## 4 Experimental Investigation of the Actuator  
The prototype of the actuator was made to perform experimental investigations (Figure 11). The geometric and physical characteristics of the prototype correspond to the characteristics used for numerical investigations. Firstly, impedance--frequency characteristics of the actuator were measured using SinPhase 16777k (SinPhase, Modling, Austria) impedance analyzer. The actuator was placed on the foam, and measurements were performed without payload. Firstly, the impedance analyzer was connected to Planar\({}_{1}\), while other segments were set to open circuit condition. The same measurement was performed while Rotary\({}_{1}\) was connected to the analyzer. The results are shown in Figure 12.  
Figure 10: Contact points trajectories when segment Planar\({}_{1}\) (**a**) and segment Rotary\({}_{1}\) (**b**) is exited by the voltage of 200 V\({}_{\text{P-P}}\). It can be seen that the resonant frequency of the actuator was obtained at frequencies of 14.67 kHz and 46.62 kHz. The differences between calculated and measured frequencies do not exceed 1.5% for a radial mode of piezoceramic ring. On the other hand, the difference between calculated and measured resonant frequencies of the first radial mode of actuator supports is 3.34 kHz or 18.5%. The difference mainly comes because of different mechanical boundary conditions used during measurements and manufacturing errors. The quality factor of the actuator when it vibrates at operating frequencies is Q\({}_{\text{planar}}\) = 983.14; Q\({}_{\text{rotary}}\) = 1014.5. The difference between impedance values at the resonant and anti-resonant frequencies is up to 260 \(\Omega\). It is mainly affected by the specific design of the actuator. Dynamic characteristics of the actuator were measured at different excitation conditions. The experimental setup was built and is shown in Figure 13. The experimental setup consisted of a computer, a function generator WW5064 (Tabor Electronics, Nesher,  
Figure 11: Prototype of the actuator with spherical payload (**a**) and without payload (**b**). Figure 12: Measured impedance—frequency characteristics of the actuator in the frequency range of 14.25–15.00 kHz (**a**) and 46.0–48.0 kHz (**b**). Israel), a power amplifier PX-200 (Piezo Drive, Shortland, Australia), oscilloscope DL2000 (Yokogawa, Tokyo, Japan), a displacement sensor ILD 2300 (Micro-Epsilon, Ortenburg, Germany), tachometer DT210 (Nidec-Shimpo, Nagaokayo-City, Japan) and a self-made switch box. The actuator was placed on the flat glass surface, and the planar velocity of the actuator was measured. Excitation voltage varied from 80 V\({}_{\text{P-P}}\) to 200 V\({}_{\text{P-P}}\), and a payload of 12.6 g, 25.1 g, and 55.68 g was applied. Firstly, measurements were made while the electrode located in segment Planar\({}_{1}\) was excited while other electrodes were set to open-circuit conditions. The payload of the actuator was changed manually by replacing the spherical payload. Results of the measurement are shown in Figure 14.  
Figure 14: The measured linear velocity of the actuator at the different preloads when segment Planar\({}_{1}\) of the actuator is excited. Figure 13: Schematics of the experimental setup: 1—computer; 2—signal generator; 3—power amplifier; 4—oscilloscope; 5—displacement sensor; 6—tachometer; 7—switch box for planar motion control; 8—switch box for angular motion control; 9—the prototype of the actuator. The lowest and highest velocities of the actuator were obtained at 80 V\({}_{\text{P-p}}\) and 200 V\({}_{\text{P-p}}\), respectively. The lowest velocity values reached 3.8 mm/s at 12.6 g, 5.4 mm/s at 25.1 g and 8.8 mm/s at 55.68 g, while the highest reached 6.9 mm/s, 12.3 mm/s and 19.8 mm/s, respectively. It can be noted that velocity characteristics are almost linear increases when voltage is increasing. Also, a higher preload value causes higher velocity because of the increment of friction force between surface and contact spheres.