# Development of a 3-DOF Cylindrical Ultrasonic Motor Based on Non-Standard Modes
## 1 Introduction  
Multi-degree-of-freedom (multi-DOF) motors perform complex motions through precise force/torque manipulation to accomplish automation tasks. Most multi-DOF motors are based on electromagnetic principles. Multi-DOF permanent magnet (PM) motors have a complex electromagnetic structure requiring high material and machining. The use of electromagnetic motors in the presence of external electromagnetic fields and other radiation sources can affect the accuracy and even the regular operation of the whole system [1; 2]. With the diversification of energy conversion methods, scholars have taken another approach and proposed ultrasonic motors based on friction drive. Ultrasonic motors utilize the inverse piezoelectric effect of piezoelectric ceramics to generate ultrasonic frequency vibrations, which generate thrust through friction between the stator and rotor friction surfaces, thus realizing the conversion of electrical energy to mechanical energy [3; 4]. Ultrasonic motors are characterized by high low-speed torque, fast action response, self-locking, simple structure, and freedom from electromagnetic interference [5; 6; 7]. Due to these attractive features, the simplicity of the structure, and the ability to quickly achieve singularity-free motion, multi-degree-of-freedom ultrasonic motors play a vital role in aerospace [8; 9], robotics [10; 11], and medical devices [12; 13] requiring precision motion and special driving environments. Depending on the stator structure, multi-DOF spherical ultrasonic motors can be categorized as clamping [14; 15], planar [16; 17; 18], cylindrical [19; 20], spherical shell [21; 22] and sandwich [23; 24]. Most multi-DOF ultrasonic motors are complex in construction. Most clamped motors, sandwich-type and planar type, need to design the external frame to fix the stator and disc spring, and the ball-shell motors need to fabricate the external ball shell to paste the piezoelectric ceramics. This greatly increases the design difficulty and process complexity. Compared to the other three types, the cylindrical multi-DOF motor, withits stator vibration pattern and piezoelectric ceramic configuration design, can drastically reduce the size of the motor. This highlights the virtues of compact ultrasonic motors, which drive the load directly and offer significant manufacturing and application advantages. Depending on the form of stator design, multi-DOF cylindrical motors can be divided into bolted and ceramic bonding types. [PERSON] et al. presented the first bolts-type multi-DOF ultrasonic motor in 1998 [25]. The motor used two bending vibrations with one longitudinal vibration to achieve 3-DOF rotation of the rotor. The stator had an overall length of 118 mm and used bolts to clamp the piezoelectric ceramics (PZT). The motor structure proposed by [PERSON] et al. added a support plate and head base, shortening the length of the motor and increasing stability [26; 27]. The motor's maximum speed and output torque values were about 250 r/min and 7 mNm. The overall length of the motor remained long, and the support shaft fabrication process was complex. [PERSON] et al. designed a multi-DOF actuator for application in robotic finger joints [28; 29; 30]. Ref. [28] described the motor stator as consisting of a bolt-clamped disk transducer and a multi-layered piezoelectric actuator. The actuator's height and diameter were 33 mm and 20 mm. The motor had a maximum torque of approximately 23.5 mNm. The motor was not equipped with a device for applying preload, and the gripping mechanism designed for the application increased the total size of the actuator by a large extent. Ref. [31] reported a sandwich-type multi-DOF motor. The piezoelectric ceramics of the motor stator were bolted between the flange and the end cap. Adjacent piezoceramics were polarized in opposite directions to achieve mixed-mode vibration. However, the motor did not take into account rotor placement. The motor designed by [PERSON] et al.