**2. Introduction to the different types of EVC**

EVC is a kind of vibration-assisted machining. Different from 1-dimensional vibration cutting and traditional cutting, the trajectory of cutting tool is an ellipse and it is located in a fixed plane (2-dimensional, 2D) or in space (3-dimensional, 3D) which is dependent on the vibration modulation of motion axis. The cutting process of different types of EVC is shown in **Figure 1**. It can be seen that for orthogonal EVC and oblique EVC, the tool trajectory is in a fixed plane despite the orientation of fixed *Design, Analysis and Testing of Piezoelectric Tool Actuator for Elliptical Vibration Cutting DOI: http://dx.doi.org/10.5772/intechopen.103837*

**Figure 1.** *Schematic illustration of different types of EVC.*

plane in oblique EVC is also dependent on the angle *i*. It only needs two motion axes to modulate the cutting tool to obtain the ellipse locus. However, for 3D EVC, the trajectory of cutting tool is in space or in an arbitrary plane of modulation range. Therefore, it needs at least three motion axes to obtain the ellipse locus.
