Design calculation and analysis of elliptical flexure hinges

Based on the bending theory of beam with variable cross-section in mechanics of materials, a novel integral formula for elliptical flexure hinge is deduced by introducing centrifugal angle as the integral variable. By defining an intermediate parameter in the integral formula, a more concise analytical equation of rotation compliance of elliptical flexure hinges is presented, thus avoiding time-consuming numerical integrals. The relationships among the rotation compliance of elliptical flexure hinges, the shapes and sizes of elliptical notches, and the minimum hinge thickness of them are analyzed. A number of elliptical flexure hinges with different shapes are analyzed with ANSYS finite element software. The results of the finite element analysis and the analytical ones are in good agreement, which indicates that the analytical equations are correct.