**2. Introduction to the parasitic motion principle**

Different from other kinds of motion principles, the parasitic principle belongs to a kind of dependent motion, which generally accompanies with an independent motion, as illustrated in **Figure 1(a)**. When a load F is applied at the end of a cantilever beam, it will be bent with two motion components in *x* and *y* directions. The motion component in *y* direction is the major motion, which is directly induced by the load F, while the motion component in *x* direction is called as the parasitic motion. It simultaneously occurs with the major motion, which is generally regarded as an undesired motion component in previous studies. In general, the parasitic motion is much smaller than the major motion, but this dependent motion may deteriorate positioning accuracy and lead to more issues in calibration. On the

*Parasitic Motion Principle (PMP) Piezoelectric Actuators: Definition and Recent Developments DOI: http://dx.doi.org/10.5772/intechopen.96095*

**Figure 1.**

*Schematic diagrams of the parasitic motion principle: (a) generation of parasitic motion when bending a cantilever, (b) saw-tooth wave control signal, and (c) motion principle of the PMP piezoelectric actuator in one step [23].*

other hand, if the parasitic motion of flexure hinge-based compliant mechanisms can be appropriately adopted in the design of piezoelectric actuators, it can be employed as a motion task by utilizing lower degree of freedom (DOF) with easier control, lower cost, less complexity of kinematics and simple structure. By employing specially designed control signal, for instance, the saw-tooth wave as shown in **Figure 1(b)**, applied to the piezoelectric element, the relative displacement is realized, and thus the stepping motion is achieved. Therefore, the PMP piezoelectric actuator becomes popular since its emergence in recent years.

**Figure 1(c)** shows the motion principle in one step of the PMP piezoelectric actuator. This kind of actuators is generally consisted of two sections, the stator and the slider/rotor. At the initial step (1), the stator and the slider are in separated state with an initial gap δ between each other. Then, in step (2), with a moment/ force slowly applied to the flexure hinge-based compliant mechanism, the initial gap δ is filled, leading to an initial contact between the stator and the slider/rotor. Afterwards, in step (3), both the major motion and parasitic motion increase with deformation of the flexure hinge-based compliant mechanism. The slider/rotor moves in the same direction with the parasitic motion. Finally, after the slider/rotor moves to the forward displacement/angle in one step, the moment/force is suddenly removed, and the flexure hinge-based compliant mechanism recovers to its initial state and gets ready for the next cycle. In this process, as the stator still contacts with the slider/rotor, a backward motion would generally appear in the final step. Therefore, the PMP piezoelectric actuator could move with one-step displacement Δ*S*, the one-step forward displacement minus the backward motion. By cycling from step (1) to step (4), the long working stroke can be easily achieved.

### **3. Similarities and differences with other stepping principles**

Inchworm type, friction-inertia type, and parasitic type are three main kinds of motion types in stepping principle to realize long working stroke. Inchworm type, as a kind of bionic principle, employs the driving units and clamping units to obtain long working stroke. The utilization of clamping units facilitates the enhancement on output capability for piezoelectric actuators. In general, the inchworm type actuator consists of three separate parts, one driving unit and two clamping units. The moving processes of the inchworm type piezoelectric actuator are presented in **Figure 2**.

**Figure 2.**

*Motion principle of the inchworm type actuator: (a) moving principle of inchworm in nature [34], and (b) bionic stepping motion principle of inchworm type piezoelectric actuators.*

**Figure 3** shows the schematic diagram of friction-inertia type motion principle. The motion principle for the friction-inertia type follows the law of momentum conservation. A piezoelectric stack or piezoelectric bimorph, between two objects with different weights, is driven by a special control signal. At the initial step (1), the piezoelectric element is in its original status and connects two blocks. Then, in the step (2), the piezoelectric element extends gradually with the increase of driving voltage, and one block follows the movement of the piezoelectric element due to the static friction. In this process, there is no relative motion between the two objects. Afterwards, in step (3), the driving voltage suddenly drops to zero and the piezoelectric element loses power. It quickly recovers to the initial status, but the moving block remains in its position due to the inertial force. Following these steps, a small displacement occurs in this process. Based on the moving process, the friction-inertia actuator involves two motion types: impact-friction type and stick–slip type [3]. The main difference from impact-friction type is that, in stick– slip type, one end of the driving element is connected to the base and the other end drives the mass block by surface friction.

These three motion principles have some similarities and differences. According to the previous research, the performance comparison of these three motion types of stepping principle piezoelectric actuators is listed in **Table 1**. From the list, the inchworm type piezoelectric actuators dominate the high resolution and large output capability, but the free-load motion velocity is lower than its counterparts. Whereas, the friction-inertia type and parasitic type piezoelectric actuators have superiorities on motion speed and control system but deficiency on the output capability.

Compared with the inchworm type piezoelectric actuator, the structure of the PMP piezoelectric actuator is compact and its control strategy is quite simple. The parasitic motion completes the actions of clamping and driving in inchworm type motion. The re-clamping in the inchworm type is neglected in the parasitic type motion. Therefore, the difficulty and complexity on control system drop down but the output load capability is sacrificed to some extent. As a similar motion like friction-inertia type, the main difference is on the interaction between the driver and the slider/rotor. In PMP piezoelectric actuators, the normal clamping force, as well as the friction, between the driver and the slider/rotor becomes large as the voltage increases, while the forces are generally maintained the same in frictioninertia type piezoelectric actuator. All in all, the parasitic motion principle can be treated as a combination of inchworm principle and friction-inertia principle to some extent. It simplifies the structures and control strategy of inchworm principle, and exceeds the output capability of friction-inertia motion principle by increasing the clamping force.

*Parasitic Motion Principle (PMP) Piezoelectric Actuators: Definition and Recent Developments DOI: http://dx.doi.org/10.5772/intechopen.96095*

**Figure 3.**

*Motion principles of two friction-inertia types actuators: (a) impact-drive type, and (b) stick–slip type [3].*


**Table 1.**

*Performance comparison of three motion types of stepping principle piezoelectric actuators.*
