## 3 Experimental Validation of the Mechanical Amplifier
### Comparison of the Experimental and FEA Results  
The area where the piezoelectric actuator should operate cannot be subjected to external loading because of geometric constraints. Therefore, an inverted testing method  
Figure 11: (**a**) Dots network caliber user for video calibration; (**b**) the painted probe; (**c**) 3D-printed fixture and the loading ball terminal; and (**d**) selected measurement area using the Aramis software. has been implemented. This approach involves applying a variable force from the output point of the mechanical amplifier, specifically from the upper arm toward the lower arm. The aim of the test has been to correlate its results with the FEA model of the amplification mechanism. Thus, the scope is to determine the force-deformation relationship, as well as, subsequently, the equivalent stiffness of the structure. Attempts to apply a force between the two inner arms to simulate the action of a piezo stack actuator have faced two challenges related to the geometry of the testing part, which interfered with the mechanical amplifier. First, employing a U-shaped test probe for symmetric loading (one U-shape per arm) blocked the view of the 3D Aramis camera system, and therefore the measurements. Second, when using L-shaped test parts for the inner arms, it has become necessary to design an optimized geometry that could provide a stiffness that is at least 10 times higher than that of the tested mechanism, while maintaining an optimal FOV for the 3D camera system. For the entire assembly (consisting of mechanism plus piezo stack), it was not possible to obtain a force-displacement characteristic. Therefore, we determined only the amplification ratio, which has remained consistent with our experimental test results. Finally, the compliant mechanical amplifier performs similarly for both upper loading on the upper arm and for inner loading on the inner arm. Considering how the testing is performed in real-life conditions, the same conditions were applied in the FEA environment in order to ensure a correct and consistent analysis. An important factor for this has been the exact position of the applied force in the experimental test. This position was measured based on the video footage captured by one of the cameras and was determined to be equal to 36 mm. The conducted FEA simulation utilized the Inventor software (Autodesk, San Francisco, CA, USA). It replicated real-life conditions and implied an applied force that matches the one measured experimentally using the load cells of the machine (i.e., 12 N). The obtained FEA results are presented in parallel to the 12 MP Camera Aramis system experimental results in Figure 12. The results for the two considered key points have been closely aligned. Thus, in Figure 12 one observes that at the theoretical input of the mechanical amplifier (i.e., point 2), the obtained displacement is equal to \(-6.51\)m in the FEA and \(-7\)m in the experiments, while at the tip of the upper arm, the displacement was \(-93.14\)m in the FEA and \(-93\)m in the experiments. Only vertical displacements have been considered, as this is the primary parameter of interest for this application. Therefore, considering the maximum applied force, the error for the first test (i.e., using half of the amplifier) is \(7.52\%\) at the considered point 1 and less than 1% at point 2 of the amplifier. This test confirms the good correlation between the physically manufactured part and the 3D model. It ensured that the actual amplification ratio obtained was \(14.3\):1 for half of the amplifier. These results are also important for future correlations to different mathematical models. Taking a closer look at the Y axis, there is a significant displacement that should not exist. We must highlight that the tests have been conducted on the same sample, using identical fixing and loading tools, as well as the same loading machine in order to ensure consistency. Also, the camera system acquisition has been initiated after the preload procedure.