## 3 Experimental Validation of the Mechanical Amplifier
### Comparison of the Experimental and FEA Results
Supplementary, in order to ensure the accuracy of the 3D camera system, an inductive displacement transducer Mahr P2004 (Mahr Gmbh, Gottingen, Germany) was integrated in parallel into the setup. This transducer was connected to the Mahr Milliron 1202D signal measurement and conditioning system (Mahr Gmbh, Gottingen, Germany). Thus, it offered a measurement accuracy of \(0.01\)m within a range of \(\pm 20\)m. The highest value obtained for the Y-axis displacement of the part was \(2.26\)m when measured at the fixing base. This means that the system is rigid enough to perform the test. Another measurement was performed at the upper arm level of the tested part. The Y-axis displacement increased to 5.06 \(\upmu\)m, which means that there is a supplemental 3 \(\upmu\)m deviation. The main causes of these displacements are: (i) residual misalignments in the assembly that resulted in unintended lateral forces during compression; (ii) a low preload force; (iii) structural asymmetries in the compliant mechanism introduced minor deviations during actuation (specifically, the circular joints of the compliant mechanism were not perfectly parallel, thus leading to a small deviation); (iv) regarding the Aramis system, the Y-strain measurement is generally less sensitive compared to an in-plane strain because of the limits of the camera resolution and of because of perspective errors. Regarding the latter aspect, because DIC captures surface deformation, the Y-axis strain does not accurately represent internal material behavior unless it is supplemented with additional measurement methods, such as the inductive transducer utilized in this case. Additionally, out-of-plane measurements are inherently more prone to noise, especially where complex geometries (such as one of the developed systems) are involved. Despite these potential shortcomings, after repeating the test, the results remained consistent, thus confirming the validity of the experimental setup. The mean values of the Y-axis displacements are quite stable (i.e., around 40 \(\upmu\)m), and they have an offset caused by the preload condition (Figure 13). Because of the measurement approach (i.e., using the Aramis 12 MP camera system), the Y-axis values are noisy, therefore they are not considered further on for the discussion of results. However, the X and Z in-plane values are in the \(\pm 1\)\(\upmu\)m precision class, considering the inductive transducer as a reference measuring instrument. Figure 12: Displacement results for FEA (**a**) and for the experimental analysis (**b**), where point 2 is the maximum displacement obtained for the applied force and point 1 determines the required theoretical piezo stack displacement. The next step in validating the entire FEA model involved a comprehensive test of the mechanical amplifier. Two compression tests were performed, using both a ball and a roller terminal (Figure 14). The results of these tests are shown in Figure 15. It can be observed that when the part is deformed using the roller terminal, a transverse displacement occurs along the Y-axis. This displacement should not be present if the contact line of the roller was in the same plane as the compression surface of the upper arm. However, this misalignment exists, and it induces a transverse displacement of the part of approximately 1 mm. This is unacceptable for performing comparisons to the FEA. For this reason, only the ball compression test was considered for comparative analysis, as its contact with the compression surface can be considered punctiform, ensuring a more localized and precise interaction. Figure 14: The compression terminal equipped with a roller (**a**) and with a ball (**b**). Figure 13: Measured values during experimental tests for the Y-axis strains (at points 1, 2, and at the fixing base).