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Microsyst TechnolDOI 10.1007/s00542-016-3088-8

TECHNICAL PAPER

Design and experimental validation of a linear piezoelectric micromotor for dual‑slider positioning

Yuxin Peng1,2 · Huiying Wang3 · Shu Wang4 · Jian Wang1 · Jie Cao2 · Haoyong Yu2

Received: 3 March 2016 / Accepted: 20 July 2016 © Springer-Verlag Berlin Heidelberg 2016

simple structure, high accuracy, rapid response, and large working range (Peng et al. 2011, 2012, 2016; Uchino 2008). Recently, linear piezoelectric motors with long motion range, high resolution, and compact size are highly desired in many applications, such as positioning of optical elements, alignment of measurement samples, and manipu-lation of biological specimens. In various fields, dual slid-ers should be positioned independently with a long motion range as well as a high positioning resolution (Uchino 2008; New Scale Technologies, Inc. 2010; Matsusaka et al. 2007; Oh et al. 2010; Lee et al. 2011).

One typical application of dual-slider positioning is the zoom lens with a zoom function and an auto-focus func-tion. In order to change the focal length of the whole sys-tem, two lenses should be positioned independently to con-trol the zoom and auto-focus functions (Lee et al. 2011). Moreover, with the miniaturization of contemporary con-sumer electronics, it is required that the positioning system should have a compact size but remain long motion range and high positioning resolution. Traditionally, one actua-tor is utilized to move a lens, while gears and a cam plate are used to move the other lens, resulting in a constrained motion of the lenses. However, the single-actuator structure is of relatively large size due to the gears and the cam plate (Lee et al. 2011). On the other hand, A number of efforts have been made to position dual sliders in one system in recent years (Uchino 2008; New Scale Technologies, Inc. 2010; Matsusaka et al. 2007; Oh et al. 2010). The most widely-used method is to drive dual sliders independently by two actuators. However, the dual-actuator structure may lead to space consuming and reduplicative mechanical con-struction, which limits further miniaturization of the whole system.

On the other hand, the total displacement of a PZT is extremely small (several micrometers) (Hii et al. 2010;

Abstract In this paper, a linear piezoelectric micromotor for dual-slider positioning by a single piezoelectric ele-ment (PZT) is proposed. A slider 1 and a permanent mag-net are connected by the PZT, and a slider 2 is placed on the permanent magnet by the magnetic force. The slider 1 is a small steel cuboid and can be clamped and released by an electromagnet base. When it is released, it can be driven by impact friction force generated by the PZT. When it is clamped, it keeps stationary, and the slider 2 can be posi-tioned based on the smooth impact friction drive of the micromotor. Both the sliders can be positioned indepen-dently with a long motion range as well as a high position-ing resolution. Due to a single PZT used in the micromotor and miniaturized design of the mechanism, the proposed micromotor has been constructed with a compact size as well as a relatively high loading capacity.

1 Introduction

Piezoelectric motors, which are based on the materials of piezoelectric element Pb(Zr,Ti)O3 (PZT), are attract-ing considerable attention because of merits that include

* Haoyong Yu bieyhy@nus.edu.sg

1 Department of Physical Education and Sports Science, Zhejiang University, Hangzhou 310028, China

2 Department of Biomedical Engineering, National University of Singapore, Singapore 117575, Singapore

3 Southwest Guizhou Vocational and Technical College for Nationalities, Xingyi 562400, China

4 College of Material Science and Engineering, Lanzhou University of Technology, Lanzhou 730050, China

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Zhang et al. 2015; Peng et al. 2014). Many mechanisms have been designed to amplify the small displacement by repeating the step motion of the PZT itself (Higuchi et al. 1990; Okamoto and Yoshida 1998; Peng et al. 2013; Shimizu et al. 2013; Gao et al. 2010; Peng et al. 2015a). Two typical types are impact drive mechanisms (IDMs) and smooth impact drive mechanisms (SIDMs). Both of them utilize an inertial force and a frictional force to drive the moving element over a long motion range, which are also called “inertia motors” in many publications (Higuchi et al. 1990; Okamoto and Yoshida 1998; Peng et al. 2013; Shimizu et al. 2013; Gao et al. 2010). Compared with other mechanisms, inertia motors are superior in respect of compact structure, simple operation, and wide bandwidth, while maintaining the merits of both long motion range and high resolution. However, few inertia motors can posi-tion dual sliders with only a single PZT, and it is always required two inertia motors for positioning dual sliders in one system (Matsusaka et al. 2007). In the work by Lee et al., a novel actuation method based on a single SIDM was proposed to position dual sliders in a compact zoom lens system (Lee et al. 2011). However, it is difficult to design the stick/slip condition and ensure different stick/slip frequencies between the dual sliders. In addition, the dual sliders could be only positioned independently in long stroke mode which was driven by a saw-tooth voltage of an SIDM (Okamoto and Yoshida 1998; Peng et al. 2013, 2015a; Shimizu et al. 2013; Gao et al. 2010). The dual slider would move together due to static friction in high-resolution positioning mode driven by a slowly changed DC voltage (Okamoto and Yoshida 1998; Peng et al. 2013; Shimizu et al. 2013; Gao et al. 2010; Peng et al. 2015a). Therefore, the dual sliders could not be positioned with a high resolution independently and it may limit its wider applications.

Our group has previously proposed a linear motor for positioning dual sliders by a single PZT (Peng et al. 2015b). By using an electromagnet as an IDM-SIDM con-version device, dual sliders could be positioned indepen-dently with a long motion range as well as a high position-ing resolution. The electromagnet also served as a slider 1 and could clamp on the base. However, the electromagnet should be relatively large for generating enough clamping force, which not only increased the size of the whole sys-tem, but also limited the loading capacity for positioning the slider 1. For application in a compact zoom lens sys-tem, it is necessary to design a small-sized and high load-ing capacity motor. Therefore, a miniaturized micromotor for positioning dual sliders is proposed in this paper. A small steel cuboid is used as a slider 1 to miniaturize the motor, which is also possible for mounting enough loads. In addition, an electromagnet base is utilized as a “switch” between the IDM and SIDM, and the steel cuboid can be

released and clamped by the base for positioning the slider 1 and 2, respectively. Therefore, the optimized structure and small-sized design of the micromotor make it possible to be assembled into compact devices. It is also expected the slider 1 has relatively high load capacity and can be suitable for driving zoom lens groups. A prototype has been fabricated to test the working performance and the results demonstrate that the miniaturized micromotor can position dual sliders with relatively high load capacity. Both slid-ers can be positioned with a long motion range as well as a high positioning resolution. The micromotor can be used not only in a compact zoom lens system, but also in the applications which both sliders require a long motion range as well as a high positioning resolution, such as multi-object positioning system, precision manipulator for multi-object, positioning of multi biomedical specimen.

2 Driving principle of dual sliders

As shown in Fig. 1, the linear micromotor is composed of a steel cuboid, a PZT, a permanent magnet and a steel plate. The steel cuboid is placed in a guide way with an electro-magnet base and serves as a slider 1. One end of the PZT is glued to the steel cuboid and the permanent magnet is fixed to the other end. The steel plate is attached on the perma-nent magnet by the magnetic force and serves as a slider 2. By alternating an off–on control of the electromagnet base, the slider 1 can be released and fixed, respectively. Corre-spondingly, the linear micromotor can change the operation modes between IDM and SIDM for positioning the slider 1 and the slider 2, respectively.

The driving principle of the linear micromotor in IDM mode is illustrated in Fig. 2. When there is no voltage applied to the electromagnet base, the slider 1 is released from the base. A saw-tooth voltage with slow increase and rapid decrease is applied to the PZT to move the slider 1 forward. When the applied voltage to the PZT increases slowly, the PZT expands slowly and pushes the permanent magnet with a small acceleration. During this period, the actuation force on the slider 1 is too small to overcome the static frictional force between the slider 1 and the base, and the slider 1 remains stationary on the base. Then, by decreasing the voltage quickly, the PZT shrinks quickly and pulls the slider 1 with a large impulsive force. At this time, the actuation force on the slider 1 owing to the momen-tum of the permanent magnet exceeds the maximum static frictional force of the slider 1. Consequently, the slider 1 moves forward against static frictional force. By repeating these steps, the slider 1 can move forward in theoretically infinite distance continuously. Reversing the sequence of expansion and contraction of the PZT can cause a back-ward movement of the slider 1. The positioning resolution

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of the slider 1 depends on the displacement of one step motion of the micromotor in IDM mode.

On the other hand, when a constant voltage is applied to the electromagnet base, the slider 1 is held in position on the

base. Meanwhile, the linear micromotor turns into an SIDM, and the slider 2 can be positioned subsequently. As shown in Fig. 3, long motion range of the slider 2 can be also driven by a repetitive saw-tooth voltage applied to the PZT. When the applied voltage increases slowly to push the permanent mag-net forward with a low acceleration, the slider 2 can be moved together with the permanent magnet by static frictional force. Then, the applied voltage rapidly decreases and the PZT pulls the permanent magnet with a high acceleration. As a result, the slider 2 cannot follow the fast motion of the permanent magnet and stands still due to its inertia mass. By repeating these steps, the slider 2 can be driven continuously with a long motion range. The moving direction can be reversed by exchanging the expansion and contraction sequence of the PZT. In addi-tion, high positioning resolution can be achieved when a slowly changed DC voltage is applied to the PZT. Since the slider 2 can move together with the movement of the PZT without slip-page, it is expected that slider 2 can demonstrate the same posi-tioning faculty of the PZT itself (nanometer level).

Therefore, by changing the operation modes between IDM and SIDM, the linear micromotor can position the slider 1 and the slider 2, respectively. Both of the sliders can be driven with a long motion range as well as a high positioning resolution. The drive characteristics of the dual sliders in long motion range are dependent on the param-eters of the saw-tooth voltage applied to the PZT, including the driving frequency, amplitude and duty ratio defined as

where T and t1 are the cycle and the rise time of the saw-tooth voltage waveform, respectively (see Fig. 2).

In the research of Furutani et al. 1998, when the linear micromotor is operated in IDM mode, the movement of the slider 1 can be estimated as

(1)Duty ratio =t1

T× 100%.

(2)�x =1

M + m(m�L − ft2

1).

Guide wayElectromagnet base

Slider 1

Slider 2PZT

Permanent magnet

PZT

Guide way

Slider 1(steel cuboid)

Permanent magnet

Electromagnet base

Slider 2(steel plate)

(a)

(b)

Fig. 1 Design of the linear micromotor. a Schematic of the proposed linear micromotor, b exploded perspective view of the micromotor

Fig. 2 IDM mode for position-ing the slider 1

(b) Slow expansion

(c) Rapid contraction

(a) Initial position

Slider 1Slider 2

Permanent magnet

Electromagnet basePZT

Volta

ge

Timet1 t2

T

slow increase

Volta

ge

Time

rapid decrease

X

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where M is the mass of the slider 1, m is the mass of the permanent magnet, f is the frictional force between the slider 1 and the base, Δx is the movement of the slider 1, and ΔL is the deformation of the PZT. Therefore, when the slider 1 is designed lighter and smaller, it is expected that the movement of the slider 1 can be larger in the rise time of the saw-tooth voltage waveform. Consequently, the velocity of the slider 1 can be improved. It can have a higher load capacity and can remain high velocities when the load on the slider 1 increases.

Figure 4 shows the prototype of the linear micromo-tor. To achieve a compact size of the micromotor and have enough load capacity to mount small-sized zoom lens groups, the slider 1 is made of a small steel cuboid with a size of 4 mm (L) × 5 mm (W) × 10 mm (H) and weight of 1.55 g, and the size of the slider 2 is 15 mm (L) × 8 mm (W) × 1 mm (H). To obtain a high bandwidth of the micro-motor, it is required the permanent magnet should be thin and the PZT should be short. In our design, the slider 2 is supported by a permanent magnet with a size of 4 mm (L) × 4 mm (W) × 1 mm (H). A PZT with a size of 4.5 mm (L) × 3.5 mm (W) × 5 mm (H) is employed to connect the electromagnet and the permanent magnet together. It is confirmed experimentally that the driving frequency of

the PZT voltage can be set within wide bandwidths up to 73 kHz, and the stroke of the PZT is approximately 4.6 μm with an applied voltage of 90 V. In order to measure the displacement of the dual sliders, a mirror 1 and a mirror 2 are mounted to the sliders 1 and 2, respectively.

3 Experimental results

3.1 Experimental setup

To investigate the driving characteristics of the dual sliders, an experimental setup was established as shown in Fig. 5. The linear micromotor was placed on a guide way with an electromagnet base. The guide way was fixed by a jig. Two probes of an optical fiber displacement sensor were used to measure the movement of the sliders 1 and 2, respec-tively. The size of the guide way is 30 mm (L) × 16 mm (W) × 20 mm (H). Consequently, the motion range of the slider 1, which is determined by the length of guide way and that of the slider 1, is evaluated to be 14 mm. The

(a) Slider 1 fixed

(b) Slow expansion

(c) Rapid contraction

Volta

ge

Time

slow increase

Volta

ge

Time

rapid decrease

X

Fig. 3 SIDM mode for positioning the slider 2

PZTSlider 1

Slider 2

Permanent magnet

Mirror 2Mirror 1

X

Fig. 4 Fabricated linear micromotor

X

Mirror 2

Guide way

Electromagnet base

Optical fiber displacement sensor (Probe 1)

Optical fiber displacement sensor (Probe 2)

Mirror 1

Fig. 5 Experimental setup for positioning of the sliders 1 and 2

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motion range of slider 2 is also calculated to be 14 mm, which is determined by the length of the slider 2 and that of the permanent magnet. The relative distance between the sliders 1 and 2 is dependent on the length of the dual sliders and the height of the PZT, which is evaluated to range from 1 to 15 mm.

3.2 Positioning of the slider 1

To investigate the driving characteristics of the slider 1, the linear micromotor was operated in IDM mode and there was no voltage applied to the electromagnet base. Figure 6 shows the relationship between the frequency of the PZT voltage and the velocity of the slider 1. The amplitude of the voltage was set to 30 V and the duty ratio was set to 80 %. The slider 1 began to move when the frequency reached 55 kHz. The maximum velocity was observed to be 9.6 mm/s at 68 kHz. In addition, the velocity reduced to zero at 70 kHz. This is because the output displacement waveform of PZT was distorted into a sinusoidal waveform in the vicinity of resonance (Peng et al. 2013, 2015a).

It should be noted that frictional force was also induced between the permanent magnet and the slider 2 in IDM mode. As shown in Fig. 7a, the duty ratio of the voltage was set to 80 % and the driving frequency was set to 60 kHz at 30 V. It was observed that no crosstalk error was intro-duced to the slider 2. However, crosstalk began to occur when the driving frequency increased to 62 kHz. As shown in Fig. 7b, when the slider 1 was moved 17 μm in the posi-tive direction, the slider 2 moved 4.5 μm in the negative direction, which means that the positioning crosstalk of the slider 2 was approximately −26.5 % of the movement of the slider 1. The results indicated that that slider 1 could be driven at 60 kHz without crosstalk error caused to the slider 2.

Figure 8 shows the relationship between the duty ratio of the applied voltage and the velocity of the slider 1. The driving frequency was set to 60 kHz and the voltage was set to 30 V, which caused no crosstalk error to the slider

2. Since the driving characteristics of the slider 1 in the negative direction was almost the same as that in the posi-tive direction, only the driving characteristics in the posi-tive direction was investigated in the research. It can be seen that the slider 1 kept stationary when the duty ratio was from 50 to 60 %. When the duty ratio became larger than 60 %, the slider 1 moved to the positive direction and reached the maximum velocity of 6 mm/s at 80 % of the duty ratio. The reason why the velocity decreased after 80 % was due to the relatively large distortions of the PZT displacement waveforms at higher duty ratios.

Then, the relationship between the amplitude of the PZT voltage and the velocity of the slider 1 was also inves-tigated. The driving frequency was set to 60 kHz and the

-2

0

2

4

6

8

10

12

50 55 60 65 70

Vel

ocity

mm

/s

Frequency kHz

Fig. 6 Relationship between frequency of the PZT voltage and velocity of the slider 1

(a)

(b)

-5

0

5

10

15

20

Dis

plac

emen

t µm

Time 0.5 ms/div

Displacement of the slider 1

Displacement of the slider 2

-5

0

5

10

15

20

Dis

plac

emen

t µm

Time 0.5 ms/div

Displacement of the slider 1

Displacement of the slider 2

Fig. 7 Crosstalk of the slider 2 when positioning the slider 1. a At 60 kHz, b at 62 kHz

-2

0

2

4

6

8

50 60 70 80 90 100

Vel

ocity

mm

/s

Duty ratio %

Fig. 8 Relationship between duty ratio of the PZT voltage and veloc-ity of the slider 1

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duty ratio was set to 80 %, which caused no crosstalk error to the slider 2. It can be seen from Fig. 9 that the velocity increased with the increase of the amplitude of the voltage from 6 to 30 V. The minimum voltage for moving the slider 1 was 9 V, which corresponded to a minimum velocity of 1 mm/s. It means that one step motion of the slider 1 was approximately 17 nm.

To confirm the loading capacity of the slider 1 in Z axis, experiments were carried out to verify the velocity of the micromotor at different loads. As shown in Fig. 10, the velocities of the micromotor were measured when differ-ent loads were applied on the slider 1. The duty ratio of the voltage was set to 80 % and the driving frequency was set to 60 kHz at 30 V. It can be seen that the velocity of the slider 1 decreased when the load became heavier. When the load increased as large as 40 g, the slider 1 could not move any more. The results confirmed the slider 1 has a maximum loading capacity of 35 g. To make a comparison of load performances with and without modification of the slider 1, experiments were carried out to verify the loading capacity of the slider 1 of the previous motor (Peng et al. 2015b). When the duty ratio of the voltage was set to 80 % and the driving frequency was set to 60 kHz at 30 V, which were the same as the parameters of the new micromotor.

It can be seen that the velocity of the slider 1 was about three times lower than that of the new micromotor. The maximum loading capacity of the slider 1 of the previous motor was observed to be 20 g. In addition, experiments of the slider 1 of the previous motor were also carried out when the duty ratio of the voltage was set to 90 % and the driving frequency was set to 40 kHz at 30 V, which were the parameters at its maximum velocity. It was observed that the velocities of the slider 1 were lower than that of the new micromotor. The slider 1 could not move when the load increased as 30 g. It means that the slider 1 of the pre-vious motor has a maximum loading capacity of 25 g. The results confirmed that moving velocity as well as the load-ing capacity of the slider 1 of the linear micromotor has been improved due to the new construction.

3.3 Positioning of the slider 2

On the other hand, to investigate the driving characteris-tics of the slider 2 in SIDM mode, a voltage of 18 V was applied to the electromagnet base to clamp the slider 1. Figure 11 shows the relationship between the frequency of the PZT voltage and velocity of the slider 2. It can be seen

-1

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35

Vel

ocity

mm

/s

Voltage V

Fig. 9 Relationship between amplitude of the PZT voltage and velocity of the slider 1

0

1

2

3

4

5

6

7

0 10 20 30 40 50

The new micromotor (30V, 80%, 60kHZ)The previous motor (30V, 80%, 60kHZ)The previous motor (30V, 90%, 40kHZ)

Vel

ocity

mm

/s

Load g

Fig. 10 Relationship between the load and velocity of the slider 1

-1

0

1

2

3

4

0 2 4 6 8 10

Vel

ocity

mm

/s

Frequency kHz

Fig. 11 Relationship between frequency of the PZT voltage and velocity of the slider 2

-1

0

1

2

3

4

50 60 70 80 90 100

Vel

ocity

mm

/s

Duty ratio %

Fig. 12 Relationship between duty ratio of the PZT voltage and velocity of the slider 2

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that the slider 2 began to move at 2 kHz and reached to the maximum velocity of 2.8 mm/s at 8 kHz.

The relationship between the duty ratio of the applied voltage and the velocity of the slider 2 in the positive direc-tion was also investigated when the driving frequency was set to 8 kHz and the voltage was set to 30 V. As shown in Fig. 12, the slider 2 kept stationary when the duty ratio was from 50 to 65 %. When the duty ratio became larger than 65 %, the slider 2 moved to the positive direction and reached the maximum velocity at 80 % of the duty ratio.

Figure 13 shows the relationship between the amplitude of the PZT voltage and the velocity of the slider 2. The driving frequency was set to 8 kHz and the duty ratio was set to 80 %. The minimum voltage for moving the slider 2 was observed to be 9 V. When the voltage became larger, the slider 2 began to move and the velocity increased linearly with the increase of the amplitude of the voltage from 9 to 30 V.

The loading capacity of the slider 2 in Z axis was also confirmed by experiments. As shown in Fig. 14, the veloci-ties of the slider 2 were measured when different loads were applied on the slider 2. It was verified that velocity of the slider 2 decreased when the load became heavier. When

the load increased as large as 20 g, the slider 2 could not move any more. The results confirmed the maximum load-ing capacity of the slider 2 is approximately 18 g.

To know the positioning resolution of the slider 2, small step voltages with amplitude of 0.6 V were applied to the PZT. As can be seen in Fig. 15, the stage can make a step motion down to 12 nm. It was noted that the resolution of the slider 2 was higher than that of the slider 1. This is because the static friction force played a negative role in IDM mode and required to be overcome by a relatively large voltage, which may cause a larger displacement of the slider 1. Conversely, the static friction force played a posi-tive role during the actuating movement in SIDM mode. Therefore, even an extremely small voltage could move the slider 2 with a higher resolution 17.

In addition, to confirm whether crosstalk error was intro-duced to the slider 1 in SIDM mode, the movement of the dual sliders was measured simultaneously. As shown in Fig. 16, there was almost no crosstalk or vibration induced to the slider 1 when the slider 2 was moved in the positive direction. It means that the slider 1 could keep stationary when positioning the object 2.

-1

0

1

2

3

4

0 5 10 15 20 25 30 35

Vel

ocity

mm

/s

Voltage V

Fig. 13 Relationship between amplitude of the PZT voltage and velocity of the slider 2

0

1

2

3

4

0 5 10 15 20 25

Vel

ocity

mm

/s

Load g

Fig. 14 Relationship between the load and velocity of the slider 2

-20

0

20

40

60

Dis

plac

emen

t nm

Time 10 ms/div

Fig. 15 High-resolution step positioning of the slider 2

Dis

plac

emen

t 5 µ

m/d

iv

Time 0.5 ms/div

Displacement of the slider 2

Displacement of the slider1

Fig. 16 Crosstalk of the slider 1 when positioning the slider 2

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4 Conclusions

In this paper, a linear micromotor was introduced for posi-tioning dual sliders by a single PZT. The slider 1 is made of a small steel cuboid in order to achieve a compact size and a high load capacity. By releasing and fixing the slider 1, the sliders 1 and 2 could be positioned in IDM and SIDM modes, respectively. Experimental results showed that both the sliders can achieve a long motion range as well as a high positioning resolution. The load capacity of the slid-ers 1 and 2 were confirmed to be 35 and 18 g, respectively. The methods of avoiding crosstalk errors of the dual-slider positioning have been also investigated and discussed. It was verified that there was no crosstalk for the slider 2 in IDM mode at 60 kHz, and no crosstalk was induced to the slider 1 when positioning the slider 2. Owing to a single PZT used in the micromotor and miniaturized design of the structure, the proposed micromotor has been constructed with a compact size as well as a relatively high loading capacity, which is suitable for small-space applications.

It should be noted that this paper is only a summary of the first step of the research on a miniaturized micromotor for dual-slider positioning. For verifying the micromotor in a specific small-space application, it is planned to integrate two small optical lenses into the developed micromotor, which is the next step of the research work. The design of the zoom lens system, the assembly of the zoom lens sys-tem and the micromotor, and verification of the whole sys-tem, will be carried out as our future work.

Acknowledgments This research was support in part by the Singa-pore MINDEF-NUS Joint Applied R&D Cooperation Programme (JPP) under Project No. MINDEF/NUS/JPP/14/02/02.

References

Furutani K, Higuchi T, Yamagata Y, Mohri N (1998) Effect of lubrica-tion on impact drive mechanism. Precis Eng 22(2):78–86

Gao W, Sato S, Arai Y (2010) A linear-rotary stage for precision posi-tioning. Precis Eng 34(2):301–306

Higuchi T, Yamagata Y, Furutani K, Kudoh K (1990) Precise posi-tioning mechanism utilizing rapid deformations of piezoelectric

elements. In: Micro Electro Mechanical Systems, 1990. Proceed-ings, an investigation of micro structures, sensors, actuators, machines and robots. IEEE, 1990. IEEE, pp 222–226

Hii KF, Vallance RR, Mengüc MP (2010) Design, operation, and motion characteristics of a precise piezoelectric linear motor. Precis Eng 34(2):231–241

Lee J, Kwon WS, Kim KS, Kim S (2011) A novel smooth impact drive mechanism actuation method with dual-slider for a com-pact zoom lens system. Rev Sci Instrum 82(8):085105

Matsusaka K, Ozawa S, Yoshida R, Yuasa T, Souma Y (2007) Ultra-compact optical zoom lens for mobile phone. In: Proceedings of SPIEIS&T Electronic Imaging, pp 650203-650203-10

New Scale Technologies, Inc. (2010) Tiny optical zoom module for higher-resolution imaging in smaller devices. http://www.newscaletech.com/app-notes/zoom-module.php. Accessed 03 Mar 2016

Oh CH, Choi JH, Nam HJ, Bu JU, Kim SH (2010) Ultra-compact, zero-power magnetic latching piezoelectric inchworm motor with integrated position sensor. Sens Actuat A Phys 158(2):306–312

Okamoto Y, Yoshida R (1998) Development of linear actuators using piezoelectric elements. Electron Commun Jpn (Part III Fundam Electron Sci) 81(11):11–17

Peng Y, Kaneko J, Arai Y, Shimizu Y, Gao W, Okamoto K, Chiba M, Aisawa S (2011) A linear micro-stage with a long stroke for precision positioning of micro-objects. Nanotechnol Precis Eng 9:221–227

Peng Y, Ito S, Shimizu Y, Gao W (2012) A micro-stage for linear-rotary positioning. Key Eng Mater 523–524:650–655

Peng Y, Ito S, Sakurai Y, Shimizu Y, Gao W (2013) Construction and verification of a linear-rotary microstage with a millimeter-scale range. Int J Precis Eng Manuf 14:1623–1628

Peng Y, Ito S, Shimizu Y, Azuma T, Gao W, Niwa E (2014) A Cr-N thin film displacement sensor for precision positioning of a micro-stage. Sens Actuat A Phys 211:89–97

Peng Y, Peng Y, Gu X, Wang J, Yu H (2015a) A review of long range piezoelectric motors using frequency leveraged method. Sens Actuat A Phys 235:240–255

Peng Y, Cao J, Guo Z, Yu H (2015b) A linear actuator for precision positioning of dual objects. Smart Mater Struct 24(12):125039

Peng Y, Cao J, Liu L, Yu H (2016) A piezo-driven flapping wing mechanism for micro air vehicles. Microsyst Technol. doi:10.1007/s00542-015-2762-6

Shimizu Y, Peng Y, Kaneko J, Azuma T, Ito S, Gao W, Lu TF (2013) Design and construction of the motion mechanism of an XY micro-stage for precision positioning. Sens Actuat A Phys 201:395–406

Uchino K (2008) Piezoelectric actuators 2006: expansion from IT/robotics to ecological/energy applications. J Electroceram 20(3–4):301–311

Zhang Y, Lu TF, Peng Y (2015) Three-port equivalent circuit of multi-layer piezoelectric stack. Sens Actuat A Phys 236:92–97