## 3 Experimental Validation of the Mechanical Amplifier
### Mechanical Subassembly Testing  
A comprehensive mathematical model of the assembly must account for the elasticity, inertia, and damping of the piezoelectric actuator and its associated compliant mechanism. Also, the elasticity and inertia of the spherical joint (metal wire) and of the central compliant  
Figure 17: Dynamic FEA of the mechanical amplifier. joint must be considered, as well. As demonstrated in Section 2, the simplified kinematic model of the device exhibits nonlinearity. The inclusion of these additional elasticities is expected to result in a highly complex global mathematical model. This makes developing an efficient control law a challenge. To ensure a robust demonstration of the principle, a strategic decision was made to oversize the actuators relative to the stiffness of the spherical and central joints. This choice is strongly justified by the following key observations: (i) the maximum blocking force of the actuators, as specified in their catalog, is equal to 2000 N; (ii) the expected force at the actuator output is equal to 1000 N, which results in approximately 100 N at the amplifier output; (iii) the stiffness of the upper section, consisting of the central joint, mobile platform, and spherical joints, is extremely low, which means that the force required for the desired displacement is significantly lower than the force generated by the actuator. This assumption is going to be validated further on through the final FEA testing. As a result, it can be confidently stated that the actuator and the compliant mechanism operate with an optimal load, allowing for neglecting the spherical and central joints in the primary analysis. However, in order to have rigorous results, a holistic approach to the stiffness of the system is also proposed. Thus, in order to further refine the stiffness characterization, another experimental test is conducted with the piezo actuator mounted on the amplifier. This assessment of the rigidity of the entire system was made using a motion analysis test that was conducted on the actuation subassembly with the piezoelectric actuator mounted on the mechanical amplifier. This test is important for determining both the maximum stroke of the actuator and the trajectory of the key points of interest, labeled as 1 and 2 in Figure 16. These points must be utilized further in the global system simulation to evaluate the mechanical stress occurring at the spherical joint. Also, in order to verify the measurement accuracy, sequential measurements were performed using the inductive displacement transducer across all three spatial directions. The piezoelectric actuator was controlled using a ramped voltage signal of 0-10-0 V, with a variation rate of 0.1 V/s. The control signal was generated using a MyRIO-1950 development board, with the control program implemented in LabVIEW. Then, the signal was amplified using an E472.20 high-voltage amplifier (100:1 ratio, 1000 V, 500 W) in order to drive the actuator. The Aramis video capture system has limitations in terms of a restricted area of analysis. Also, in order to perform analyses on the entire system, this should be disassembled, prepared, and reassembled for testing (including pattern painting for tracking--Figure 11a). To avoid these issues, the test was conducted on one subassembly only. Also, one must point out that the 3 DOF system was assembled using cyanoacrylate adhesive in order to maintain its structural integrity; therefore, it would have been impossible to disassemble it without producing significant damage. It is worth mentioning that constructive limitations of the utilized load measuring machine include the requirement to maintain collinear measurement samples while the part is rotating. Therefore, it is not possible to determine directly the force-deformation characteristic for the entire system. Moreover, inserting a traction tool between points 1 and 2 would introduce a bending force on the load cell, rendering the force measurements unreliable and unusable.