Investigation on a Linear Piezoelectric Actuator Based on Stick-Slip/Scan Excitation

To perform a high resolution and long stroke application in optical precision instruments, a linear piezoelectric actuator operated in stick-slip/scan modes for driving a linear motion table is presented. The proposed piezoelectric actuator is a piezoelectric composite structure, which includes a metal elastomer, a piezoelectric stack, and a frictional ball. The purpose of this paper is to describe the operation principle, design, and the running test and resolution test of the linear motion table driven by the proposed piezoelectric actuator. The notable feature is the flexible hinges of the actuator, including composite hinge, pre-pressure adjustment flexible hinge, and transmission flexible hinge, which are designed for decoupling the motion in the action direction of the piezoelectric stack and the direction in which the pre-pressure is applied. A prototype has been fabricated and two operation modes of the piezoelectric actuator, stick-slip and scan mode, were utilized to test the driving characteristics of the linear motion table. Experimental results show that the finest step resolutions in stick-slip mode and scan mode achieved 12 nm and 4 nm, respectively.


Introduction
Operating processes on objects at micro-scales need high-precision motion servo systems. Moreover, the requirements for the resolution and travel of linear motion systems are also increasing with the rapid development of technology. For example, wafer processing or testing equipment has a higher demand in resolution and travel. To meet these requirements, numerous variations of micro-motion device technology have been developed [1][2][3]. Among these, piezoelectric actuators are one type of prevailing micro-actuation technology, which have been widely used in linear precision motion stages [4] for their inherent characteristics of compact sizes, high displacement resolutions, self-locking when power is off, fast response, lower thermal generation, and high electromagnetic immunity.
Piezoelectric actuators produce force and displacement by using the inverse piezoelectric effect of the piezoelectric element. Generally, the deformation of the piezoelectric element, even as a multilayer piezoelectric stack, is very small (micron) compared to their size [5,6]. To achieve long travel actuation, many piezoelectric actuators with different operation principles were developed, which can be divided into four main categories: ultrasonic motors, piezoelectric compliant mechanism, inchworm motors, and inertia motors: (1) the typical configurations for ultrasonic motors are the traveling wave type [7][8][9] and the standing wave type [10][11][12][13][14][15]. The working principle of the ultrasonic motor is almost based on a piezoelectric actuator, which utilizes piezoelectric elements to activate the desired vibration of an elastic body, and the driving points of the elastic body perform elliptical motions at a frequency in the ultrasonic range. A slider or rotor, pressed on the driving points of the vibrating body by a normal force, is driven by a friction force to achieve linear motion and rotation motion. Herein, the linear ultrasonic motor is mostly a standing wave type, Figure 1 shows the structure of the piezoelectric actuator with a dimension of 17 × 5 × 6 mm 3 . The actuator includes a metal elastomer, a piezoelectric stack, and a frictional ball. The metal elastomer is composed of four parts: fixed blocks, flexible hinges, inertial mass, and spring structure. The piezoelectric stack is clamped between the fixed block and the inertial mass block. Figure 2 shows the overall structural design of the linear motion stage. The actuator is mounted on the bottom of the base plate by a screw; a ceramic strip used as a friction strip is attached at a corresponding position under the moving table; the ceramic ball at the front end of the actuator is pressed on the surface of the frictional strip by one adjustment screw; the commercially available cross roller rails are used for guiding the moving table.
Actuators 2021, 10,39 3 of 13 by one adjustment screw; the commercially available cross roller rails are used for guiding the moving table. For the linear motion stage driven by the proposed piezoelectric actuators, the main difficulty lies in how to decouple the motion in the action direction of the piezoelectric stack and the direction in which the pre-pressure is applied. At the same time, in order to achieve miniaturization of the motion table, it is best to integrate functional components into the overall structural design. Furthermore, for the stick-slip driving method, there is only "slip" during the stick-slip process if both contact surfaces are rigid; thus, the mobile unit cannot be effectively driven. On the other hand, there is only "stick" during the stickslip process if both contact surfaces are flexible; thus, the moving unit will follow the motion of the actuator. The mobile unit must be rigid; therefore, the actuator should be designed as a flexible body. Here, three flexible hinges are designed for transferring the displacement of the piezoelectric stack and applying pre-pressure between this actuator and the moving table which is pressed on the frictional ball (see Figure 2b). The prepressure adjustment flexible hinge and the transmission flexible hinge should be designed to facilitate the transmission of displacement of piezoelectric stack and the preloading between the friction ball and the moving table, respectively. The composite flexible hinge is designed as one type of composite functional hinge, which is used for coordinating the deformation of the two flexible hinges described above.

Operation Principle
The operation principle of the proposed actuator is described in Figure 3. The piezoelectric stack changes its length proportionally to the applied voltage. The moving table will follow the movement of the piezoelectric stack with the same acceleration when the piezoelectric stack is not accelerated too high; this state is called stick-phase (see Figure  3b). Correspondingly, the inertial force of the accelerated motion table is higher than the friction force if the piezoelectric stack is accelerated very high. In this case, the friction   For the linear motion stage driven by the proposed piezoelectric actuators, the main difficulty lies in how to decouple the motion in the action direction of the piezoelectric stack and the direction in which the pre-pressure is applied. At the same time, in order to achieve miniaturization of the motion table, it is best to integrate functional components into the overall structural design. Furthermore, for the stick-slip driving method, there is only "slip" during the stick-slip process if both contact surfaces are rigid; thus, the mobile unit cannot be effectively driven. On the other hand, there is only "stick" during the stickslip process if both contact surfaces are flexible; thus, the moving unit will follow the motion of the actuator. The mobile unit must be rigid; therefore, the actuator should be designed as a flexible body. Here, three flexible hinges are designed for transferring the displacement of the piezoelectric stack and applying pre-pressure between this actuator and the moving table which is pressed on the frictional ball (see Figure 2b). The prepressure adjustment flexible hinge and the transmission flexible hinge should be designed to facilitate the transmission of displacement of piezoelectric stack and the preloading between the friction ball and the moving table, respectively. The composite flexible hinge is designed as one type of composite functional hinge, which is used for coordinating the deformation of the two flexible hinges described above.

Operation Principle
The operation principle of the proposed actuator is described in Figure 3. The piezoelectric stack changes its length proportionally to the applied voltage. The moving table will follow the movement of the piezoelectric stack with the same acceleration when the piezoelectric stack is not accelerated too high; this state is called stick-phase (see Figure  3b). Correspondingly, the inertial force of the accelerated motion table is higher than the friction force if the piezoelectric stack is accelerated very high. In this case, the friction  For the linear motion stage driven by the proposed piezoelectric actuators, the main difficulty lies in how to decouple the motion in the action direction of the piezoelectric stack and the direction in which the pre-pressure is applied. At the same time, in order to achieve miniaturization of the motion table, it is best to integrate functional components into the overall structural design. Furthermore, for the stick-slip driving method, there is only "slip" during the stick-slip process if both contact surfaces are rigid; thus, the mobile unit cannot be effectively driven. On the other hand, there is only "stick" during the stick-slip process if both contact surfaces are flexible; thus, the moving unit will follow the motion of the actuator. The mobile unit must be rigid; therefore, the actuator should be designed as a flexible body. Here, three flexible hinges are designed for transferring the displacement of the piezoelectric stack and applying pre-pressure between this actuator and the moving table which is pressed on the frictional ball (see Figure 2b). The pre-pressure adjustment flexible hinge and the transmission flexible hinge should be designed to facilitate the transmission of displacement of piezoelectric stack and the preloading between the friction ball and the moving table, respectively. The composite flexible hinge is designed as one type of composite functional hinge, which is used for coordinating the deformation of the two flexible hinges described above.

Operation Principle
The operation principle of the proposed actuator is described in Figure 3. The piezoelectric stack changes its length proportionally to the applied voltage. The moving table will follow the movement of the piezoelectric stack with the same acceleration when the piezoelectric stack is not accelerated too high; this state is called stick-phase (see Figure 3b). Correspondingly, the inertial force of the accelerated motion table is higher than the friction force if the piezoelectric stack is accelerated very high. In this case, the friction surface of the actuator slips over the surface of the motion table, and as a result, the piezoelectric stack can change its length while the moving table stays its position, which is called the slip-phase (see Figure 3c). Thus, a continuous motion can be realized by repeating the sequence from Figure 3a-c. In order to achieve a high motion accuracy, a special operation mode called scan mode can be realized by slowly elongating the piezoelectric stack during the stick-phase (see Figure 3d). surface of the actuator slips over the surface of the motion table, and as a result, the piezoelectric stack can change its length while the moving table stays its position, which is called the slip-phase (see Figure 3c). Thus, a continuous motion can be realized by repeating the sequence from Figure 3a-c. In order to achieve a high motion accuracy, a special operation mode called scan mode can be realized by slowly elongating the piezoelectric stack during the stick-phase (see Figure 3d).

Actuator Design
There are three main issues that should be considered during the structural design process of this actuator: (1) the dimensional design of the composite flexible hinge to ensure the respective stiffness characteristics of the driving and pre-pressure applying directions; (2) the matching problem between the rigidity of the flexible transmission mechanism and the piezoelectric stack; (3) calculating the natural frequency of the actuator to avoid self-excitation during actuator operation.

Modeling of Actuator
Here, 65Mn was selected as the material of the metal elastic body (density is 7820 kg/m 3 , elasticity modulus is 2.11 × 10 11 Pa, and Poisson's ratio is 0.288), and one ceramic ball made of Al2O3 was used as a friction ball (density is 3950 kg/m 3 , elasticity modulus is 3.55 × 10 11 Pa, and Poisson's ratio is 0.27). One PZT stack (NAC2003, Noliac Company, Kvistgaard, Denmark, density is 7650 kg/m 3 , elasticity modulus is 0.9× 10 11 Pa and Poisson's ratio is 0.3) was chosen as the piezoelectric component, which had a size of 5 × 5 × 2 mm 3 , output displacement up to 2.6 μm at 60 V, and stiffness up to 350 N/µ m. The finite element model of the actuator is shown in Figure 4.

Actuator Design
There are three main issues that should be considered during the structural design process of this actuator: (1) the dimensional design of the composite flexible hinge to ensure the respective stiffness characteristics of the driving and pre-pressure applying directions; (2) the matching problem between the rigidity of the flexible transmission mechanism and the piezoelectric stack; (3) calculating the natural frequency of the actuator to avoid self-excitation during actuator operation.

Modeling of Actuator
Here, 65Mn was selected as the material of the metal elastic body (density is 7820 kg/m 3 , elasticity modulus is 2.11 × 10 11 Pa, and Poisson's ratio is 0.288), and one ceramic ball made of Al 2 O 3 was used as a friction ball (density is 3950 kg/m 3 , elasticity modulus is 3.55 × 10 11 Pa, and Poisson's ratio is 0.27). One PZT stack (NAC2003, Noliac Company, Kvistgaard, Denmark, density is 7650 kg/m 3 , elasticity modulus is 0.9 × 10 11 Pa and Poisson's ratio is 0.3) was chosen as the piezoelectric component, which had a size of 5 × 5 × 2 mm 3 , output displacement up to 2.6 µm at 60 V, and stiffness up to 350 N/µm. The finite element model of the actuator is shown in Figure 4.

Composite Hinge Design
Due to the limitation of the already selected piezoelectric stack (5 × 5 × 2 mm 3 ) and the overall size of the motion table, the length and width of the composite hinge have been determined to be 5 mm. Therefore, this section focuses on the thickness design of the

Composite Hinge Design
Due to the limitation of the already selected piezoelectric stack (5 × 5 × 2 mm 3 ) and the overall size of the motion table, the length and width of the composite hinge have been determined to be 5 mm. Therefore, this section focuses on the thickness design of the hinge. The influences of the thickness of the composite flexure hinge on the output displacement of the actuator and the vertical displacement of the inertial mass block under the pre-pressure of 20 N are analyzed through the workbench software (see Figure 5). It can be seen from Figure 5a that the output displacement of the actuator linearly increases with the hinge thickness from 0 to 0.2 mm, and when the hinge thickness reaches more than 0.2 mm, the output displacement of the actuator gradually approaches the maximum output displacement of the piezoelectric stack. From Figure 5b, it can be seen that the displacement of the inertial mass block in the vertical direction under the fixed pre-pressure of 20 N decreases with the hinge thickness from 0 to 0.2 mm and gradually becomes stable when greater than 0.2 mm. Therefore, synthesizing the strength requirements, the thickness of the composite flexible hinge was selected to 0.25 mm. When the input displacement is 2.6 µm, the output displacement of the actuator also achieved 2.6 µm.

Composite Hinge Design
Due to the limitation of the already selected piezoelectric stack (5 × 5 × 2 mm 3 ) and the overall size of the motion table, the length and width of the composite hinge have been determined to be 5 mm. Therefore, this section focuses on the thickness design of the hinge. The influences of the thickness of the composite flexure hinge on the output displacement of the actuator and the vertical displacement of the inertial mass block under the pre-pressure of 20 N are analyzed through the workbench software (see Figure 5). It can be seen from Figure 5a that the output displacement of the actuator linearly increases with the hinge thickness from 0 to 0.2 mm, and when the hinge thickness reaches more than 0.2 mm, the output displacement of the actuator gradually approaches the maximum output displacement of the piezoelectric stack. From Figure 5b, it can be seen that the displacement of the inertial mass block in the vertical direction under the fixed prepressure of 20 N decreases with the hinge thickness from 0 to 0.2 mm and gradually becomes stable when greater than 0.2 mm. Therefore, synthesizing the strength requirements, the thickness of the composite flexible hinge was selected to 0.25 mm. When the input displacement is 2.6 μm, the output displacement of the actuator also achieved 2.6 μm.

Model Analysis
According to the working principle, in order to prevent the elastic metal element of the actuator from being excited to resonance state when the piezoelectric stack is excited, it is necessary to conduct modal analysis on the actuator without a piezoelectric element. Figure 6 shows the model analysis results. The natural frequencies of the first mode to the fourth mode are 7376 Hz, 9666 Hz, 12,440 Hz, and 12,538 Hz, respectively. It is clear that if the inherent modes shown in Figure 6 are excited, the elastomer of the actuator will produce undesirable deformation, resulting in abnormal operation or damage of the

Model Analysis
According to the working principle, in order to prevent the elastic metal element of the actuator from being excited to resonance state when the piezoelectric stack is excited, it is necessary to conduct modal analysis on the actuator without a piezoelectric element. Figure 6 shows the model analysis results. The natural frequencies of the first mode to the fourth mode are 7376 Hz, 9666 Hz, 12,440 Hz, and 12,538 Hz, respectively. It is clear that if the inherent modes shown in Figure 6 are excited, the elastomer of the actuator will produce undesirable deformation, resulting in abnormal operation or damage of the actuator. Therefore, the operating frequency of the actuator must be less than 7376 Hz, or between the above and subsequent model frequencies.

Stiffness Calculation of Transmission Flexible Hinge
Here, it can be seen from the actuator structure that the stiffness of the transmission flexible hinge has a great influence on the actual output displacement of the actuator (see Figure 1). In theory, the smaller the stiffness of the flexible drive mechanism, the less influence on the actual output displacement of the actuator. However, pure piezoelectric ceramics can produce high pushing forces, but cannot withstand high tensile forces.

Stiffness Calculation of Transmission Flexible Hinge
Here, it can be seen from the actuator structure that the stiffness of the transmission flexible hinge has a great influence on the actual output displacement of the actuator (see Figure 1). In theory, the smaller the stiffness of the flexible drive mechanism, the less influence on the actual output displacement of the actuator. However, pure piezoelectric ceramics can produce high pushing forces, but cannot withstand high tensile forces. As for the proposed inertia actuator, the resetting force must be introduced into the system to achieve a more symmetrical push-pull performance. Moreover, the preload mechanism for resetting force should provide a high force but with a stiffness as low as possible; the preload force, therefore, does not vary with the piezo element's motion and the maximum stroke can thus be achieved. At the same time, the resetting force is required to be high enough to reset the mass block attached to the actuator fast enough. Generally, a passive preload mode by using the transmission flexible hinge is often utilized for providing the resetting force of the piezoelectric stack. Usually, to achieve symmetrical push-pull performance, the preload force applied sometimes on the piezoelectric stack ceramics is up to 50% of actuator's maximum load capability, and the preload stiffness is a few percent of the piezoelectric stack's stiffness. Therefore, in order to meet the above requirements, the stiffness of the transmission flexible hinge of the designed actuator was calculated as shown in Figure 7. As for the proposed inertia actuator, the resetting force must be introduced into the system to achieve a more symmetrical push-pull performance. Moreover, the preload mechanism for resetting force should provide a high force but with a stiffness as low as possible; the preload force, therefore, does not vary with the piezo element's motion and the maximum stroke can thus be achieved. At the same time, the resetting force is required to be high enough to reset the mass block attached to the actuator fast enough. Generally, a passive preload mode by using the transmission flexible hinge is often utilized for providing the resetting force of the piezoelectric stack. Usually, to achieve symmetrical push-pull performance, the preload force applied sometimes on the piezoelectric stack ceramics is up to 50% of actuator's maximum load capability, and the preload stiffness is a few percent of the piezoelectric stack's stiffness. Therefore, in order to meet the above requirements, the stiffness of the transmission flexible hinge of the designed actuator was calculated as shown in Figure 7. Here, the constraint of the fixed block is set as a fixed constraint. The end of the spring structure is in contact with the pre-pressure adjusting screw, so the only movement in the driving direction is allowed at the end of the elastic element. Thus, when a force of 50 N Here, the constraint of the fixed block is set as a fixed constraint. The end of the spring structure is in contact with the pre-pressure adjusting screw, so the only movement in the driving direction is allowed at the end of the elastic element. Thus, when a force of 50 N along the driving direction is applied to the end face of the composite flexible hinge, the inertial mass block produces a displacement of 91.5 µm along the driving direction. Then, the stiffness of the transmission flexible hinge in the driving direction is 50 N/91.5 µm = 0.546 N/µm, which is much less than the stiffness of the adopted piezoelectric stack (350 N/µm). Hence, at this stiffness level, the actual output displacement of the actuator is approximately the output displacement of the piezoelectric stack. Generally, the preload should be high enough, but not too high, to avoid depolarization. Thus, we choose 10% of the maximum output force of the piezoelectric stack as its pre-load. Here, the maximum output force of the adopted piezoelectric stack is 1050 N, so the pre-load of the stack should be about 100 N, and the mounting space of the piezoelectric stack should have a pre-deformation of about 0.18 mm (100 N/0.546 N/µm).

Experimental Investigation
The prototype of the motion table driven by the proposed actuator was fabricated as shown in Figure 8a. The overall size of the motion table was 40 × 40 × 18 mm 3 , with a mass of about 32 g and a maximum stroke of 22 mm. A test system was built to measure the performance of the motion table, as shown in Figure 8b. One signal generator (AFG3022C, Tektronix Co., LTD. Suzhou, China) was utilized to produce a driving signal and amplified by a power amplifier to drive the actuator, and one oscilloscope was used to monitor the change of the driving signal. The dynamic and static characteristics of the stage were investigated by using a laser micrometer (LG-2MM, KEYENCE CORPORATION, Shanghai, China) with a measuring range of 2 mm; the maximum measuring range can be up to 10 mm with a different probe.

Running Test of Motion Table in Open Loop
In the process of the running test, a sawtooth wave signal with an amplitude of 60 V, frequency of 1 Hz, and step time of 30 ms was adopted to activate the actuator. At the same time, the sampling frequency of the laser micrometer was set to 1 kHz. The test results are shown in Figure 9. It can be observed that both the forward and backward motions are in the form of sawtooth waves, in which the average step size of the forward motion is 1.841 μm, while the average step size of the backward motion is 1.766 μm. It is known that the piezoelectric element has a characteristic of capacitive load. Herein, in the case of the driving circuit having no discharge loop, the charge time constant of the stator equals the discharge time constant; the response of the stator cannot keep up with the changing of the driving signal.

Running Test of Motion Table in Open Loop
In the process of the running test, a sawtooth wave signal with an amplitude of 60 V, frequency of 1 Hz, and step time of 30 ms was adopted to activate the actuator. At the same time, the sampling frequency of the laser micrometer was set to 1 kHz. The test results are shown in Figure 9. It can be observed that both the forward and backward motions are in the form of sawtooth waves, in which the average step size of the forward motion is 1.841 µm, while the average step size of the backward motion is 1.766 µm. It is known that the piezoelectric element has a characteristic of capacitive load. Herein, in the case of the driving circuit having no discharge loop, the charge time constant of the stator equals the discharge time constant; the response of the stator cannot keep up with the changing of the driving signal. frequency of 1 Hz, and step time of 30 ms was adopted to activate the actuator same time, the sampling frequency of the laser micrometer was set to 1 kHz. T results are shown in Figure 9. It can be observed that both the forward and ba motions are in the form of sawtooth waves, in which the average step size of the f motion is 1.841 μm, while the average step size of the backward motion is 1.766 μ known that the piezoelectric element has a characteristic of capacitive load. Herein case of the driving circuit having no discharge loop, the charge time constant of th equals the discharge time constant; the response of the stator cannot keep up w changing of the driving signal. To solve this problem, the discharge circuit was used to improve the re characteristics of piezoelectric elements and achieved good results [28]. Therefore, developed a driving circuit with a discharge loop to improve the response charac of this proposed actuator and achieved the desired results (see Figure 10). Figure 1 the speed characteristics of the stage under different driving frequencies. Here, a s sawtooth wave signals with an amplitude of 60 V, frequencies of 0~1000 Hz, and time of 30 ms were adopted to drive the actuator. The sampling frequency of t micrometer was set to 5 kHz. Both the forward and backward speed of the stage c To solve this problem, the discharge circuit was used to improve the response characteristics of piezoelectric elements and achieved good results [28]. Therefore, we also developed a driving circuit with a discharge loop to improve the response characteristics of this proposed actuator and achieved the desired results (see Figure 10). Figure 10 shows the speed characteristics of the stage under different driving frequencies. Here, a series of sawtooth wave signals with an amplitude of 60 V, frequencies of 0~1000 Hz, and a step time of 30 ms were adopted to drive the actuator. The sampling frequency of the laser micrometer was set to 5 kHz. Both the forward and backward speed of the stage changed linearly with the driving frequency when the driving frequency changes from 0 to 1 kHz; however, when the driving frequency was above 1 kHz, the reverse speed increased slowly and reached its maximum speed of 1.8 mm/s at 1.4 kHz and the forward speed reached its maximum speed of 2.5 mm/s at 2.2 kHz. The main reason for the difference was that the push-pull performance of the actuator was not completely symmetric due to the differences between the elongation and contraction characteristics of the piezoelectric stack.
Actuators 2021, 10,39 linearly with the driving frequency when the driving frequency changes from 0 to however, when the driving frequency was above 1 kHz, the reverse speed in slowly and reached its maximum speed of 1.8 mm/s at 1.4 kHz and the forwar reached its maximum speed of 2.5 mm/s at 2.2 kHz. The main reason for the di was that the push-pull performance of the actuator was not completely symmetri the differences between the elongation and contraction characteristics of the piezo stack.

Resolution Test
To achieve precise motion, the stepping operation mode of the actuator is used. By controlling the number of the driving signal, different resolutions

Resolution Test
To achieve precise motion, the stepping operation mode of the actuator is usually used. By controlling the number of the driving signal, different resolutions can be obtained. Figure 11 presents the stepping test results of the stage in open-loop operation mode. Here, the driving signal is a sawtooth wave with a frequency of 100 Hz, and voltage amplitude of 2.2 V. Driven by a signal train of 0.1 s (driving signal cycle number is 10) for a driving period of 5.1 s, the finest resolution of 100 nm was achieved (see Figure 11a). Driven by a signal train of 0.01 s (driving signal cycle number is 1) for a driving period of 5.1 s, the finest resolution of 12 nm was achieved (see Figure 11b). There is a slight difference in the step displacement between the forward and backward directions. The reasons are mainly in addition to the asymmetric push-pull performance of the actuator; there are slight differences in the surface quality of the friction interface between the ceramic ball and the friction plate bonded on the motion table. As described in Section 2, there are two operation modes of the proposed actuator: stick-slip mode and scan mode. As the described operation principle of the actuator, in stick-slip mode, the actuator is driven by the mode of the piezoelectric stack's fast stretch and slow shrink, or slow stretch and fast shrink, which is used to achieve continuous motion over a long distance; in scan mode, the actuator is driven by slowly elongating the piezoelectric stack, which is used to achieve high precision motion within a small displacement. Therefore, the resolution test was carried out to study the minimum displacement output of the stage operated in scan mode. Here, the square wave signal was selected as the driving signal to measure the resolution. To clearly observe the movement of the stage, the period of the square wave was set to 10 s. The voltage amplitude of the drive signal started from 0 V and increased at intervals of 0.2 V. The results show that the displacement response of the stage exhibited a discernible square waveform until the voltage value reached 1.6 V (see Figure 12a); however, the displacement resolution was difficult to predict. When the driving voltage was 2 V, the displacement resolution of 4 nm could be recognized (see Figure 12b). When the voltage reached 3 V, the displacement curve was mostly like the square waveform with a resolution of 5 nm (see Figure 12c). As described in Section 2, there are two operation modes of the proposed actuator: stick-slip mode and scan mode. As the described operation principle of the actuator, in stick-slip mode, the actuator is driven by the mode of the piezoelectric stack's fast stretch and slow shrink, or slow stretch and fast shrink, which is used to achieve continuous motion over a long distance; in scan mode, the actuator is driven by slowly elongating the piezoelectric stack, which is used to achieve high precision motion within a small displacement. Therefore, the resolution test was carried out to study the minimum displacement output of the stage operated in scan mode. Here, the square wave signal was selected as the driving signal to measure the resolution. To clearly observe the movement of the stage, the period of the square wave was set to 10 s. The voltage amplitude of the drive signal started from 0 V and increased at intervals of 0.2 V. The results show that the displacement response of the stage exhibited a discernible square waveform until the voltage value reached 1.6 V (see Figure 12a); however, the displacement resolution was difficult to predict. When the driving voltage was 2 V, the displacement resolution of 4 nm could be recognized (see Figure 12b). When the voltage reached 3 V, the displacement curve was mostly like the square waveform with a resolution of 5 nm (see Figure 12c).

Conclusions
This paper presents a piezoelectric actuator based on stick-slip and scan operation principles for the application of the linear motion stage. Herein, the notable features of the actuator are the flexible hinges, including the composite hinge, pre-pressure adjustment flexible hinge, and transmission flexible hinge, which are designed for decoupling the motion in the action direction of the piezoelectric stack and the direction in which the prepressure is applied. Moreover, the use of two kinds of operation modes, stick-slip mode and scan mode, realizes the function of a continuous long-distance motion and high precision motion within a small distance. Finally, a prototype was fabricated, and the performances of the stage were demonstrated. To improve the response performance of the actuator, the driving circuit with a discharge loop was utilized to drive the actuator. Under the sawtooth wave driving signal with an amplitude of 60 V, the forward speed of the stage reached its maximum of 2.5 mm/s at 2.2 kHz, and the backward speed reached its maximum of 1.8 mm/s at 1.4 kHz. In stick-slip mode, when the actuator was driven by a signal train of 0.01 s (driving signal cycle number is 1 and voltage amplitude is 2.2 V) for a driving period of 5.1 s, the finest resolution of the stage achieved 12 nm. In scan mode, to clearly observe the movement of the stage, a square wave signal with a period of 10 s was selected as the driving signal to measure the resolution. The displacement response of the stage exhibited a discernible square waveform until the voltage value reached 1.6 V. A displacement resolution of 4 nm could be recognized when the driving voltage was 2 V, and the displacement curve was mostly like the square waveform with a resolution of 5 nm when the driving voltage reached 3 V.

Conclusions
This paper presents a piezoelectric actuator based on stick-slip and scan operation principles for the application of the linear motion stage. Herein, the notable features of the actuator are the flexible hinges, including the composite hinge, pre-pressure adjustment flexible hinge, and transmission flexible hinge, which are designed for decoupling the motion in the action direction of the piezoelectric stack and the direction in which the prepressure is applied. Moreover, the use of two kinds of operation modes, stick-slip mode and scan mode, realizes the function of a continuous long-distance motion and high precision motion within a small distance. Finally, a prototype was fabricated, and the performances of the stage were demonstrated. To improve the response performance of the actuator, the driving circuit with a discharge loop was utilized to drive the actuator. Under the sawtooth wave driving signal with an amplitude of 60 V, the forward speed of the stage reached its maximum of 2.5 mm/s at 2.2 kHz, and the backward speed reached its maximum of 1.8 mm/s at 1.4 kHz. In stick-slip mode, when the actuator was driven by a signal train of 0.01 s (driving signal cycle number is 1 and voltage amplitude is 2.2 V) for a driving period of 5.1 s, the finest resolution of the stage achieved 12 nm. In scan mode, to clearly observe the movement of the stage, a square wave signal with a period of 10 s was selected as the driving signal to measure the resolution. The displacement response of the stage exhibited a discernible square waveform until the voltage value reached 1.6 V. A displacement resolution of 4 nm could be recognized when the driving voltage was 2 V, and the displacement curve was mostly like the square waveform with a resolution of 5 nm when the driving voltage reached 3 V.