# Triangular-Shaped 5-DOF Piezoelectric Robot for Optical Lens Positioning
## 2 Design and Operation Principle of Robot  
The robot consists of a triangular-shaped passive layer made from stainless steel and a piezo ceramic ring glued on top of the passive layer (Figure 1). The passive layer consists of three trapezoidal cantilevers joined in the center of the structure. Piezo ceramic ring is made from hard type ceramic PIC181 (PI Ceramics, Lederhose, Germany). The top electrode of the piezo ceramic ring is divided into six equal segments that are used to control planar and angular motions. The ring is in contact with the passive layer only at the bases of trapezoidal cantilevers, while the other three segments of the piezo ceramic ring are free from the passive layer. In addition, each trapezoidal cantilever has cuts near the piezo ceramic ring that were made to reduce the vibrations coupling between different segments of the piezo ceramic ring and trapezoidal cantilever. Alumina oxide semispherical contacts are glued at the end of each trapezoidal cantilever and are in contact with the plane used for the planar locomotion of the robot. Three additional semispherical contacts are placed on the top of the ring and are used to place the payload on the robot and rotate it. Vibrations of the particular contact are excited by the corresponding section of the piezoceramic ring. The geometrical parameters of the robot are shown in Figure 2. The volume of the presented piezoelectric robot is 2.69 cm\({}^{3}\), while the total weight without payload is 12.92 g. The robot occupies an area of 310 mm\({}^{2}\). The payload can have a spherical or flat surface. The payload is moved in the plane when it has a flat contacting surface, and rotated when the surface is spherical. Later in this paper, the only rotational option of the spherical payload will be analyzed. The planar locomotion of the robot is limited only by the size of the manipulation surface. Figure 1: Design of the piezoelectric robot; (**a**)—assembled view of the robot; (**b**)—exploded view of the robot; 1—passive layer; 2—piezo ceramic ring with the segmented top electrode; 3—alumina oxide contacts placed at ends of trapezoidal cantilevers; 4—alumina oxide contacts placed on top of the piezoceramic ring; 5—payload. The operation principle of the robot is based on the excitation of the third radial vibration mode of the ring and the first bending mode of the trapezoidal-shaped cantilever. The radial mode of the ring is used to induce rotation of the payload, while the bending mode of the cantilever generates planar locomotion of the robot. Control of planar and rotational motions can be implemented using two digitally controlled switch boxes and two harmonic electric signals where the first signal is used to obtain planar motion and the second rotational motion. Excitation schematics of the robot are given in Figure 3.  
Planar locomotion of the robot is obtained when a harmonic signal with a frequency of the first bending mode of the trapezoidal cantilever is applied to segment L\({}_{\text{0 deg}}\), L\({}_{\text{120 deg}}\) or L\({}_{\text{240 deg}}\). The selection of the segment depends on the needed motion direction of the robot. Contraction and extraction of the ring segment excite the first bending mode of trapezoidal cantilever, and the semispherical contact impacts the manipulation surface and in this way generates planar locomotion of robot. Reverse motion is obtained by applying the same harmonic signal to the other two segments of the piezoceramic ring. Because of the different stiffness obtained via uneven contact between piezo ceramic ring and cuts made at the passive layer, vibrations of contact generated by an activated segment have low coupling with the vibrations of other semispherical contacts. Therefore, the vibrations of these contacts have a minor effect on the needed direction of planar or angular motions.