An improved design method for the dimensional synthesis of flexure-based compliant mechanisms: optimization procedure and experimental validation

Monolithic Flexure-based Compliant Mechanisms (MFCM) can be used to conceive nonlinear springs with a desired load-displacement profile at one point of their structure. For a given MFCM topology, these particular springs can be conveniently dimensioned by resorting to the well-known Pseudo-Rigid-Body approximation, whose accuracy strongly depends on the modelling 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 accuracy of these relations is limited to slender, beam-like hinges undergoing rather 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 dimensioning of circular, elliptical, and corner-filleted flexural hinges with general aspect ratios, on the basis of both principal compliance and maximum bearable stress. At first, an accuracy comparison with previously published results is provided. Then, as a case study, a nonlinear spring based on a double slider-crank MFCM and with a desired load-displacement profile is dimensioned and verified via finite element analysis. The corresponding MFCM prototype, produced by means of water jet cutting, is finally tested on a tensile stage. Both numerical and experimental results confirm that the aforementioned empirical equations outperform the closed-form solutions provided in the past literature when modelling thick cross-section hinges undergoing significant deflections.