Optimal design and experiment of a three-axis out-of-plane nano positioning stageusing a new compact bridge-type displacement amplifierHak-Jun Lee, Hyun-Chang Kim, Hyo-Young Kim, and Dae-Gab Gweon Citation: Review of Scientific Instruments 84, 115103 (2013); doi: 10.1063/1.4827087 View online: http://dx.doi.org/10.1063/1.4827087 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/84/11?ver=pdfcov Published by the AIP Publishing

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REVIEW OF SCIENTIFIC INSTRUMENTS 84, 115103 (2013)

Optimal design and experiment of a three-axis out-of-plane nanopositioning stage using a new compact bridge-type displacement amplifier

Hak-Jun Lee, Hyun-Chang Kim, Hyo-Young Kim, and Dae-Gab GweonDepartment of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon,South Korea

(Received 27 February 2013; accepted 10 October 2013; published online 4 November 2013)

This paper presents the development of a new compact three-axis compliant stage employing piezo-electric actuators and a new flexure structure. A proposed stage works out-of-plane (Z, θx, θy) direc-tion. The stage consists of 4 amplification flexures mounted piezoelectric actuators. New structure offlexure reduces height and enhances dynamic performance of stage. To certify excellent performanceof the stage, comparison accomplished between conventional amplification flexure and new compactbridge type flexure. Modeling and optimal design of new type nano positioning stage performed.The optimal design is executed on the geometric parameters of the proposed flexure structure usingSequential Quadratic Programming. Experiments are carried out to verify the static and dynamic per-formance of the stage. The proposed out-of-plane nano-positioning stage has a Z-directional motionrange 190 μm and a θx, θy-directional motion range ±2 mrad. The resolution of the stage is 4 nm,40 nrad, and 40 nrad in the Z-, θx-, and θy-directional motions, respectively. The size of stage is150 × 150 × 30 mm3. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4827087]

I. INTRODUCTION

Recently, many industrial products are getting smallerand smaller. So it is necessary to make small semiconductorswhich are used in manufacturing of many industrial products.A micro/nano technology is a key technology in industrialfield. A micro/nano positioning has become an essential is-sue in modern technologies including biological cell manipu-lation, micro surgery operation, scanning tunnel microscopy,micromachining, atom force microscopy, and so on. These ap-plications have one common task, that is, to manipulate ob-ject with long range, nanometer precision, and high speed.Therefore, the requirements of a nano positioning systemare high resolution, long range, compact size, high dynamicperformance, and multi-axis motion.

A conventional precision positioning consists of revo-lute joints and prismatic/sliding joints, such as a ball-screwmechanism. A ball-screw is commonly utilized to convertrotational motion to linear motion. To achieve higher pre-cision motion of positioning, linear motor and voice coilmotor (VCM) developed to apply nano positioning system.However, these mechanical components have many short-comings, such as backlash, friction, stick-slip, and slow re-sponse. To overcome these shortcomings, a flexure structurewas proposed. A flexure is well suited for precision applica-tion because they have backlash-free, no wear, no friction,and good repeatability. Also they have a monolithic struc-ture that reduces assembly errors. Thus, flexure mechanism iscommonly used in recent nano positioning technology.1 Apartfrom flexure mechanism, piezoelectric actuator is suitable andcommonly used in nano positioning technology. Piezoelec-tric actuator has great advantages, such as sub-nanometerlevel resolution, high dynamic performance, and compactsize. However, piezoelectric actuator has low moving range.This drawback of piezoelectric actuator can be overcomeusing a displacement amplifier.2 Displacement amplifier is

integrated with actuator to make lengthy range. Thus, re-cently ultra-precision positioning system uses piezoelectricactuator with displacement amplifier which is called flexure.There are many stages which have in-plane (X, Y, θ z) direc-tional motion,13, 14 but there are not many 3-DOF out-of-planestages.

There are a large number of researches of ultra-precisionpositioning using piezoelectric actuator with flexure. Xuet al. proposed displacement amplifier for flexure hinge.2

Zhang et al. developed 3-DOF out-of-plane stage which has11.8 μm of z-axis working range and 22.7 arc sec of tiltangle.3 This stage’s dynamic performance is 587 Hz which isthe first natural frequency of the stage. However, this stage hassmall working range. Dong et al. proposed 6-DOF positionerusing piezoelectric actuator.4 This stage has ±5 mm (X, Y,Z), ±3◦(θx, θy, θ z) moving range. This stage has big size andlow resolution. Hu et al. made compact 6-DOF stage whichhas 24.56 μm of z-axis and 1 mrad of tilt axis.5 This stagehas compact size but small moving range. Kim et al. pro-posed compact 3-DOF out-of-plane stage which uses spher-ical hinge and lever amplifier6 but this stage also has smallrange.

As shown in previous research, there is no 3-DOF out-of-plane stage that has long range, high dynamic perfor-mance, and compact size. Also, there is no hollow type out-of-plane stage. A hollow type stage has many usages, such asbiomedical measurement, various transmit type microscope,and wafer alignment.

In this paper, a novel hollow type 3-DOF out-of-planestage using new compact bridge type amplifier is proposed.The stage achieved long range, compact size, and highdynamic performance using novel design of amplifier.Section II introduces the mechanical system of the 3-DOFstage and the new compact bridge type (NCBT) amplifier.Section III presents high performance of NCBT amplifiercomparing conventional bridge type. Modeling of the 3-DOF

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FIG. 1. (a) Schematic diagram of tripod parallel configuration, and (b) proposed semi-parallel mechanism.

stage and optimal design of the stage are presented inSecs. IV and V, respectively. Section VI presents exper-imental results which are carried out to verify the staticand dynamic performance. Finally, conclusions are given inSec. VII.

II. MECHANICAL SYSTEM DESIGN

A. System configuration

The design objective is to develop a compact and piezo-actuated three-axis compliant stage with nanometer resolu-tion. Achieving a large range of motion, we use semi-parallelcompliant mechanism which is consists of four actuationunits. The schematic diagram of the tripod parallel configura-tion is shown in Fig. 1(a).6 The tripod parallel configuration iscommonly used in out-of-plane nano positioning stage. How-

ever, the tripod parallel configuration has some disadvantagesthat are difficulty of control, i.e., small range of motion. Theproposed semi-parallel mechanism is depicted in Fig. 1(b),which is consists of the upper plate to support the specimen,four actuation units, and the base plate to fasten the actuationunits. Each actuation unit is located in each side of a square.The configuration of the proposed semi-parallel mechanismis symmetric to reduce the effects of thermal gradients.

The proposed semi-parallel mechanism was designedand constructed from 6061 aluminum because the materialoffered a good machinability and a high ratio of yield stressto elastic modulus for good repeatability. But 6061 aluminumhas a high thermal expansion coefficient. To overcome thisproblem, we installed an immersion circulator in laboratoryto maintain temperature. The size of the proposed stage is150 × 150 × 30 mm3. The aperture size of the proposedstage is 50 × 50 mm2. The proposed stage is shown in Fig. 2.

FIG. 2. (a) 3D drawing of proposed stage, and (b) deal drawing of proposed stage.

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115103-3 Lee et al. Rev. Sci. Instrum. 84, 115103 (2013)

FIG. 3. Commonly used bridge type amplification mechanism.

Figure 2(a) shows assembly drawing of the stage. Figure 2(b)shows a deal drawing of the stage. The stage consists of abase plate, four actuation units, three sensor jigs, and a upperplate. The base plate is fixed in optical table. The actuationunit consists of a NCBT amplifier and a coupler hinge. Adetail explanation of NCBT amplifier is given in Sec. II B.A sensor jig fastens a capacitance sensor. The sensor jigs arelocated in triangular position of the base plate to measuredisplacement z, θx, θy displacements.

B. Amplification mechanism

The proposed stage uses amplification mechanism toachieve long range motion. To amplify the motion of stage,bridge amplification mechanism is commonly used in flex-ure stage. The commonly used bridge type amplificationmechanism is shown in Fig. 3.

The bridge type amplification mechanism generatesdownward direction displacement when a piezo-electric de-vice expands. The other way, the reverse bridge type amplifi-cation mechanism generates upward direction displacement.

In this study, a new compact bridge type amplifica-tion mechanism (NCBT amplifier) is proposed and shown inFig. 4. Figure 4(a) shows 3D modeling of a NCBT amplifier.The NCBT amplifier consists of two double-faced bridge typeamplifiers: a coupler hinge and a piezoelectric actuator. Piezo-electric actuator is inserted between two double-faced bridge

amplifiers. A front view and a bottom view of NCBT ampli-fier are shown in Figs. 4(b) and 4(c). The coupler hinge is onthe NCBT amplifier. The coupler hinge prevents distortion ofNCBT amplifier in lateral direction when other NCBT am-plifier is actuating. This structure can make small height of awhole stage.

III. CONVENTIONAL BRIDGE TYPE VS. NEWCOMPACT BRIDGE TYPE

The NCBT amplifier has advantages compared with con-ventional bridge type. First, the NCBT amplifier has smallerheight than the conventional bridge type amplifier, sincea height of piezo actuator is reduced by structure. In thissection, comparisons between the NCBT amplifier and aconventional bridge type amplifier will be shown.

A FEM simulation was performed to compare the twoamplifiers. The boundary condition of FEM simulation isshown in Fig. 5. Each amplifier fixed at bottom part and ap-plied 100 N at both side of amplifier. The NCBT amplifier’ssize is 29 mm × 46 mm × 12.5 mm. The conventional bridgetype amplifier’s size is 20 mm × 46 mm × 19.5 mm. Wecompare natural frequency of amplifiers when each ampli-fier’s moving ranges are same. The moving range means up-ward displacement of moving plate when piezoelectric actu-ator was equipped. The moving range is calculated by usingEq. (1) and simulation data:

DMoving = N × DPZT. max

(KPZT

KPZT + Kf lexure

), (1)

where DMoving is the moving range of amplifier, DPZT.max isthe maximum displacement of piezoelectric actuator, and N isthe amplification ratio of amplifier. KPZT and Kflexure are thestiffness of piezoelectric actuator and flexure, respectively.The FEM simulation tool is ProEnginner/Mechanica. Themulti-pass adaptive method and automatic triangular meshelements were used, and polynomial order was up to eight.

Figure 6 shows natural frequency of two amplifiers whenmoving range of each amplifier is varied. As shown in thefigure, there is about 30∼200 Hz difference between conven-tional bridge type amplifier and NCBT amplifier. This showsthat the NCBT amplifier has higher dynamic performancethan the conventional bridge type amplifier. But the naturalfrequency of amplifier is greatly influenced by mass of eachamplifier’s links. Therefore, we compare two amplifiers insame link mass condition.

FIG. 4. (a) 3D drawing of NCBT amplifier, (b) front view of NCBT amplifier, and (c) bottom view of NCBT amplifier.

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FIG. 5. FEM simulation condition of each amplifier.

FIG. 6. Comparison between conventional bridge type amplifier and NCBTamplifier when moving range is varied.

Figure 7 shows natural frequency of two amplifierswhen each amplifier has same mass of link and mov-ing ranges of amplifier are varied. As shown in the fig-ure, there is about 0∼200 Hz difference between con-ventional bridge type amplifier and NCBT amplifier. Thisshows that NCBT amplifier has higher dynamic perfor-mance than conventional bridge type amplifier when theamplifier has 0∼250 um moving range. In order to equalmass of link, we decrease the thickness of forced link.This gives rise to deflect of forced link more than NCBTamplifier.

As shown in Figs. 6 and 7, the NCBT amplifier has bet-ter dynamic performance than the conventional bridge typeamplifier. Thus, the NCBT amplifier has advantages, suchas dynamic performance and size. Proposed 3-DOF out-of-plane stage uses the NCBT amplifier to achieve good dynamicperformance, long range, and compact size. To carry out anoptimal design, modeling of 3-DOF stage is established inSec. IV.

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FIG. 7. Comparison between conventional bridge type amplifier and NCBTamplifier when link mass are same.

IV. MODELING OF THE SYSTEM

Before performing an optimization process, a mathemat-ical model of the proposed system is required. In previousstudies, many mathematical models of flexure were proposed.Paros7 analyzed stiffness of a circular hinge. Smith8 analyzedmotion stiffness of a leaf spring in desired motion. Kang9

derived a 6-DOF stiffness equation for a clamped leaf spring.Koseki10 analyzed compliance matrix of prismatic bar,circular hinge, and cylindrical bar. Ryu11 proposed multi-body dynamics of flexure system. In this study, Koseki’scompliance matrix method and Ryu’s multi-body dynamicsare used.

The proposed system consists of 64 leaf springs, 8 circu-lar hinges, and 49 rigid bodies. So a 6 × 6 compliance matrixis needed for leaf spring and hinge. The compliance matrix ofhinge is shown in Eq. (2).⎡

⎢⎢⎢⎢⎢⎢⎢⎣

δx

δy

δz

θx

θy

θz

⎤⎥⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎣

c1 0 0 0 c3 0

0 c2 0 −c4 0 0

0 0 c5 0 0 0

0 −c4 0 c6 0 0

c3 0 0 0 c7 0

0 0 0 0 0 c8

⎤⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎣

fx

fy

fz

Mx

My

Mz

⎤⎥⎥⎥⎥⎥⎥⎥⎦

. (2)

The compliance of leaf spring and circular hinge is shown inTable I:

k = c−1, (3)

where E is the elastic modulus, G is the shear modulus, andk2 is a geometric parameter by the ratio of b/t.

From Ryu’s modeling algorithm and the compliancematrix, the following equation is obtained:

Mx + Kx = F, (4)

M =

⎡⎢⎣

M1 0. . .

0 MNb

⎤⎥⎦

6Nb×6Nb

, (5)

TABLE I. Compliance of leaf spring and circular hinge.

Leaf spring Circular hinge

c1 = 4l3

Ea3bc1 = 9πr

52

2Ebt52

+ 3πr32

2Ebt32

c2 = 4l3

Eab3 c2 = 12πr2

Eb3

{(rt

) 12 − 1

4

}

c3 = 6l2

Ea3bc3 = 9πr

32

2Ebt52

c4 = 6l2

Eab3 c4 = 12r

Eb3

{π

(rt

) 12 − 2+π

2

}

c5 = lEab

c5 = 1Eb

{π

(rt

) 12 − π

2

}

c6 = 12l

Eab3 c6 = 12Eb3

{π

(rt

) 12 − 2+π

2

}

c7 = 12l

Ea3bc7 = 9πr

12

2Ebt52

c8 = l

Gk2a3bc8 = 9πr

12

4Gbt52

M = [mi mi mi I i

x I iy I i

z

], (6)

K =

⎡⎢⎣

K11 · · · K1Nb

.... . .

...KNb1 · · · KNbNb

⎤⎥⎦

6Nb×6Nb

, (7)

Kij ={∑Nh

k=1 T iTk kkT

ik , f or i = j

−T iTk kkT

j

k , f or i �= j, (8)

F = [f 1 , · · · , f i , · · · , f Nb

]T

6Nb×1 , (9)

x = [q1 , · · · , qi , · · · , qNb

]T

6Nb×1 , (10)

where M and K in Eq. (4) are the system mass matrix andthe system stiffness matrix, respectively. mi is the mass of ithbody. I i

x , I iy , and I i

z are the moments of inertia with respect tolocal coordinate systems. T i

k is the transformation matrix tochange a coordinate from local to global. Nb and Nh representa number of rigid body and a number of hinge of the out-of-plane system. In this study, 49 rigid bodies, 64 leaf springs,and 8 circular hinges were used. One NCBT amplifier consistsof 12 rigid bodies, 12 leaf springs, and 2 circular hinges.

A moving range of the system is obtained by followingequation:

Kx = F. (11)

TABLE II. Static performance verification of proposed stage.

Analytic model FEM simulation Error

Kx 1.838 N/μm 1.852 N/μm 0.756%Ky 1.838 N/μm 1.825 N/μm 0.712%Kz 0.531 N/μm 0.515 N/μm 3.10%Kθx 5.613 × 10−4 Nm/μrad 5.605 × 10−4 Nm/μrad 0.143%Kθy 5.613 × 10−4 Nm/μrad 5.613 × 10−4 Nm/μrad 0.001%Kθz 1.427 × 10−3 Nm/μrad 1.559 × 10−3 Nm/μrad 8.467%

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TABLE III. Verification of dynamic performance.

Analytic model FEM simulation Error

Mode 1 (rotation x) 144.779 Hz 151.726 Hz 4.58%Mode 2 (rotation y) 144.779 Hz 151.75 Hz 4.59%Mode 3 (rotation z) 176.153 Hz 176. 924 Hz 0.436%

Static displacement of all bodies is calculated under agiven K matrix and F vector. Dynamic performance of thesystem is calculated by Eq. (12):

∣∣K − ω2M∣∣ = 0. (12)

Moving range and natural frequency, the most important per-formance of the stage, can be obtained using Eqs. (11) and(12). Tables II and III show a comparison of modeling andFEM simulation. Table II explains static performance andTable III explains dynamic performance. Tables II and III ex-ecuted to verify preciseness of the analytical model. We useProEngineering/Mechanica simulation tool to check the ef-fectiveness of the analytic model.

As shown in Table II, the largest error of static perfor-mance is 8.467%. The analytic model shows the reasonableprediction of stiffness with less than 10%.

Also, the dynamic performance error is shown inTable III. The dynamic performance error is less than 5%.The conditions of analytic model and FEM simulation aresame. Figure 8 shows modes of the system. Mode 1 isrotation x-axis, Mode 2 is rotation y-axis, and Mode 3 isrotation z-axis. The results of dynamic performance werecalculated without the piezoelectric actuator.

V. OPTIMIZATION

The design goal of the system is shown in Table IV. Tosatisfy the design goal, it is necessary to optimize the param-eters for wanted performance. Because of the performanceof the system is greatly influenced by the design parameters,such as leaf spring thickness, length, and width, before opti-mization, it needs the model of the whole system that is pre-sented in Secs. II–IV. The relationship between the designparameter and the performance of the system is very compli-cated. Thus, it is very difficult to determine the optimal de-sign parameters manually. To determine the design parame-ters, a sequential quadratic programming (SQP) method andMATLAB have been used.

TABLE IV. Design goal of the system.

Target spec

Type 3-DOF out-of-plane hollow typeMoving range 200 um(z), ±1 mrad(θx, θy)Resolution ±1 nm(z), ±15 nrad(θx, θy)Size 150 mm × 150 mm × 30 mm

The cost function of the optimal design is determined tomaximize the system bandwidth for improving dynamic char-acteristics. Equation (13) shows the cost function of the opti-mal design for the system. There are five design parameters,all of which are presented in Fig. 9:

Minimize f (l, t, r, t1, gap) =(

1

ωn,1

)2

. (13)

As shown in Fig. 9, l, t, gap relate to the bridge flexurestructure and t1, r relate to coupler hinge. The optimal designobjective is to minimize the cost function. The problem in-cludes several constraints, for example, maximum stress inthe leaf spring, moving range of the system, and distortion ofNCBT amplifier. Thus, it is necessary to make constraints forsuccessful design. In this study, there are three constraints.

First, considering the moving range of the system,Eq. (14) shows the constraint of moving range:

g1 = 200 × 10−6 − N×(38×10−6) × KPZT

KPZT + Kf lexure

≤ 0,

(14)where N is amplification ratio of NCBT amplifier, 200 × 10−6

means moving range of the stage, and 38 × 10−6 means max-imum displacement of piezo actuator. Second, consideringthe maximum stress constraint, Eq. (15) shows the maximumstress constraints:

g2 = σmax − Kstress

(Et

2Lθ + (Fext/2)

bt

)≤ 0. (15)

This equation was obtained by Kim et al.12 Kstress is thestress concentration factor. Deformation angle of the hinge: θ

is obtained from static model. Third, when the stage tilts, theNCBT amplifier should not distort. Equation (16) shows thedistortion constraint of the NCBT amplifier:

g3 = θdistort − 1 × 10−6(rad) ≤ 0. (16)

The SQP method does not vouch for always yielding aglobal minimum. Table V shows the design variable set forthe optimal design and five different starting points of optimal

FIG. 8. Mode shape of proposed stage.

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115103-7 Lee et al. Rev. Sci. Instrum. 84, 115103 (2013)

FIG. 9. Design parameters of proposed stage.

design. The five different starting points verify that the globalminimum had been found.

In Table V, Sopt shows the results of the optimal design.The value of optimal design results is unsuitable for manufac-turing. Thus, reasonable design values (Sdesign) were used inmanufacturing. Table VI shows comparison of systems whichdesign value and optimal value use.

VI. EXPERIMENTS

The NCBT amplifier was manufactured by wire elec-trical discharge machining (WEDM). The material ofproposed stage was used Al6061-T6 whose yield strengthis 276 MPa. Figure 10 shows the manufactured stage. Fourpiezoelectric actuators (P-887.91, PI) and amplifiers (SVR350, Piezomechanik. GmbH) were used to drive the stage.The whole size of the stage is 150 × 150 × 30 mm3. Threecapacitive sensors (CPL190, Lion Precision) were used formeasuring the displacement of the moving part of the stage.The experimental setup is shown in Fig. 11. The controller

used in Fig. 11 was DS1103 (dSPACE corp.), which is a realtime controller.

Figure 12 shows the first resonance frequency of thestage. The result in Fig. 12 was obtained by impulse responseof the system without the piezoelectric actuator. The first res-onance frequency of the stage is 165.5 Hz. The first resonancefrequency of the stage shows a reasonable prediction with er-rors less than 10%.

The experimental results of closed-loop maximum dis-placement are presented in Fig. 13. As shown in Fig. 13(a),the Z-directional motion range of stage is 190 μm. Also, theθy-directional and θx-directional motion ranges are ±2 mradas shown in Figs. 13(b) and 13(c). A PID controller was usedto verify the closed-loop control performance.

Figure 14 shows resolutions of the stage. The Z-directional resolution is 4 nm as shown in Fig. 14(a). Theθ y-directional and θx-directional resolutions are 40 nrad. Allerrors of comparing experimental results with design resultsare less than 10%. The difference between the experimentalresults and design results is the error of the manufacturingprocess.

TABLE V. Optimal design results.

Design variable sets

Symbol Design variables Design range (mm) S1 S2 S3 S4 S5 Sopt Sdesign (mm)

L Length of leaf spring 0.5 ≤ l ≤ 2 0.5 1 1.7 0.9 2 0.996 1T Thickness of leaf spring 0.3 ≤ t ≤ 1.5 1.5 0.5 0.7 1.2 1 0.474 0.5r Radius of hinge 0.3 ≤ r ≤ 1.5 1 1.2 0.5 0.7 0.3 0.517 0.5T1 Thickness of hinge 0.3 ≤ t ≤ 1.5 1.2 1 0.3 0.5 0.7 0.469 0.5Gap Vertical distance between leaf springs 0 ≤gap ≤3 2.5 2 1.5 1 0.5 1.364 1.4

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115103-8 Lee et al. Rev. Sci. Instrum. 84, 115103 (2013)

TABLE VI. Comparison of performance between using optimal values anddesign values.

FEM (optimal values) FEM (design values)

Max displacement (Z) 206.08 μm 195.16 μmMax displacement (θ x, θ y) ±2.32 mrad ±2.19 mradMode 1 (rotation X) 141.873 Hz 151.726 HzMode 2 (rotation Y) 142.026 Hz 151.75 HzMode 3 (rotation Z) 170.33 Hz 176. 924 Hz

FIG. 10. Manufactured stage.

FIG. 11. Experimental setup.

FIG. 12. First resonance frequency of the stage without piezoelectricactuator.

FIG. 13. Motion range of proposed stage.

Figure 15 shows undesirable in-plane (X, Y, θ z) motionof the stage. Actually, this stage does not have guide system.Therefore, the stage can be generated undesirable in-planemotion. We checked undesired motion of the stage using laserinterferometer. Figure 15(a) shows undesired X-axis motion

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115103-9 Lee et al. Rev. Sci. Instrum. 84, 115103 (2013)

FIG. 14. Resolution of proposed stage.

of stage when stage travels 190 um on Z-axis. As shown inFig. 15(a), the run-out motion is less than 100 nm. This iscaused by mirror flatness. Figures 15(b) and 15(c) show un-desired Y and θ z motion of stage when stage travels 190 um

FIG. 15. Undesired motion of proposed stage.

on Z-axis. Undesired Y-axis motion is less than 150 nm. Un-desired θ z-axis motion is less than 0.5 urad. As shown inFig. 15, there are no coupled in-plane motions during trav-eling in Z-axis.

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115103-10 Lee et al. Rev. Sci. Instrum. 84, 115103 (2013)

VII. CONCLUSION

A 3-DOF out-of-plane nano positioning system was pro-posed in this paper. The stage has the aperture to measure abio-specimen. To achieve a long moving motion, a new com-pact bridge type amplification mechanism was developed.The dynamic performance enhancement of a NCBT ampli-fier has been compared with a conventional bridge type am-plifier. The stage consists of four NCBT amplifiers integratedwith piezoelectric actuator. The optimization procedure wasperformed and the performance of the stage was verified byexperiment. The stage has a closed-loop Z-directional mo-tion range of 190 μm, θ y-directional and θ x-directional mo-tion range of ± 2 mrad, and closed-loop resolutions of 4 nm,40 nrad, and 40 nrad in the Z-, θ y-, and θ x-directional mo-tions, respectively. The first resonance frequency of stage is165.5 Hz. Therefore, the new compact bridge type amplifi-cation mechanism can be applied to many applications thatrequire good dynamic performance and nano precision withcompact size.

ACKNOWLEDGMENTS

This research was supported by the World Class Uni-versity (WCU) program through the National Research

Foundation of Korea Funded by the Ministry of Education,Science and Technology (R31-2008-000-10045-0).

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