Generalized model and performance analysis of two-axis flexure hinges based on quadratic rational Bezier curve

This article presents a generalized model of two-axis flexure hinges based on quadratic rational Bezier curve. The generalized closed-form compliance equations are derived based on the virtual work theory and the superposition relationship of the deformation. Then, how to determine the number of sensitive axes, the location of the primary and secondary sensitive axes, and the configuration of the notch profile are discussed. There are 20 types of notch profiles derived from single or mixed, symmetrical or asymmetrical curves. And, the correctness of the compliance equations is verified by finite-element analysis. The maximum relative error does not exceed 10%. Finally, the precision of rotation, the maximum stress, and the effect of structural parameters on the compliance are analyzed. The results show that for two-axis flexure hinges with a flush single curve notch profile, the proximity of the center of rotation to the load end does not significantly affect the axial compliance as well as the torsional compliance. For hybrid two-axis flexure hinges with symmetric structure, the ability to maintain the center of rotation under lateral forces is better than that under the same torque. The proposed generalized model provides a reference for the design of spatial compliant mechanisms.