Closed-form compliance equations for power-function-shaped flexure hinge based on unit-load method

A new type of flexure hinge, called power-function-shaped flexure hinge, is presented in this paper. Based on the unit-load method, the closed-form compliance equations of the flexure hinge are derived, and the motion accuracy is investigated. These equations are verified through finite element analysis, which shows that the maximum error is less than 15%. Based on the compliance equations, numerical simulations are conducted to discuss the performance of the flexure hinge. The results indicate that, the stiffness of the power-function-shaped flexure hinge decreases as r increases, increases as β increases, and increases as t increases; the displacement along axis y is the dominant parasitic motion; and based on the same l, h and b, the power-function-shaped flexure hinge can rotate more accurately than circular flexure hinge with the same β and V-shaped flexure hinge with the same β and r. The equations obtained can be utilized to design the power-function-shaped flexure hinges, and can achieve higher motion accuracy than the commonly used circular flexure hinge and V-shaped flexure hinge.