Tractable model for concave flexure hinges

In this article we prove that approximate solutions previously developed by us, with inverse conformal mapping, for concave flexure notch hinges rotational compliance in correct applications are accurate enough in comparison with the more complicated "precision" solutions for the conic profiles based on the integration of differential equations, finite element model, and experimental data at uncertainty within 10% or less. This is also true with the developed, in this article, simple computer aided evaluation of the approximating circles and their shift to contiguity even without its analytical expression and estimation of the hinge rotation instantaneous center position on this basis. (C) 2011 American Institute of Physics. [doi:10.1063/1.3505114]