CLOSED-FORM TORSIONAL COMPLIANCE OF TWO-AXIS FLEXURE HINGES

This paper focuses on closed-form equations of torsional compliance for two-axis flexure hinges with variable rectangular cross-section (VRC) which can serve as the alternatives of flexure spherical hinges in flexure-based spatial compliant mechanisms. To obtain high-accuracy solutions of torsional compliance of VRC flexure hinges, different equations of torsional moment of inertia for constant rectangular cross-section (CRC) beams are discussed. The equations of torsional compliance of a commonly used two-axis flexure hinge with elliptical-arc notches are formulated by introducing several integral factors. The accuracy of different equations of torsional compliance is determined based on finite element analysis to provide a better choice for designers. The ratio of torsional compliance between two-axis flexure hinge and flexure spherical hinge with the identical notch curve is analysed and the result reveals that the former can obtain 70% torsional deformation of the latter. Finally, several numerical simulations with respect to geometric parameters are performed.