Out-of-Plane (Diaphragm) Compliances of Circular-Axis Notch Flexible Hinges with Midpoint Radial Symmetry

Abstract

A small-displacement analytical model is proposed for the out-of-plane compliances of notch flexure hinges with circular longitudinal axis and midpoint radial symmetry that function as monolithic joints in flexible mechanisms. The hinges are constructed from several serially connected segments with small and constant out-of-plane width, variable in-plane thickness, and are subjected to coupled bending and torsion. The six compliances of a symmetric notch hinge are obtained as linear combinations of compliances defining the segments that form one half of the full flexible hinge. The general analytical model is applied to the circular-axis, right circularly corner-filleted hinge design whose compliances are validated by finite element simulation. A comparison is performed between the out-of-plane and the in-plane compliances of this flexure hinge. The right circularly corner-filleted configuration is also compared to the circular-axis, constant-thickness flexure hinge with respect to the out-of-plane static response.