Theoretical, numerical, and experimental investigation on the compliance and natural frequency of sinusoidal flexure hinges

Abstract

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.