Torsional stiffness of several variable rectangular cross-section flexure hinges for macro-scale and MEMS applications

The paper develops approximate closed-form equations for the torsional stiffness of several variable rectangular cross-section flexure hinges for macro-scale and MEMS applications. Specifically, corner-filleted, elliptic, parabolic and hyperbolic flexure configurations, either longitudinally symmetric or non-symmetric, are studied. The model gives the tools for a preliminary assessment of the static/modal response of flexure-based devices that deform torsionally. Several numerical simulations are conducted based on the model, which indicate that, for similar values of the geometric parameters, the hyperbolic flexure is the stiffest, followed by the parabolic, corner-filleted and elliptic configurations. The modal response is studied for a two-flexure torsional micro-mirror by sequentially considering four different pairs of longitudinally symmetric flexure designs. The results of the simulation confirm the stiffness predictions and are also in agreement with finite element analysis results.