**Abstract**

In the field of ultraprecision machining, the structured surfaces with various micro/nano characteristics may have different advanced functions, such as wettability modifications, tribological control and hybrid micro-optics. However, the machining of micro/nano structured surfaces is becoming a challenge for present cutting method. Especially for the difficult-to-cut materials, it is impossible to manufacture complex micro/nano features by using traditional cutting methods. The complex features require a cutting tool no longer confined to the traditional motion guide. The cutting tool should have more quick response velocity and flexible modulated ability. This chapter aims to make an introduction for piezoelectric tool actuator used in elliptical vibration cutting, which can be offering tertiary cutting operations with quick response and flexible modulated ability. The content covers the working principle of piezoelectric tool actuator, compliant mechanism design, static modeling, kinematic and dynamic modeling, structure optimization and offline testing.

**Keywords:** piezoelectric actuator, elliptical vibration cutting, compliant mechanism, ultraprecision machining, structured surface
