Closed-form compliance equations of filleted V-shaped flexure hinges for compliant mechanism design

This paper presents the closed-form compliance equations for the filleted V-shaped flexure hinges. The in-plane and out-of-plane compliances of the flexure hinges are developed based on the Castigliano's second theorem. The accuracy of motion, denoted by the midpoint compliance of the flexure hinges, is also derived for optimized geometric design. The influences of the geometric parameters on the characteristics of the flexure hinges are investigated. It is noted that the filleted V-shaped flexure hinges have diverse ranges of compliance corresponding to different filleted radius R and angle θ. These types of hinges can provide both higher and lower stiffnesses than circular flexure hinges. This makes filleted V-shaped flexure hinges very useful for wide potential applications with different requirements. The finite element analysis is used to verify the established closed-form compliance equations for these filleted V-shaped flexure hinges.