**Abstract**

Stepping piezoelectric actuators have achieved significant improvements to satisfy the urgent demands on precision positioning with the capability of long working stroke, high accuracy and micro/nano-scale resolution, coupled with the merits of fast response and high stiffness. Among them, inchworm type, frictioninertia type, and parasitic type are three main types of stepping piezoelectric actuators. This chapter is aimed to introduce the basic definition and typical features of the parasitic motion principle (PMP), followed by summarizing the recent developments and achievements of PMP piezoelectric actuators. The emphasis of this chapter includes three key points, the structural optimization, output characteristic analysis and performance enhancement. Finally, the current existing issues and some potential research topics in the future are discussed. It is expected that this chapter can assist relevant researchers to understand the basic principle and recent development of PMP piezoelectric actuators.

**Keywords:** parasitic motion principle, piezoelectric actuator, long working stroke, flexure hinge-based compliant mechanism, backward motion

## **1. Introduction**

Nowadays, long working stroke precision positioning systems with micro-to-nano resolution are significantly demanded in many scientific studies and industrial fields [1–3]. Most of the conventional actuators can hardly satisfy the requirements on positioning resolution for precision positioning systems, such as hydro-motors, direct/alternating current motors, pneumatic elements, et al., even with the merits of large output capability, fast response, and long working stroke [4–6].

The piezoelectric actuator is one of the potential alternatives for high-resolution precision positioning systems [7–10]. Up to now, various of piezoelectric-driven positioning systems with flexure hinge-based compliant mechanisms have been developed and widely applied in many scientific and industrial applications, such as atomic force microscopy (AFM) [11–13], fast tool servo (FTS) single-point diamond turning [14–16] and optical adaptive mirror [17–19], et al. Generally, restricted by the inverse piezoelectric effect of current piezoelectric materials, the displacement of a single piezoelectric element is limited within tens of nanometers to several micrometers [20]. The applications of such positioning stages are only employed within limited scopes due to micro-scale working stroke. In order to

extend the working stroke of piezoelectric elements, several methods have been proposed and investigated [21–23], which can be classified according to the motion principle into the direct-driven principle, ultrasonic principle, and stepping principle. Direct-driven principle is the initial application in piezoelectric actuators. With the assistance of flexure hinge-based compliant mechanisms, it is found that the working stroke can be amplified up to several times of the original displacement of a single piezoelectric element. The maximum working stroke is extended to tens of micrometers [24–26]. However, it is still not long enough for most of the applications, and furthermore complicated flexure hinge-based compliant mechanisms deteriorate the static and dynamic characteristics of the piezoelectric actuators, reducing structural stiffness and intrinsic resonant frequency. Therefore, the direct-driven principle gradually loses its popularity in the recent years. Ultrasonic principle utilizes the resonance of stators to drive the slider/rotor. However, the interfacial wear and heat generation are lack of adequate solution to date, especially in high-speed & full-load motion [27, 28]. Stepping principle realizes the long working stroke by step displacement accumulation. By this way, high-precision positioning accuracy can be achieved in long working stroke. Hence, stepping principle has attracted much attention in the piezoelectric actuator development in the recent decades.

Various of stepping piezoelectric actuators can be further classified into three motion types, involving inchworm type, friction-inertia type, and parasitic type [3, 29–31]. Inchworm type, as a kind of bionic driving type, mimics the motion principle of inchworms in nature, which alternates the clamping and driving units to move forward and backward. Thus, its control strategy, structural assembly and the motion sequence are generally complicated. Friction-inertia type refers to a kind of spontaneous jerking motion that can occur, while two mass blocks alternate between sticking to each other and sliding over each other, with a corresponding tuning the friction and inertia forces. Compared with the inchworm type, the basic structure and control system of friction-inertia type are largely simplified but associated with loss on loading capability.

Parasitic type is a new solution to acquire both long working stroke and large output capability by adopting the parasitic motion of flexure hinge-based compliant mechanisms, which is commonly restricted in previous designs [32, 33]. Up to now, tens of PMP piezoelectric actuators based on various of flexure hinge-based compliant mechanisms have been developed with great success and achievement on improving working stroke and output capability. The purpose of this chapter is to introduce the basic parasitic motion principle, review the developments and achievements in recent years, and finally point out some potential issues and current challenges in this research.
