## 1 Introduction  
An ultrasonic motor (USM) is a kind of actuator which converts electrical energy into mechanical energy. By using the inverse piezoelectric effect of piezoelectric (PZT) ceramics, a micro high-frequency mechanical vibration is generated in the motor stator, and it creates an elliptical trajectory to drive the slider by frictional force at the interface. Compared with the electromagnetic motor, the ultrasonic motor has many advantages such as a large power-to-weight ratio, high torque at low speed, high position accuracy, compact structure without reduction gears and no electromagnetic emissions. The ultrasonic motor with its unique operating features has been applied in all kinds of fields such as high precision instruments, micro-robots, and spatial mechanism [1; 2; 3; 4].  
The linear ultrasonic motor (LUSM) is one type of USM which has drawn much attention. According to the working mode of PZT, LUSMs have been classified into bonded-type motors [5; 6; 7; 8; 9; 10; 11; 12] and bolt-clamped-type motors [13; 14; 15; 16; 17; 18; 19; 20]. Recently, bonded-type motors, which are small in size, have attracted many researchers' interests, but their extremely low thrust is a serious drawback. In particular, some kinds of bonded-type motors' thrusts are below 1 N [5; 6; 7; 8], while a few of the bonded-type motors' thrusts have been improved to reach a value of less than 10 N [9; 10; 11; 12]. Moreover, the excitation voltage, applied on the ceramics, has a limit due to the insulation and weakness of the bond. Thus, bonded-type motors are not suitable for the occasions of high speed and large thrust.  
To overcome the aforementioned demerits of bonded-type motors, the bolt-clamped-type motors are a good choice [17], and researchers have carried out much work on this type of LUSM [13; 14; 15; 16; 17; 18; 19; 20]. The research on bolt-clamped-type motors has been ongoing since the 1990s. By using two sandwich-type transducers, a high-power LUSM was proposed by [PERSON] _et al._, and it achieved a maximum output thrust of 51 N at the driving voltage of 500 V\({}_{\text{rms}}\) in 1998 [13]. Moreover, it has been improved by other researchers [14]. [PERSON] _et al._ presented a T-shaped motor using longitudinal vibration transducers, and its maximum output force is 20 N at a voltage of 200 V\({}_{\text{rms}}\)[15]. A U-shaped LUSM using longitudinal vibration transducers with double feet has obtained a no-load speed of 854 mm/s and a maximum output thrust of 40 N [16]. There are also some other high-power LUSMs [17; 18; 19; 20]. All these initiative research studies soundly proved that most of the high-power ultrasonic motors adopted the \(d_{33}\) working mode. Compared with the \(d_{31}\) working mode, the \(d_{33}\) working mode adopts the bolt-clamped-type structure and, therefore, it can bear a higher exciting voltage. Besides, it has a higher electromechanical coupling efficiency and a better mechanical output characteristic.  
In order to achieve the desired high mechanical power output, a modified T-shaped motor using longitudinal vibration transducers with a single foot has been proposed. Compared with the previous motor [15], the horn and driving foot of the modified motor have been redesigned so that the energy-gathered effect and rigidity could be improved. The modified structure and the optimization design of the proposed motor are discussed in Sections 2 and 4. The driving principle and design method are introduced in this paper. After fabricating the prototype and working platform, the mechanical output performances are investigated through experiments.