# Triangular-Shaped 5-DOF Piezoelectric Robot for Optical Lens Positioning
## 1 Introduction  
Today, modern optical instruments are widely used for industrial, measurement, laser, and manufacturing systems. An optical lens is one of the key components of the system that focuses or disperses a light beam. The position of the lens axis determines the focal point. Therefore, it is important to align the lens axis properly. Usually, optical lenses are fixed in the holders, so the centering of the lens axis to the holder axis determines the precision of the optical system. Proper position of the lens in the holder allows obtaining the focal point in the required position and to achieve required characteristics of the optical system. The assembly process of the lens and holder requires a mechanical system that can provide 2-DOF planar and 3-DOF angular motions to move the lens into the center of the holder and rotate is not that axis of the lens would coincide with the holder axis. Usually, the position of the lens in the holder is adjusted using a micrometric resolution positioning system with several actuators and motors, because most of the actuators and motors are single degrees of freedom devices [1; 2; 3]. Therefore, two or more devices must be combinedto obtain several degrees of freedom system. However, such compound systems have a complicated structural design, and motion control is implemented using complex driving and control electronics. Moreover, synchronization of several high-precision devices is a challenging task that affects the accuracy and reliability of the entire positioning or manipulation system [4; 5]. Therefore, multi-degree-of-freedom actuators and motors must be developed that will meet the requirements of the modern positioning systems. Usually, electromagnetic actuators and motors are employed to move payloads at different speeds and resolutions. However, these types of motor are unable to provide motion of several degrees of freedom. Also, the resolution of motion is limited [6]. Moreover, technological aspects limit the miniaturization of electromagnetic actuators and motors, while the electromagnetic field induces additional motion errors because of remnant magnetization [7; 8; 9; 10]. Therefore, scalable, high-resolution, several-degrees-of-freedom actuators and motors must be developed to overcome the aforementioned disadvantages, and piezoelectric systems are a reasonable option [6; 11; 12; 13; 14; 15; 16]. The state of the art of several degrees of freedom piezoelectric actuators, motors, and robots that provide planar or angular motion is given below in this section. [PERSON] et al. reported on a milli-size robot developed for planar motion [17]. The robot has three identical piezoelectric legs consisting of eight pieces of piezo ceramic. The planar motion of the robot is generated by imitating arthropod-metamerism motion that is induced by the exciting bending vibration of the legs. The robot can provide bi-directional planar motion and perform steering as well as generate rotation motion around the main axis of the robot. Numerical and experimental investigations showed that the robot achieves a planar speed of 516.3 mm/s and a resolution of 0.44 \(\upmu\)m when a payload of 200 g is applied. However, the authors did not consider the possibility to generate angular motion of the payload. [PERSON] and [PERSON] introduced a piezoelectric planar motion robot with multiple degrees of freedom [18]. The robot consists of a rectangular bronze plate with a trapezoidal cross-section and eight piezo ceramic plates glued on a bronze plate. Four driving feet are used to move the robot. The operation of the robot is based on the excitation of four different vibration modes. Linear motion of the robot is induced employing superposition of the first order longitudinal and third-order bending modes while superposition of the second-order in-plane and out-of-plane bending modes are used to control motion direction and achieve rotation of the robot about the \(Z\)-axis. The robot achieves a maximum linear speed of 37 mm/s and rotation speed of 6.28 rad/s.