A generalized model for conic flexure hinges.

Flexure hinges have been used to produce frictionless and backlashless transmission in a variety of precision instruments. Many kinds of flexure profile were proposed during the past decade. The present work brings elliptical arc, parabolic, and hyperbolic profiles together by proposing a generalized conic flexure hinge model. By utilizing the generalized equation for conic curves in polar coordinates, all the elements in the compliance and precision matrices for conic flexure hinges are deduced. These equations were verified by finite element analysis and experimentation. The analytical results are within 11% error compared to the finite element results and within 6% error compared to the experimental results.