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.

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.

Compliant amplification mechanisms amplify input displacement in the desired output direction. However, owing to structural design, parasitic motion can easily be produced in an unexpected direction. The parasitic motion has a negative effect on the motion accuracy of the mechanism. To solve this problem, a topology optimization method for compliant amplification mechanisms with low parasitic displacement was proposed. Based on the variable density topology optimization method, the topology optimization model of the compliant amplification mechanism was established with the goal of increasing the output displacement and reducing the parasitic displacement. Volume ratio was set as constraint condition. The optimization criterion (OC) method were used to solve the problem and topology optimized amplification mechanisms were obtained. Simultaneously, the configuration characteristics and displacement amplification ratios of the mechanism under different virtual spring stiffnesses were compared. To verify the validity of the method, the performance of the topology optimized amplification mechanism and the typical amplification mechanism were compared using finite element simulation. The displacement amplification ratio is 5.95 and 3.17, and the relative parasitic displacement is 0.6% and 10.27%, respectively. Finally, the performance of the topology optimized amplification mechanism and the typical amplification mechanism was verified by experiments. The displacement amplification ratio is 5.72 and 3.06, and the relative parasitic displacement is 0.95% and 10.64%, respectively. Simulation and experimental results show that the topology optimized amplification mechanism has a larger displacement amplification ratio and a lower parasitic displacement, which verifies the validity of this method.

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