This paper proposes a new type of flexure hinge: the sinc flexure hinge. A theoretical compliance and precision factor model of the sinc flexure hinge is developed based on the transfer matrix method. The finite element simulation is carried out using ANSYS Workbench. The error between the modeling and simulation results obtained is less than 7.0%. The influence of structural parameters on the compliance, precision factor, and compliance–precision ratio is analyzed. The results show that the compliance and precision are contradictory and that the minimum thickness has the most significant influence on performance. Compared with the other seven types of flexure hinges, the sinc flexure hinge delivers a good overall performance. Finally, a sinc flexure hinge is machined and its compliance is measured. The error between the experimental and theoretical values is less than 7.6%. Both the simulation and experimental results verify the effectiveness of the model.

To design a flexure hinge with high precision and high natural frequency, the sinusoidal flexure hinge is proposed in this article. First, the formulae for the compliance and precision factors of the hinge were derived based on the Euler–Bernoulli beam theory and the Gauss–Legendre quadrature formula. The natural frequency was also investigated based on the transfer matrix method. Compared with the simulation results of ANSYS Workbench, the results show that the modeling error is less than 6.7%. Second, the influence of structural parameters on compliance, precision factor, compliance precision ratio, and natural frequency was analyzed. The results show that compliance and precision are often contradictory, and the minimum thickness significantly influences the hinge's performance. Compared with conic flexure hinges in terms of compliance, precision, compliance precision ratios, and natural frequency, the sinusoidal flexure hinges have a better comprehensive performance. Finally, a flexure hinge was manufactured, and compliance was measured. The experimental results show that the error between the experimental value and the modeling value is 7.8%. Both simulation and experimental results verify the effectiveness of the sinusoidal flexure hinge model.

Flexure hinges are susceptible to fatigue damage under cyclic loading, resulting in performance degradation. This paper investigates the stiffness degradation of the right circular flexure hinges (RCFHs) under cyclic loading. Fatigue damage experiments are conducted to obtain the stiffness degradation curves, which can be divided into several stages by feature points. A relationship between feature lives and alternating stress amplitudes is established. A fatigue damage stiffness degradation piecewise curve model for RCFHs is proposed. The effect of notch stress concentration on fatigue damage is analyzed. Fatigue damage experiments under non-zero mean stress are conducted, and an equivalent fatigue stress equation is obtained. Finally, a generalized fatigue damage stiffness degradation model for RCFHs is developed, which establishes a relationship between residual stiffness and cycle number. On this basis, a fatigue damage performance modeling method for flexure hinge mechanisms is proposed. The fatigue damage performance of a compliant bridge mechanism was modeled and tested. The experimental results of input stiffness degradation are generally in agreement with the predicted results, which verify the validity of the method.