Compliant four-bar linkage synthesis with second-order flexure hinge approximation

The paper discusses an original methodology for addressing the synthesis of a compliant four-bar mechanism for prescribed finite coupler motion. The proposed method is based on the modelling of the four flexure hinges by using a planetary arrangement (two external cylinders rolling without slipping one on the other) able to accurately reproduce the relative motion between connected parts for a large range of deformation. The adopted approach allows a trade-off between accuracy and limited complexity in deducing the closure loop equations of the whole mechanism. The methodology is applied on a test case of a four-bar compliant linkage whose coupler occupies a prescribed set of finitely separated positions. The synthesized linkage has been analysed both with a pseudo-rigid model (built with mid-sized hinges) and a nonlinear finite element model.