Compliance and precision modeling of general notch flexure hinges using a discrete-beam transfer matrix

Compliance and precision are two key aspects in designing flexure hinges for use in compliant mechanisms. A generalized method with the finite-discrete idea and beam transfer matrix is developed for quickly predicting the kinetostatic behaviors of single and multiple-axis notch flexure hinges. The transfer matrix of Timoshenko beams explicitly including the shear deformation effect is derived in a concise form of Taylor series expansion. The compliance and rotational precision matrices of general notch flexure hinges are then derived targeting for arbitrary cutout profiles with a step-by-step modeling procedure. It is easy to operate for comparing and synthesizing different flexure hinges within a unified modeling framework. All a designer has to do is to prepare the concerned profile function without being caught into the laborious and even unsolvable derivation of mechanics. Several groups of single and multiple-axis notch flexure hinges are adopted to verify the feasibility of the presented approach by comparing with the numerical and experimental results available in literature. The comparative results indicate the high prediction accuracy and easy operation of the proposed approach for a wide applicability of complex notch flexure hinges.