# A Novel Piezoelectric Ceramic Actuator with Scissoring Composite Vibration for Medical Applications
## 2 Design Principle and Modeling  
The schematic illustration of the proposed scissoring actuator is presented in Figure 1a. The actuator consists of a back mass, a piezoelectric stack, a front mass and a beam with a special end effector on the free tip. The actuator size can be easily miniaturized due to its simple structure. The piezoelectric stack is formed by combining several thin piezoceramic layers, which are polarized in the longitudinal direction and adjacent layers experienced opposite polarization. The horn structure is designed at one side of the front mass to amplify the longitudinal driving vibration. In order to enhance the output of piezoceramic stack, the stack is embedded in a hollow cylinder with a netted pre-stressed structure, which is closed to another side of the front mass. The free beam tip is split into two small beams by a centerline slit at the end effector. Two opposite grooves, with the slanted surface, are cut on the top and bottom surfaces of the small beams, respectively. Furthermore, the working mechanism is illustrated in Figure 1b. When the driving voltage is applied on the piezoceramic stack, the ceramic layers expand in the axial direction of the actuator, resulting in longitudinal vibrations in the front mass. Moreover, the vibrations are amplified by the horn structure. The longitudinal vibration wave propagates to the beam and reaches the grooves. Moreover, a part of the longitudinal elastic wave passes through groove structure and reaches to the beam tip due to solid connection. However, a major portion of the longitudinal elastic wave impinges on the slanted surfaces of the grooves and induces wave reflection. In addition, the direction of longitudinal vibration changed from longitudinal to the vertical direction. Thus, the wave distribution in vertical direction generates a bending moment on the small beam tip. Furthermore, the bending directions of both beam tips should be in the opposite direction because both slanted surfaces lie on the opposite sides of the grooves, leading to a scissoring vibration of the beam tip. It has been reported that the deflection on the small beam tip causes bending vibrations on other parts of the beam, which is highly undesirable in the proposed design. However, theoretically, the bending moments on both beam tips should counteract each other due to their opposite direction and the beam should be maintained in the horizontal direction without bending vibrations. Hence, the longitudinal vibrations from the power source are successfully converted into scissoring-type vibrations at the distal tip of the actuator. As we know, in most cases the bigger output amplitude and higher resonance frequency can be expected by the actuator, the more efficient cutting or stirring function would be obtained. With this new structure, both the output frequency and amplitude based on the surgery requirements can be easily modified by adjusting the input voltage and structure parameters including the length, width, thickness, groove length and so on. It should be noted that the angle of the slanted surface of the groove has a significant influence on the reflection of the vibration wave and the bending rigidity of the groove. An optimal groove angle is required to achieve high conversion efficiency, however, the detailed description of the influence of groove angle is beyond the scope of the current study. As shown in Figure 1a,b, a grooved structure is positioned as a vibration converter between the beam and distal tip, where the driving longitudinal vibration from the power source can degenerate into two opposite bending vibrations at the distal tip. Hence, the beam can be divided into two parts, i.e., the longitudinal vibration bar and bending beam tip, as illustrated in Figure 2. One should note that the left end of the bar is connected with the horn, which supplies longitudinal elastic force, and the left clamped boundary of the bar can be described as a spring (\(\mathrm{k_{s}}\)).