Design calculations for flexure hinges

This article presents design equations for calculating the compliance or spring rate of rectangular single-axis hinges and right circular hinges. The design equations are the result of an exact deduction and are concise in their expressions, so it is more convenient to use them in calculating and analyzing flexure hinges and flexure hinge mechanisms. Comparing these with the exact design equations of Paros and Weisboro [Mach. Des. 37, 151 (1965)], it is suggested that the equations of this article are effective. Limitations of the simplified equations of Paros and Weisboro and the approximate equation of Smith et al. [J. Phys E 20, 977 (1987)] are discussed. While calculating the compliance of flexure hinges, several important points are mentioned.