## 3 Experimental Validation of the Mechanical Amplifier
### Setup for the Experimental Static Analysis  
Two experimental tests were performed and are presented in the following. The first test was for half of the mechanism. The scope was to determine the amplification ratio for half of the amplifier. The second test was performed with the scope to validate the 3D model for the entire mechanism and thus, to determine the error between the physical and theoretical models. In order to validate the amplification performance of the mechanism, an in-house developed experimental setup was employed (Figure 10). It integrates two testing systems: the Zwick-Roell Z010 testing machine (ZwickRoell, Ulm, Germany) with two 10 kN and 5 kN load cells using the HBM MGC AB 12 Amplifier (Hottinger Bruel & Kjaer, Darmstadt, Germany), along with the ARAMIS 12 MP camera measuring system (ZEISS AG, Oberkochen, Germany), equipped with an appropriate blue lighting system. The testing procedure involved placing the sample in the lower grip of the Zwick Roell loading machine on a custom support specifically designed for the tested part. A rapid prototyping technique was utilized to develop this support. The loading machine enables a controlled displacement with micrometric precision of the upper grip, where compression tools (that were specially designed for this test) were mounted. In series with these compression tools (mounted on the upper grip), load cells were integrated to measure the applied force. The upper grip moves downward in a controlled manner, and the machine records the force applied throughout the test. Figure 10: Experimental stand for the static deformation analysis of the mechanical amplifier. Figure 9: Measurement of the geometry for the spherical joint (**a**), for the centering hemisphere (**b**), and for the fillet radius generated by the wire-cutting process in the area of right angles (**c**). In order to enhance the measurement accuracy and map the deformation field of the tested component, the Aramis video camera system was integrated in parallel to the setup described above. This Aramis system captures video frames during the deformation process; based on the analysis area, it determines deformations at specific points of interest. The method is based on Digital Image Correlation (DIC), which primarily measures in-plane strains on the X and Y directions. However, with a 3D stereo-DIC setup, it is also possible to capture out-of-plane deformations and strains (i.e., in the Z direction). Therefore, it provides a comprehensive evaluation of the mechanical behavior of the sample. An evaluation using the Aramis camera systems must follow the following steps:  
1. _The setup of the 3D system_ requires two cameras that are positioned at different angles to capture stereoscopic images of the speckle pattern on the specimen. These cameras create a 3D reconstruction of the surface using triangulation. 2. _A precise calibration_ process using a known pattern, such as the checkerboard presented in Figure 11a. This phase is essential to determine the orientation of the camera and the spatial relationships. The calibration defines the transformation from 2D image coordinates to 3D world coordinates. 3. _Speckle pattern tracking_. The specimen is coated with a random speckle pattern, as shown in Figure 11b. As the sample is deformed, the Aramis DIC Zeiss Correlate software tracks the movement of these speckles in both images. The displacement fields are calculated in 3D (i.e., along the coordinates X, Y, and Z). 4. _Calculus of the strain_. The strain is derived from the gradients of the displacement field. In practice, because the DIC measures surface data, the Z-strain often refers to out-of-plane surface deformation gradients rather than through-thickness strain. 5. _Data analysis with ZEISS Correlate_, where one can visualize displacement and strain components, including out-of-plane (i.e., along the Z axis) deformations. The testing phases that are required in order to obtain accurate results imply the same constraints as in the FEA simulation, as shown in Figure 11c.