**2.1 Trapezoid-type piezoelectric stick-slip actuator**

In this work, a trapezoid-type piezoelectric stick–slip actuator adopts a flexure four-bar mechanism and driving foot with trapezoid beam to obtain the oblique motion, which can make the slider move by oblique displacement of flexure hinge mechanism [10], as shown in **Figure 2**.

The structure diagram of the trapezoid-type piezoelectric stick–slip actuator is illustrated in **Figure 2(a)**. The *ox*, *oy*, and *oz* represent the horizontal, axial and vertical directions, respectively. The actuator is mainly comprised of a flexure hinge mechanism, a slider, a piezoelectric stack, a shim block, a preload screw, a base and a preload mechanism. The preload between the flexure hinge mechanism and

#### **Figure 2.**

*Research on the trapezoid-type piezoelectric stick–slip actuator. (a) Configuration of the proposed actuator, and (b) the detailed structure of the flexure hinge mechanism. (c) Operation principle of the actuator. (d) and (e) simulation results of the flexure hinge mechanism. (f)–(h) The test results of the actuator. [10].*

piezoelectric stack in the initial state is adjusted by the preload screw. The flexure hinge mechanism is preload by the preload mechanism. The needed driving force is generated by the stack which is mounted in the flexure hinge mechanism.

The flexure hinge mechanism is a key component, and its detailed structure is shown in **Figure 2(b)**. The material of the flexure hinge mechanism is AL7075. Four right circular notch joints are employed to the flexure hinge mechanism and thereby the displacement along the axial direction is generated when the piezoelectric stack occurs deformation. It is important that the flexure hinge mechanism utilizes the uneven stiffness distribution of the trapezoid beam to cause needed lateral motion on the driving foot.

The principle of the trapezoid-type stick–slip actuator is depicted in **Figure 2(c)**. In the initial state, when time *t* = *t*0, the stack and flexure hinge mechanism keep the original state. The point P is a contact point between the slider and driving foot. The preload force *F*0 is equal to *F*p generated by the preload mechanism.


After the two stages, a small distance of positive direction Δ*x* is generated on the horizontal axis in terms of the slider. The repetition of the above stages makes the actuator generate a long-stroke linear motion.

The lateral displacement of the driving foot can be adjusted by adjusting the angle between the hypotenuse of the trapezoid beam and horizontal axis. To determine the lateral movement on the driving foot, the finite element method (FEM) is used to analyze the angle adjustment process, as shown in **Figure 2(d)** and **(e)**. From the ratio Ux/Uy, a smaller *θ* rad is needed for better actuation. From the equivalent stress, a larger *θ* has smaller equivalent stress. Besides, a smaller *θ* is also essential to meet the requirement of compact size. Finally, *θ* = π/6 rad is selected in this work.

To research the characteristics of the trapezoid-type piezoelectric stick–slip actuator, the prototype and experimental system are established. And a series of experiments are carried out to research the influence of locking force, driving frequency and driving voltage on the performance, as shown in **Figure 2(f )**–**(h)**.

It is worth noting that the locking force between the driving foot and the slider could change the system stiffness and thereby, the optimal frequency appears the slight change. When the voltage is 100 Vp-p, and the frequency is inferior to 500 Hz respectively, the velocity rises with the increase of frequency. When the frequency exceeds 500 Hz, the velocity decreases, which results from that the time of deforming to theoretical length is too short for the stack. It can be seen from **Figure 2(f)** that the maximum velocity is 5.96 mm/s under the locking force of 3.5 N. The velocity increases linearly with an increasing voltage. When the voltage is 100 Vp-p, and the locking force is 3.5 N respectively, a maximum velocity of 5.96 mm/s is achieved. Meanwhile, when the voltage is 45.17 Vp-p, the minimum starting voltage of the actuator, the displacement resolution of 50 nm is achieved under the locking force of 5 N.

In the initial state, the mass of the slider is 35 g. The standard weight is used to measure the load along the horizontal axis of the actuator. The various loads along the positive direction on the horizontal axis are applied in the slider through a pulley and a steel wire. It is conspicuous that the velocity decreases with the

*The Asymmetric Flexure Hinge Structures and the Hybrid Excitation Methods for Piezoelectric… DOI: http://dx.doi.org/10.5772/intechopen.95536*

increase in load. The maximum loads of the actuator that can be sustained are 3 N, 1.6 N and 1.6 N when locking forces are 5 N, 3.5 N and 2 N, respectively. The linear relationship between the load and velocity does not emerged, which results from the influence of the assembly errors and the preloading gap.
