Elasto-Kinematics and second-order pseudo-rigid model of cross-axis flexure hinges

The paper deals with the investigation of the elasto kinematics of the cross-axis flexure hinge and its first- and second-order motion invariants in order to propose an equivalent pseudo-rigid embodiment able to accurately reproduce the relative motion between the connected bodies in a large angle range. Cross-axis flexure hinges are quite common in compliant mechanisms and flexible structures. The main challenge in the study of such flexible links is represented by the statically-indeterminate arrangement that implies the non-trivial deduction of their mechanical response. For this reason, the study is based on the development of an analytical model; this drives the synthesis of a surrogate pseudo-rigid model based on an epicycloidal arrangement requiring a single degree of freedom. The design equations for the general applications are deduced in the paper, in a form ready to use for both analyses and synthesis problems. Both analytical model and pseudo-rigid model have been verified through numerical simulations.