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 by 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 have been proposed which express 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 analysis, 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 bearable 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.