**2.6 Finite element analysis**

Before the experimental verification, it is necessary to ensure that the flexure hinge driving mechanism can achieve the desired displacement amplification effect, thus the finite element analysis is carried out. AL7075 is selected as the material of the driving mechanism, the Young's modulus, density and Poisson's ratio of this material are 7.17 � <sup>10</sup><sup>4</sup> MPa, 2810 kg/m<sup>3</sup> and 0.33, respectively. Take the contact point *<sup>P</sup>* at the top of the driving mechanism as the reference, and the two holes are defined as fixed constraints. The elongation of the piezoelectric stack is set to 10 *μ*m to simulate the deformation of piezoelectric elements. The static simulation deformation is displayed in **Figure 8a**, the total displacement from point *P* to *P*<sup>0</sup> is 52.415 *μ*m, the displacement in the positive direction of *y*-axis direction is 10.006 *μ*m, and the displacement along the negative direction of the *x*-axis direction is 51.195 *μ*m. Then the analysis of equivalent stress is shown in **Figure 8b**, the maximum equivalent stress of the driving mechanism is 128.68 MPa near the point *Q*, which is less than the allowable stress of AL7075 to ensure the safe operation of the actuator. The static simulation results verify the feasibility and reliability of the flexure hinge driving mechanism. Further, the first-order mode of the mechanism is shown in **Figure 8c**. To ensure the operation stability of the actuator, the driving frequency should be lower than this value as much as possible.
