An improved method for designing flexure-based nonlinear springs.

Monolithic Flexure-based Compliant Mechanisms (MFCM) can functionally act as nonlinear springs by providing a desired load-displacement profile at one point on their structure. Once the MFCM topology is chosen, these particular springs can be conveniently synthesized resorting to the well-known Pseudo- Rigid-Body approximation, whose accuracy strongly depends on the modeling precision of the flexures’ principal compliance. For various types of flexures, closed-form solutions are available for what concerns the compliance factors as functions of the flexure dimensions. Nonetheless, the reliability of these analytical relations is limited to slender, beam-like, hinges undergoing small deflections. In order to overcome such limitations, this paper provides empirical equations, derived from finite element anal- ysis, that can be used for the optimal design of circular, elliptical, and corner-filleted flexural hinges with general aspect ratios on the basis of both principal compliance and maximum achievable stress. As a case study, a nonlinear spring conceived as a four-bar linkage MFCM is synthesized and simulated by means of finite element analysis. Numerical results confirm that the aforementioned empirical equations outperform their analytical counterparts when modeling thick cross-section hinges undergoing large deflections.