# Triangular-Shaped 5-DOF Piezoelectric Robot for Optical Lens Positioning
## 4 Experimental Investigation of the Robot  
The prototype of the robot was made to perform experimental investigations. The geometrical and physical characteristics of the robot were set in accordance with the numerical model (Figure 13). The goal of the investigation was to validate the operation of the robot and measure the electrical and dynamic characteristics. Figure 12: Motion trajectories of contact points: (**a**)—motion trajectory of contact point located at the tip of trapezoidal cantilever driven by segment L\({}_{\text{ddeg}}\); (**b**)—motion trajectory of contact point located on top of R\({}_{\text{ddeg}}\) segment. Impedance-frequency characteristics were measured to find resonant frequencies of the robot. Impedance analyzer SinPhase 16777k (SinPhase, Modling, Austria) was used. The robot was placed on a soft surface and measurements were made without payload. Firstly, the impedance analyzer was connected to the L\({}_{\text{ddeg}}\) segment, while other segments were set to open-circuit condition. The same measurements proceeded using segment R\({}_{\text{ddeg}}\). The results are shown in Figure 14. Resonance frequencies of the first bending mode of the trapezoidal cantilever and the third radial mode of the piezo ceramic ring were obtained at the frequencies of 14.55 kHz and 93.15 kHz, respectively. The differences between calculated and measured resonance frequencies are 1.44 kHz or 5.1% for the first bending mode and 2.36 kHz or 2.47% for the radial mode. Mismatch of the resonant frequencies comes because of the calculation errors, differences in boundary conditions during calculations and measurements, and slight differences in material characteristics. On the other hand, differences do not exceed 5%. Effective coupling factor \(k_{\textit{eff}}\) was calculated for both modes. The first bending mode of the trapezoidal cantilever has \(k_{\textit{eff}}\) = 0.056, while for the radial mode \(k_{\textit{eff}}\) = 0.071. Compared to the calculated values, the difference does not exceed 8.2%. The next step of the experimental investigation was to measure the planar and angular speed of the robot. Supplementary Materials Videos S1 and S2 represents robot operation. The experimental setup was built for this purpose (Figure 15). The experimental setup included a computer, a function generator WW5064 (Tabor Electronics, Nesher, Israel), a power amplifier PD200X4 (Piezo Drive, Shortland, Australia), oscilloscope DL2000 (Yokogawa, Tokyo, Japan), a displacement sensor ILD 2300 (Micro-Epsilon, Ortenburg, Germany), tachometer DT210 (Nidec-Shimpo, Tokyo, Japan) and self-made switch boxes. Figure 13: Prototype of the robot: (**a**)—side view with payload; (**b**)—top view without payload; (**c**)—side view without payload. Figure 14: Impedance of the robot in the frequency domain for the first bending mode of the trapezoidal cantilever (**a**) and the third radial mode of the piezoceramic ring (**b**). Figure 15: Schematics of the experimental setup; 1—computer; 2—signal generator with two independent channels; 3—power amplifier; 4—oscilloscope; 5—laser displacement sensor for planar motion measurements; 6—the prototype of the robot; 7—two-channel switch box; 8—tachometer for measurements of angular motion. Planar motion characteristics were measured when segment L\({}_{\text{\text{\text{\text{deg}}}}}\) was affected by an excitation signal in the range from 80 V\({}_{\text{\text{P-p}}}\) to 200 V\({}_{\text{\text{P-p}}}\) with an increment of 20 V\({}_{\text{\text{p-p}}}\). Segments R\({}_{\text{\text{\text{deg}}}}\)-R\({}_{\text{\text{\text{240 deg}}}}\) and L\({}_{\text{\text{\text{120 deg}}}}\), L\({}_{\text{\text{\text{240 deg}}}}\) were set to open-circuit condition for this investigation. In addition, the investigation was made when different payloads were applied to the robot, i.e., 6.8 g, 12.6 g, and 25.1 g. Experiments were made by placing the robot on glass.