Elasto-kinematic comparison of flexure hinges undergoing large displacement

The design of precision compliant mechanisms requires the assessment of the elasto-kinematic characteristics of the flexure hinges connecting bulky parts. Due to geometrical nonlinearities, a comprehensive analysis requires the functional properties to be evaluated within the feasible range of relative displacement. This investigation proposes the use of kinematic invariants to characterize the main features of a compliant mechanism. In particular, this paper offers the comparison of five common flexure hinges in terms of the relative motion kinematic invariants. By using the dynamic spline formulation, for each hinge typology, a flexible multibody model is developed to obtain the fixed and moving centrodes and the diameter of the inflection circle of the relative motion. In order to fully characterize the elasto-kinematic behaviour, the simulative models are also used to compute the equivalent stiffness as a function of the rotation angle. The results show that the differences among the various types of hinges is relevant in terms of both kinematic and compliance characteristics. The findings and the methodology herein outlined are new tools for the optimal design and synthesis of flexure joints.