Analysis and design of a cartwheel-type flexure hinge

Abstract

This paper presents an analytic model of cartwheel flexure. 6-DOF (degrees of freedom) stiffness equations for cartwheel flexure are derived and verified by comparing the model's predictions with FEM (finite element method) simulations and experiments. The model prediction accuracy relative to FEM simulations is found to be satisfactory, with errors of less than 10%. The deviation of the model's prediction from the experiments’ results is slightly higher because of body deformations and manufacturing errors. The effects of manufacturing errors on the model accuracy are analyzed, with the results indicating that the first mode is greatly affected by the manufacturing errors, while the thickness variation of the cartwheel flexure hinge has the largest effect on the model prediction accuracy. The cartwheel flexure hinge is evaluated in terms of the motion range, stiffness and stiffness ratio and compared with the conventional right circular hinge to confirm the appropriateness of the cartwheel flexure hinge as a large displacement flexure joint. Finally, an example of cartwheel flexure design is presented to show that the analytic stiffness model can provide a set of optimized design parameters in less time than FEM simulations.