Second-order approximation pseudo-rigid model of circular arc flexure hinge

The paper presents a novel pseudo-rigid model for describing the elasto-kinematic behaviour of circular arc flexure hinge subjected to a pure moment. The model is based on the kinematic study of flexure hinge large deflection using second-order motion invariants (polodes and inflection circle), which accurately describes the relative motion between the connected bodies. The proposed pseudo-rigid model has a single degree of freedom. It is an epicyclic arrangement with two rolling without slipping external circles with the same radius and a torsional spring with constant stiffness. Analytical formulas for computing the radius and the location of the two rolling circles and the rotational spring stiffness are deduced. The proposed model has been compared with analytical formulas and structural finite element models in different configurations. The results show very good accordance even for large deflections, confirming the model's effectiveness.