Elliptical-arc-fillet flexure hinges: Toward a generalized model for commonly used flexure hinges

Flexure hinges have been used to produce frictionless and backlashless transmissions in a variety of precision mechanisms. Although there are many types of flexure hinges available, designers often chose a single type of flexure hinge (e.g., circular flexure hinges) without considering others in the design of flexure-based mechanisms. This is because the analytical equations are unique to each kind of flexure hinge. This work offers a solution to this problem in the form of a generalized flexure hinge model. We propose a new class of flexure hinges, namely, elliptical-arc-fillet flexure hinges, which brings elliptical arc, circular-arc-fillet, elliptical-fillet, elliptical, circular, circular-fillet, and right-circular flexure hinges together under one set of equations. The closed-form equations for all the elements in the compliance and precision matrices of elliptical-arc-fillet flexure hinges have been derived. The analytical results are within 10 percent error compared to the finite element results and within 8 percent error compared to the experimental results. The equations for evaluating the strain energy and stress level for elliptical-arc-fillet flexure hinges are also provided. This model can be used as a complementary model for the generalized model for conic flexure hinges.