Analysis of the displacement amplification ratio of bridge-type flexure hinge

The bridge-type flexure hinge is a classic displacement amplification mechanism. The existing models of theoretic displacement amplification ratio of bridge-type flexure hinges are not perfect. This makes it very difficult to design and manufacture a satisfactory structure using these models. Kinematic theory was used to analyze the ideal displacement amplification ratio of a bridge-type flexure hinge in this paper, and the flexure hinge was regarded as a pure multi-rigid body with ideal pivots. Elastic beam theory was used to analyze the theoretic displacement amplification ratio when considering the translational and rotational stiffness of the flexure pivots. The model of theoretic displacement amplification ratio explains why the bridge-type displacement amplification mechanism has an amplification ratio extremum and where the threshold is. The finite element method was used for comparison with the mathematical model, and similar results were obtained. Finally, the finite element method was used to analyze the shape mode of the structure. The result showed that increasing the amplification ratio by decreasing the thickness of the flexure pivots led to a decrease in the mode shape frequency of the bridge-type structure. Thus, redesigning of the structure was needed to solve the problem.