficient for
characterizing the snap-through properties of a bistable buckled beam. Based on
these analytical formulas, we investigate the influence of a bistable buckled
beam's key design parameters, including its actuation position and
precompression, on its critical behavioral values, with our results validated
by FEA simulations. This way, our method enables fast and computationally
inexpensive design of bistable buckled beams and can guide the design of
complex systems that incorporate bistable mechanisms.
