# A Novel Impact Rotary-Linear Motor Based on Decomposed Screw-Type Motion of Piezoelectric Actuator
## 2 Working Principle
### Working Principle of the Impact Rotary-Linear Motor  
The simplified piezoelectric motor consists of a spring, a snap ring, a coupler, a PA, and a shaft. The coupler includes a pair of cone-shaped bushings. The outer surface of the cone-shaped bushing is mainly used as the contact surface for rotary motion and the inner surface of the coupler is used as the contact surface for linear motion. The piezoelectric motor realizes rotary motion through the line contact and realizes the linear motion through the surface contact. The coupler has different functions in rotary and linear motion. The working principle is shown in Figure 2. With an axial prepressure applied between the PA and the coupler, a friction force or friction torque will be produced when there is a trend of relative movement among them. Also, with a radial prepressure applied between the coupler and the shaft, a friction force or friction torque will be produced when there is a trend of relative movement among them. According to the different working conditions, the value of the friction force or friction torque between the coupler and the shaft and friction force or friction torque between the coupler and PA can be adjusted by choosing different sizes of snap ring and changing different positions of the spring. The piezoelectric motor is driven by a saw-shaped voltage signal. The duty ratio in Figure 2 can be defined by:  
\[Duty\ ratio=t_{1}/T\times 100\%=[t_{1}/(t_{1}+t_{2})]\times 100\%, \tag{4}\]  
where \(T\) is the cycle time, \(t_{1}\) is the rising time of the saw-shaped driving voltage, and \(t_{2}\) is the falling time of the saw-shaped driving voltage. The PA is excited by a saw-shaped driving voltage signal. The working cycle of the piezoelectric motor can be divided into two steps and three states [30]. The piezoelectric motor can realize  
Figure 2: Working principle of the piezoelectric motor: (**a**) rotary motion; (**b**) linear motion. independent rotary and linear motions by the appropriate snap ring and appropriate position of spring through the main two different friction interfaces. For the rotary motion [see Figure 2a]:  
In state 1, adjusting the spring to the suitable position and choosing the appropriate snap ring, the motor is at the starting position with the angle of \(\theta_{0}\) and it is at the starting position with a displacement of \(x_{0}\) when the driving voltage is beginning to apply. In state 2, with the slow increase of the driving voltage, the PA produces a screw-type motion, in other words, the PA is extended in axial direction and twisted in circumferential direction simultaneously. The friction torque between the coupler and PA, also the friction torque between the coupler and shaft, are appropriate for the coupler and shaft to move along with the PA in circumferential direction. The friction force between the coupler and PA, also the friction force between the coupler and shaft, are appropriate for the coupler and shaft to move along with the PA in axial direction. So the shaft and the PA realize the same torsional angle of \(\theta_{1}\) and the same longitudinal displacement of \(x_{1}\) at the time of \(t_{1}\). In state 3, with the sudden decrease of the driving voltage, the PA moves back to its initial position quickly. The coupler cannot catch the PA by the dynamic friction torque between the coupler and PA, so a small slip angle of \(\theta_{2}\) is generated by the coupler at the time of \(t_{2}\). At the same time, the friction torque between the coupler and the shaft is enough for the shaft to follow the motion of coupler in circumferential direction, so the coupler and shaft can be regarded as a whole at this condition. Thus, a slip angle of \(\theta_{2}\) is generated by the shaft at the time of \(t_{2}\). Finally, the shaft has the net rotary angle of \(\theta_{1}-\theta_{2}\) in one cycle, because the coupler can move back to its initial axial position under the effect of the restoring force which is produced by spring in axial direction.