Key features of flexure hinges used as rotational joints: Transition from concentrated to distributed compliances

This article is supposed to serve as a guide for the design of flexure hinges that act as rotational joints. Firstly, flexure hinges with concentrated and distributed compliance are reviewed. They can be modeled by linear beam theories or by the theory of Elastica, respectively. Secondly, the transition between these limit cases is investigated by finite element methods (FEM). A planar symmetric flexure hinge with a circular notch serves as an exemplary geometry. By extending the notch the compliance is distributed. The deflection curves and the kinetics of desired and parasitic motions are chosen as key features to be studied. The corresponding results are compressed into a pseudo-rigid-body model (PRBM) approximation for a range of geometries. It turned out that the concentrated compliance matches best with an ideal rotational joint, but even for small displacements large stresses occur so that its range of operation is small. Distributing the compliance increases the range of operation, however stiffness within the task space decreases dramatically so that the design of a flexure hinge becomes a tradeoff between the two concurring goals large stiffness and large range of operation.