[14]1.4817695

A novel flexure-based microgripper with double amplification mechanisms formicro/nano manipulationXiantao Sun, Weihai Chen, Yanling Tian, Sergej Fatikow, Rui Zhou, Jianbin Zhang, and Manuel Mikczinski Citation: Review of Scientific Instruments 84, 085002 (2013); doi: 10.1063/1.4817695 View online: http://dx.doi.org/10.1063/1.4817695 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/84/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Particle manipulation using an ultrasonic micro-gripper Appl. Phys. Lett. 101, 163504 (2012); 10.1063/1.4759127 A novel driving principle by means of the parasitic motion of the microgripper and its preliminary application in thedesign of the linear actuator Rev. Sci. Instrum. 83, 055002 (2012); 10.1063/1.4711869 Design and fabrication of a novel microgripper with four-point contact fingers J. Vac. Sci. Technol. A 29, 011007 (2011); 10.1116/1.3520645 Development of novel hybrid flexure-based microgrippers for precision micro-object manipulation Rev. Sci. Instrum. 80, 065106 (2009); 10.1063/1.3147062 Characterization and operation of a mechanically actuated silicon microgripper J. Vac. Sci. Technol. B 24, 3239 (2006); 10.1116/1.2357961

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

REVIEW OF SCIENTIFIC INSTRUMENTS 84, 085002 (2013)

A novel flexure-based microgripper with double amplification mechanismsfor micro/nano manipulation

Xiantao Sun,1 Weihai Chen,1,a) Yanling Tian,2 Sergej Fatikow,3 Rui Zhou,1 Jianbin Zhang,4

and Manuel Mikczinski31School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China2School of Mechanical Engineering, Tianjin University, Tianjin 300072, China3Division of Microrobotics and Control Engineering, University of Oldenburg, Oldenburg 26111, Germany4School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China

(Received 27 May 2013; accepted 23 July 2013; published online 13 August 2013)

This paper describes the design, modeling, and testing of a novel flexure-based microgripper for alarge jaw displacement with high resolution. Such a microgripper is indispensable in micro/nano ma-nipulation. In achieving a large jaw displacement, double amplification mechanisms, namely, Scott-Russell mechanism and leverage mechanism arranged in series, are utilized to overcome the limitedoutput of microgrippers driven by piezoelectric actuators. The mechanical performance of the micro-gripper is analyzed using the pseudo rigid body model approach. Finite element analysis is conductedto evaluate the performance and validate the established models for further optimum design of the mi-crogripper. The prototype of the developed microgripper is fabricated, with which experimental testsare carried out. The experimental results show that the developed microgripper is capable of handlingvarious sized micro-objects with a maximum jaw displacement of 134 μm and a high amplificationratio of 15.5. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4817695]

I. INTRODUCTION

Micro/nano manipulation mainly refers to manipulatingmicro-objects for different assembly and fabrication tasks.1–6

For micro/nano manipulation, the manipulated objects usu-ally have very small sizes, typically ranging from 1 μmto 1 mm, and are difficult to handle. Hence, microgripperswith high precision and dexterity are essential for micro/nanomanipulation. The dexterity implies that an efficient micro-gripper should possess the capacity to implement complexmanipulations especially for microassembly process, whichmainly encompasses picking, grasping, moving, and insert-ing minute objects to obtain a miniature system steadilywithout any damages.7 Different implementations of micro-grippers have been reported.8–11 Of them, the flexure-basedmicrogrippers provides great potential towards ultimately re-alizing high precision manipulation due to the inherent meritsof flexure hinges.12

For the flexure-based microgrippers, research attentionshave been focused on three main issues, namely, micro-manufacturing technologies, actuation techniques, and me-chanical structures here to be considered.13–18 The develop-ment of new micro-manufacturing technologies such as wireelectrical discharge machining (WEDM), surface, bulk andlaser machining have advanced the micrograsping technique,and further enable the miniature, compact, and efficient mi-crogripper to be realized. It is well known that the resolu-tion and positioning accuracy of end-effectors mainly dependon the source of actuation. Various microgrippers with differ-ent actuation techniques have been developed, including elec-tromagnetic, electrothermal, piezoelectric, electrostatic actua-

a)Author to whom correspondence should be addressed. Electronic mail:[email protected].

tions, etc.19–23 Further, the microgrippers driven by piezoelec-tric actuators (PZTs) have been widely adopted to implementhigh precision grasping manipulation due to the inherent ad-vantages of piezoelectric actuator in comparison with otheractuators. However, the output motion of piezoelectric actu-ator is relatively small (typically about 10 μm–20 μm) andat most 1‰ of the length of piezoelectric actuator. In orderto overcome this problem, displacement amplification mecha-nisms are usually employed. In addition, the closed-loop con-trol can be utilized to eliminate the hysteresis and creep be-haviors of piezoelectric actuator and to further improve thepositioning accuracy.24–26

Recently, a number of piezo-actuated microgrippers havebeen developed and widely utilized in micro/nano manipula-tion tasks. Nah and Zhong27 presented a flexure-based micro-gripper with a small displacement amplification ratio of 3.0and a maximum stroke of 170 μm, where a long piezoelec-tric actuator with the length of 91 mm and output displace-ment of 60 μm was employed. Zubir et al.28 developed a hy-brid flexure-based microgripper integrating the corner-filletedflexure hinge and bias spring structure. A maximum outputdisplacement of 25 μm and a displacement amplification ratioof 3.68 were achieved. Salim et al.29 described a new piezo-actuated microgripper based on the UV-lithographic processin the microstructurable and photosensitive glass. Glass mi-crostructures were utilized as solid state hinges of the micro-gripper. Experiments have demonstrated that a grasping-jawdeflection of about 75 μm without grasping forces can be ob-tained under the applied voltage of 100 V. Haddab et al.30

designed a microgripper using smart piezoelectric actuators.The dynamic model for the piezoelectric unimorphs has beendeveloped, and the performance of the microgripper has beenexperimentally investigated.

0034-6748/2013/84(8)/085002/10/$30.00 © 2013 AIP Publishing LLC84, 085002-1

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

085002-2 Sun et al. Rev. Sci. Instrum. 84, 085002 (2013)

However, most of the reported microgrippers have asmall displacement amplification ratio, thus confining the jawdisplacement for various sized micro-objects. In addition, inmany special situations, the limited manipulation space fur-ther restricts the geometrical properties of microgrippers par-ticularly the length, width, and thickness. This will adverselydecrease the jaw displacement to a great extent. Thus, in orderto solve the above problems, a miniature microgripper withlarge amplification ratio is needed. Furthermore, in the appli-cations of flexure-based mechanisms, the most widely usedflexure hinges are right circular, corner-filleted, and ellipti-cal flexure hinge type, respectively.31–34 Compared with othertwo flexure hinges, right circular flexure hinge has better ro-tational accuracy and repeatability due to the smaller drift ofrotational center.35, 36 In this light, it is the best choice as therevolute joint for mechanical structure design of the micro-gripper.

In this paper, a novel piezo-actuated flexure-based mi-crogripper is presented. The microgripper is constructed withdouble amplification mechanisms driven by piezoelectric ac-tuator to achieve a large jaw displacement and high grasp-ing accuracy. Based on the configuration of the developedmicrogripper, the kinematic model is developed, which es-tablishes the relationships between the inputs (displacementand force) and outputs (displacement and force). The dynamicmodel considering the influence of piezoelectric actuator isalso developed using the pseudo rigid body model (PRBM)approach. Subsequently, finite element analysis (FEA) is con-ducted to evaluate the performance and validate the estab-lished models to further refine the geometrical parameters ofparticularly flexure hinges. Finally, the microgripper proto-type is fabricated for performance tests, and the actual grasp-ing manipulation is performed to demonstrate its considerablepotential for the applications in handling various sized micro-objects.

II. MECHANICAL DESIGN

The novel flexure-based microgripper is shown inFig. 1. The entire system consists of a PZT, a motion trans-mission mechanism, a pair of grasping jaws, and a base. Inorder to guarantee the geometrical accuracy of flexure hinges,the microgripper is fabricated using the WEDM technique. Apiezoelectric actuator is fixed to the stationary base and lo-cated against the input terminal of the microgripper. The mi-crogripper is designed symmetrically along the longitudinalaxis of piezoelectric actuator to avoid shear force and bend-ing torque acting on the piezoelectric actuator. The graspingjaws can implement closed and open operations with the aidof the expansion and retraction motions of the piezoelectricactuator, respectively.

Each grasping jaw is connected to the stationary basethrough two sets of serial right circular flexure hinges. Theyare composed of a leverage mechanism (DEF) integratedwithin a parallelogram mechanism (EFGH) and a Scott-Russell mechanism (OABC), which are connected by twoflexure hinges of the connecting linkage CD. With this mech-anism layout, the microgripper can generate a large jaw dis-placement under a small displacement of the actuator. In ad-

FIG. 1. Developed flexure-based microgripper. (a) A prototype, (b)schematic diagram.

dition, the parallelogram mechanisms will ensure the parallelmovement of the grasping jaws, thus avoiding the slippage ofunstructured micro-objects associated with other two grasp-ing manners, namely, angular and vacuum suction graspingmanners.37–39 The preload on the piezoelectric actuator is pro-vided by tightening the screw behind the actuator. In orderto prevent the undesirable rotation and end damage of piezo-electric actuator from the preload screw, a shim with suit-able thickness is placed between the actuator and the preloadscrew.

The piezoelectric actuator (model: AE0505D16F, fromThorlabs, Inc.) adopted in the developed microgripper cangenerate a nominal displacement of up to 17.4 μm at the max-imum drive voltage of 150 V, and can provide a maximumdriving force of 850 N. The normal drive voltage for con-tinuous operation is between 0 and 100 V. The actual outputdisplacement of piezoelectric actuator mainly depends on thestiffness of flexure hinges and the magnitude of preload forcedue to the finite stiffness of piezoelectric actuator. In this case,the larger the stiffness of flexure hinges and preload force,the smaller the output displacement of piezoelectric actuator.Conversely, the smaller preload force will affect the contact

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

085002-3 Sun et al. Rev. Sci. Instrum. 84, 085002 (2013)

condition between the piezoelectric actuator and the input ter-minal of the microgripper, adversely resulting in the degrad-ing of grasping accuracy especially in the high-bandwidthmotion. Thus, the design of flexure hinges and a suitablepreload are very crucial for the development of the flexure-based microgripper.

III. MODELING AND ANALYSIS

A. Kinematic modeling

According to the PRBM approach, from the kinematicpoint of view, each flexure hinge can be equivalent to an idealsingle-axis revolute joint with a torsional spring.40 During thekinematic analysis, the drift of the rotational centers and thestiffness of flexure hinges are not taken into consideration,and the linkages connected by flexure hinges are consideredas rigid bodies. Due to the symmetrical configuration, onlyhalf of the flexure-based microgripper is considered, and thekinematic model is shown in Fig. 2, where i (i = O, A,. . . ,H) denotes the rotational centers of flexure hinges. In addi-tion, it should be noted that the Scott-Russell mechanism is amechanism with identical length of linkages, i.e., lOB = lAB

= lBC.The fundamental structure of the microgripper is a spe-

cial six-bar linkage mechanism as illustrated in Fig. 3. Theinput and output displacements of the microgripper are rep-resented by xin and xout, respectively. Thus, the theoreticaldisplacement amplification ratio Ramp of the microgripper isdefined as

Ramp = 2xout

xin

. (1)

The instantaneous velocities of the points A and F areutilized to find the amplification ratio. The instantaneous cen-ters of the corresponding linkages are first determined by in-tersecting the perpendicular lines of the velocity directions oftwo different points on the linkage as shown in Fig. 3(a). Thus,

FIG. 2. Kinematic model of the flexure-based microgripper with preliminarygeometrical parameters.

FIG. 3. Special six-bar linkage mechanism: (a) the vector diagram and(b) the displacement diagram.

the instantaneous velocities of the points A, C, D, and F canbe obtained, respectively, and given as follows:

vA = w2 · lO1A, (2)

vC = w2 · lO1C = w3 · lO2C, (3)

vD = w3 · lO2D = w4 · lDE, (4)

vF = w4 · lEF, (5)

where w2, w3, and w4 are the instantaneous angular velocitiesof the linkages AC, CD, and EF, respectively.

Based on the geometrical relationships of the microgrip-per, as the deformations of flexure hinges are very small andwithin the micrometer level, the displacement amplificationratio can be simplified and rewritten as

Ramp = 2xout

xin

∼= 2vF

vA= 2ae

bd. (6)

It can be seen from the linear displacement relationshipof Eq. (6) that the microgripper has a constant amplificationratio only depending on the geometrical parameters a, b, d,and e, as shown in Fig. 2.

Assuming that a small displacement xin from the piezo-electric actuator is applied to the input terminal of the micro-gripper, the angle increments θ1 ∼ θ4 of all moving linkagescan be obtained as shown in Fig. 3(b). Furthermore, the rota-tional angles ψO, ψA ∼ ψH of the flexure hinges O, A ∼ Hare separately given as follows:

ψO = θ1 = −ψA = −θ2 = −xin

2b, (7)

ψB = θ1 − θ2 = −xin

b, (8)

ψC = θ2 − θ3 = xin

2b− axin

bc cot γ2, (9)

ψD = θ4 − θ3 = −axin

bd− axin

bc cot γ2, (10)

ψE = ψF = ψG = ψH = θ4 = −axin

bd, (11)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

085002-4 Sun et al. Rev. Sci. Instrum. 84, 085002 (2013)

FIG. 4. Free-body diagrams of the moving linkages for the flexure-based microgripper.

where negative signs of the angles indicate that the rotationalmotion of flexure hinge is along the clockwise direction. γ 2

is the angle made by linkages DE and EF, and satisfies

cot γ2 = d

rD + (tE/2).

B. Static modeling

In this section, the static modeling of the microgripper isperformed with the PRBM approach to describe the force-deflection relationship of flexure hinges. Before the staticmodeling, several design requirements should be first empha-sized in terms of a large jaw displacement, long-term linearityand repeatability, and manufacturing limitation as follows:

Ramp = 2xout

xin

= 19.8, (12)

(σmax)i ≤ σa = σp

λi = O, A, . . . , H, (13)

0.1 mm ≤ ti ≤ 0.3 mm i = O, A, . . . , H, (14)

where σ a is the allowable stress of flexure hinge, σ p is theyield strength of the material, λ is an assigned safety factor (atleast λ ≥ 3), and ti denotes the minimum thickness of flexurehinge.

By transforming the flexure hinge into equivalent rev-olute joint with a torsional spring, the geometrical parame-ters of flexure hinge are linked to a constant torsional stiff-ness k. With reference to Fig. 1, there are two flexure hingeconfigurations within the microgripper mainframe, namely,single-notch right circular flexure hinge from the parallel-ogram mechanism and double-notch right circular flexurehinge from the Scott-Russell mechanism. According to theformulation derived by Paros and Weisbord,41 the rotationalstiffness of two right circular flexure hinges can be estimatedand expressed as

ki = 2Ebt5 / 2i

9πr1 / 2i

i = O, A, . . . , D, (15)

ki =√

2Ebt5 / 2i

9πr1 / 2i

i = E, . . . , H, (16)

where ri and b are the radius and height of the ith flexurehinge, respectively, and E is the elastic modulus of the mate-rial. We assume here that all parts have identical height b.

Consequently, the torque mi, generated at the rotationalcenter of the ith flexure hinge, can be expressed as

mi = −kiψi, (17)

where the negative sign indicates that the torque has the op-posite direction with the rotational motion of flexure hinge.

Consider the PRBM of the microgripper with externalforces on the input terminal and jaw, and torques at each joint,as shown in Fig. 4. The total virtual work of the system δWSYS

can be given as

δWSYS = �Fin · δ�xin + �Fout · δ�xout +H∑

i=O

�mi · δ �ψi, (18)

where the first term denotes the virtual work due to the inputforce �Fin generated by the piezoelectric actuator with a vir-tual displacement δ�xin. The second term signifies the virtualwork due to the output force �Fout from the external environ-ment and the corresponding virtual displacement δ�xout . Thelast term represents the virtual work caused by the torsionalsprings with torque mi and virtual angular deformation δ �ψi .

Based on the principle of virtual work, δWSYS = 0, sub-stituting Eqs. (6)–(11) and (17) into Eq. (18) yields the re-lationship among the input displacement, input force, outputforce, and displacement amplification ratio as

Fin = Ramp

2Fout +

[kO + kA+4kB

4b2+

(1

2b− a

bc cot γ2

)2

kC

+(

a

bd+ a

bc cot γ2

)2

kD +H∑

i=E

a2

b2d2ki

]xin. (19)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

085002-5 Sun et al. Rev. Sci. Instrum. 84, 085002 (2013)

It is noted from Eq. (19) that the larger the amplificationratio, the smaller the output force. During the object manip-ulation for the microgripper, the grasping procedure mainlyconsists of closing both jaws to approach and contact with theobject, and firmly holding the object. Before the jaws contactwith the object, if there are no external disturbances, the out-put force Fout equals to zero and Eq. (19) can be utilized toestimate the input stiffness of the flexure-based microgripper.Subsequently, the jaws contact with the object and then arefixed due to the rigid object, thus the input and output dis-placements will almost no longer change but the output force,in this case, i.e., the reaction force of the grasping force, willgradually increase with the increasing input force.

In order to further evaluate the stress concentration ateach flexure hinge, the reaction forces and torque of each flex-ure hinge have to be determined as shown in Fig. 4. Throughthe static equilibrium analysis of each rigid linkage, the re-lated equations are given as follows:

fAy = Fin, (20)

fDy = fCy = mC + mD

c, (21)

fOy = fBy = Fin − mC + mD

c, (22)

fBx = mO + mB

a− b

afBy, (23)

fDx = fCx = b

afCy − 1

2fBx + b

2afBy + mA − mB + mC

2a,

(24)

fGy = fHy = fFy = g

fFout − mH + mF

f, (25)

fEy = fDy + fFy. (26)

For each flexure hinge, the maximum stress occurs at theouter surface of the thinnest section and can be expressed as

(σmax)i =∣∣∣∣∣4Et

1/2i ψi

3πr1/2i

∣∣∣∣∣ +∣∣∣∣fiy

bti

∣∣∣∣ i = O, A, (27)

(σmax)i =∣∣∣∣∣4Et

1 / 2i ψi

3πr1 / 2i

∣∣∣∣∣ +∣∣∣∣fix

bti

∣∣∣∣ i = B, C, D, (28)

(σmax)i =∣∣∣∣∣2

√2Et

1 / 2i ψi

3πr1 / 2i

∣∣∣∣∣ +∣∣∣∣fiy

bti

∣∣∣∣ i = E, F, G, H. (29)

C. Dynamic modeling

From the dynamic point of view, a piezoelectric actuatorcan be approximately equivalent to an undamped mass-springsystem with a lumped mass mPZT and a linear stiffness kPZT.Due to the utilization of flexure hinges, the microgripper hasnegligible friction and thus almost no damping. Further, withthe stiffness of flexure hinges and the inertia of moving link-ages also being considered, the equivalent dynamic model ofthe flexure-based microgripper can be obtained as shown inFig. 5.

For such an undamped system, Lagrange’s equation canbe utilized to establish the dynamic model and calculate the

FIG. 5. Dynamic model of the flexure-based microgripper.

natural frequencies as

d

dt

(∂T

∂qi

)− ∂T

∂qi

+ ∂V

∂qi

= Fi i = 1, 2, . . . , n, (30)

where T and V represent the total kinetic and potential en-ergies of the system, respectively, qi denotes the generalizedcoordinate, n is the number of generalized coordinates, whichis equal to the degree of freedom (DOF) of the system, andFi represents the generalized nonconservative force. The de-veloped flexure-based microgripper only has one degree offreedom, and the motion relationship of each part has beendiscussed in the kinematic analysis.

Since the kinetic energy is given by the motions of thepiezoelectric actuator and moving linkages, the total kineticenergy of the entire system is expressed as

T = 1

2(min + mPZT)x2

in + IOBw21 + IACw2

2 + ICDw23

+2IEFw24 + mout x

2out , (31)

where min and mout are the mass of the input and output ter-minals of the microgripper, respectively. IOB, IAC, ICD, and IEF

represent the moments of inertia of the linkages OB, AC, CD,and EF with respect to their corresponding instantaneous cen-ters, respectively.

On the other hand, the potential energy is given by theelastic deformations of the piezoelectric actuator and flexurehinges. Thus, the total potential energy of the entire system isexpressed as

V = 1

2kPZTx2

in +H∑

i=O

kiψ2i . (32)

Combining Eqs. (2)–(6), and substituting Eqs. (31) and (32)into Eq. (30) yields the governing differential equation of the

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

085002-6 Sun et al. Rev. Sci. Instrum. 84, 085002 (2013)

system as follows:

Mxin + Kxin = 2Fin − 2ae

bdFout , (33)

where

M = min + mPZT + IOB + IAC

2b2+ 2a2ICD

b2c2 cot2 γ2+ 4a2IEF

b2d2

+2a2e2

b2d2mout ,

K = kPZT + kO + kA + 4kB

2b2+

(√2

2b−

√2a

bc cot γ2

)2

kC

+(√

2a

bd+

√2a

bc cot γ2

)2

kD +H∑

i=E

2a2

b2d2ki .

The term 2Fin represents the total input force from the piezo-electric actuator, and the term −(2ae/bd)Fout the equivalentforce applied to the input terminal by two output forces act-ing on the jaws along the opposite directions.

Thus, the natural frequency of the system can be obtainedas

f = 1

2π

√K

M. (34)

It is noted that in order to improve the dynamic performanceof the flexure-based microgripper, the equivalent mass Mshould be as small as possible, while the stiffness K shouldmaintain a large value. Furthermore, it can be seen thatthe stiffness of the piezoelectric actuator has significanteffects on the total stiffness compared with that of flexurehinges. Thus, the utilization of piezoelectric actuator willfurther enable the flexure-based microgripper to achieve ahigh dynamic response and thus effectively isolate from theexternal vibration disturbances.

IV. FINITE ELEMENT ANALYSIS

In order to further refine the geometrical parametersof particularly flexure hinges and examine the performanceof the flexure-based microgripper, the FEA is conductedwith commercial software ANSYS. Based on the geometri-cal model in Fig. 2, the finite element model is establishedand utilized to investigate the displacements of the jaw as wellas flexure hinges and moving linkages, maximum stress con-centration, stiffness, and dynamic performance, etc. The finiteelement model is meshed using SOLID 95, which is a three-dimensional 20-node solid element. The meshes are refined atflexure hinges to guarantee the computational accuracy.

The actuation source is the displacement applied by thepiezoelectric actuator on the input terminal of the flexure-based microgripper. The displacements of the jaw as well asflexure hinges and moving linkages under the input displace-ment of 10 μm in view of the attainable output of the em-ployed piezoelectric actuator are shown in Fig. 6. It is ob-served that a large jaw displacement of 80.4 μm can be ob-tained, and meanwhile the jaw strictly follows parallel trajec-tory, thus enabling the firm and robust grasping operation witha large range of objects. Figure 7 illustrates the corresponding

FIG. 6. Deformation behavior of the flexure-based microgripper.

stress distribution acting on the microgripper during move-ment. The figure suggests that the stress concentration onlyoccurs at flexure hinges, and the maximum stress of 81.1 MPais generated at the flexure hinge D and is far less than the yieldstrength (503 MPa) of the material. All computational resultsindicate the validity of the established design and modelingapproaches.

After a few refinement procedures, the optimum pa-rameters of flexure hinges for the Scott-Russell mechanism,t = 0.2 mm, r = 0.7 mm, b = 5 mm, the parallelogrammechanism, t = 0.2 mm, r = 1.2 mm, b = 5 mm, and thelinkage connecting the above two mechanisms, t = 0.2 mm,r = 0.8 mm, b = 5 mm, are obtained. The stiffness and dis-placement amplification ratio plots for the input terminal sub-jected to input force and the grasping jaw free are providedby Fig. 8. Due to the effect of inevitable resistance from theparallelogram mechanism on the Scott-Russell mechanism,the actual displacement amplification ratio of approximately8.0 is smaller than the theoretical amplification ratio of 9.9(i.e., Ramp/2). Furthermore, the drift of the rotational centersof flexure hinges during movement is another reason for thisdifference. Thus, it can be concluded that there will be a smalldiscrepancy between the computational and analytical forcedata, as shown in Fig. 8. However, the relationships betweenthe input force and the input displacement remain linear.

It is well known that the modal analysis is a very ef-fective analysis method to examine the dynamic performanceof the flexure-based microgripper. For the free vibration, thefirst mode shape of the microgripper is along the grasping di-rection and the corresponding natural frequency is 426.3 Hz.Considering the significant effect of piezoelectric actuator on

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

085002-7 Sun et al. Rev. Sci. Instrum. 84, 085002 (2013)

FIG. 7. Stress distribution of the flexure-based microgripper.

the dynamic performance in practical applications, a springelement with the same longitudinal stiffness as the actuatoris added at the input terminal, whereas the mass of the inputterminal is scaled up appropriately to compensate for the ex-tra mass caused by the actuator. It is obvious that the naturalfrequency of about 2467.5 Hz for the grasping mode shapeis much larger than the natural frequency without the additionof piezoelectric actuator. In addition, the above computationalresults all coincide with the analytical results of 392.2 Hz and2316.1 Hz, respectively.

V. EXPERIMENTAL TESTS

Experimental tests are carried out to investigate the me-chanical performance of the flexure-based microgripper. Theschematic diagram of the experimental procedure is shown inFig. 9. The basic operation of the flexure-based microgripperis to change the drive voltage from the voltage control unit

FIG. 8. Stiffness and displacement amplification ratio of the flexure-basedmicrogripper.

FIG. 9. Schematic diagram of the experimental procedure.

(model: DWY-3, from CETC 26th Research Institute) to thepiezoelectric actuator to further drive the microgripper. Thedisplacements on the input and output terminals are recordedvia an electronic length measuring instrument (model: TT 80,from Tesatronic, Inc.). For the displacement sensor, nine mea-suring ranges with numerical interval to 10 nm can be se-lected, which is sufficient for accurate data acquisition. Ad-ditionally, the case of grasping a metal wire is performed, andthe grasping process is captured by a CCD camera with highpixel resolution.

The prototype of the flexure-based microgripper is fabri-cated from a piece of high grade aluminum alloy (AL7075-T651) using the WEDM technique with a 200 μm diametermolybdenum wire. Figure 10 shows the experimental setupfor the microgripper measurement, which is composed of thedeveloped microgripper, displacement measuring and voltage

FIG. 10. Experimental setup of the flexure-based microgripper: (a) devel-oped flexure-based microgripper and (b) top view of the flexure-based mi-crogripper.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

085002-8 Sun et al. Rev. Sci. Instrum. 84, 085002 (2013)

supply instruments, etc. In order to reduce the external vibra-tion disturbances, all experimental tests are performed on avibration-isolated optical platform. A stack piezoelectric ac-tuator is employed to provide high resolution actuation inputto the flexure-based microgripper. It can offer stable open-loop operation by changing the drive voltage to implementcontinuous expansion and retraction motions. The preload onthe piezoelectric actuator is provided by tightening the screwagainst the stationary base as shown in Fig. 10(b). It pro-vides the piezoelectric actuator with the essential contact onthe input terminal of the flexure-based microgripper. Further-more, the starting clearance of the jaws can be set throughthe adjustable preload screw. It offers an alternative solutionto grasp a large range of objects with a certain jaw displace-ment which is primarily restricted by the microgripper’s mo-tion capacity. The predesigned initial clearance of the jawsis 500 μm, and the close view of grasping jaws with dif-ferent starting clearances is shown in Fig. 11, which alsohighlights the smooth parallel motion of both jaws to someextent.

In order to evaluate the grasping capacity of the flexure-based microgripper, a grasping operation for a metal wire witha diameter of 250 μm is presented. Fig. 12 provides thor-ough observation of the grasping process, including the non-grasping state and the grasping state. The successful grasp-ing operation demonstrates the considerable potential of theflexure-based microgripper for the applications in handlingmicro-objects. After finishing the grasping operation, the jawswill return to their starting positions with the aid of externalforces from flexure hinges during the retraction process of thepiezoelectric actuator.

The stack piezoelectric actuator consists of many waferelements that are assembled in series, and can be driven us-ing voltage. However, due to the crystalline polarization ef-fect and molecular friction, it exhibits the hysteresis behav-ior when the voltage signal is applied to the piezoelectric ac-tuator. It can be experimentally verified under the open-loopcontrol, as shown in Fig. 13. When a 100 V voltage signal isprovided to drive the piezoelectric actuator, the maximum in-put displacement of the flexure-based microgripper is approx-imately 8.62 μm. It can be seen that due to the effect of thestiffness of flexure hinges and preload force, the actual inputdisplacement is obviously less than the nominal output dis-placement of the piezoelectric actuator. Thus, it makes clearthat the design of flexure hinges and a suitable preload arevery crucial for the development of the piezo-actuated flexure-based mechanisms.

Further, in order to quantitatively describe the hysteresisbehavior of the piezoelectric actuator, the input displacementerror analysis for the drive voltage is shown in Fig. 14. It isobserved that the relationship between the displacement errorand drive voltage is approximately a quadratic function, andthe maximum error reaches up to 1.27 μm at the voltage of50 V. The similar phenomenon occurs at the jaw response, asshown in Figs. 15 and 16. According to the above experimen-tal results, it is determined that the flexure-based microgrip-per has a high amplification ratio of about 15.5, which existsa small discrepancy with the FEA result. The main reason forthis discrepancy is attributed to the measurement errors from

FIG. 11. Different starting clearances for the jaws.

FIG. 12. Grasping process of the flexure-based microgripper: (a) beforegrasping the metal wire and (b) after grasping the metal wire.

FIG. 13. Input displacement versus the drive voltage.

FIG. 14. Input displacement error for the drive voltage.

FIG. 15. Output displacement versus the drive voltage.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

085002-9 Sun et al. Rev. Sci. Instrum. 84, 085002 (2013)

FIG. 16. Output displacement error for the drive voltage.

the contact measurement technique as shown in Fig. 10(b).Another potential error source is associated to the manufac-turing errors from the WEDM technique. However, the resultsare acceptable in terms of the evaluation of the microgripperperformance.

In the future research work, the laser-based measure-ment system will be established to improve the measurementaccuracy. With this non-contact measurement technique, theclosed-loop control can be implemented to eliminate the hys-teresis and creep behaviors of the piezoelectric actuator andto further improve the grasping accuracy of the developed mi-crogripper.

VI. CONCLUSIONS

The design, modeling, and testing of a novel flexure-based microgripper have been presented. The configurationof two amplification mechanisms in series has proven to beeffective in overcoming the limited output of flexure-basedmicrogrippers driven by piezoelectric actuators. The combi-nation of two modeling approaches is proposed to expeditethe realization of the optimum structure. First, the PRBM ap-proach is applied in the kinematic, static, and dynamic mod-eling to predict the primary behavior and response of theflexure-based microgripper using the preliminary geometri-cal parameters. Second, finite element analysis is conductedto further refine the geometrical parameters of particularlyflexure hinges and meanwhile evaluate the validity of the es-tablished models. The prototype of the flexure-based micro-gripper is fabricated using the WEDM technique in order toguarantee the manufacturing accuracy. Experimental studiesshow that the developed microgripper can achieve a parallelgrasping motion for the jaws with variable starting clearances,and has superior performance in grasping various sized ob-jects. In addition, the microgripper has a large jaw displace-ment of 134 μm corresponding to the 100 V drive voltage anda large displacement amplification ratio of 15.5. All experi-mental results indicate that the developed microgripper has agreat potential in the micro/nano scale manipulation tasks.

ACKNOWLEDGMENTS

This work is financially supported by National Natu-ral Science Foundation of China (NSFC) under Grant Nos.

91023036 and 51275018. The authors acknowledge Profes-sor Shaoping Bai from Mechanical and Manufacturing Engi-neering, Aalborg University for his discussion and effort forimprovement of quality.

1Y. Tian, B. Shirinzadeh, D. Zhang, and G. Alici, Mech. Syst. Signal Pro-cess. 23, 957–978 (2009).

2K. Tsui, A. A. Geisberger, M. Ellis, and G. D. Skidmore, J. Micromech.Microeng. 14, 542–549 (2004).

3D. Kang and D. Gweon, Rev. Sci. Instrum. 83, 035003 (2012).4Y. Tian, B. Shirinzadeh, and D. Zhang, Sens. Actuators, A 153, 96–104(2009).

5L. Wang, J. K. Mills, and W. L. Cleghorn, IEEE Trans. Electron. Packag.Manuf. 31, 316–325 (2008).

6E. T. Enikov, L. L. Minkov, and S. Clark, IEEE Trans. Ind. Electron. 52,1005–1012 (2005).

7B. Kim, J. Park, B. Kang, and C. Moon, Rob. Comput.-Integr. Manufact.28, 50–56 (2012).

8R. K. Jain, S. Majumder, and A. Dutta, Rob. Auton. Syst. 61, 297–311(2013).

9X. Li and T. Kagawa, Rob. Comput.-Integr. Manufact. 29, 63–70 (2013).10M. N. M. Zubir, B. Shirinzadeh, and Y. Tian, Mech. Mach. Theory 44,

2248–2264 (2009).11D. H. Wang, Q. Yang, and H. M. Dong, IEEE/ASME Trans. Mechatron.

18, 138–147 (2013).12S. T. Smith, Flexures: Elements of Elastic Mechanisms (Gordon and Breach

Science, New York, 2000).13C. J. Kim, A. P. Pisano, and R. S. Muller, J. Microelectromech. Syst. 1,

31–36 (1992).14Y. Suzuki, Jpn. J. Appl. Phys. 33, 2107–2112 (1994).15M. J. Mosley and C. Mavroidis, J. Dyn. Syst., Meas., Control 123, 103–112

(2001).16Z. W. Zhong and C. K. Yeong, Sens. Actuators, A 126, 375–381

(2006).17M. N. M. Zubir and B. Shirinzadeh, Precis. Eng. 33, 362–370

(2009).18T. Chen, L. Chen, L. Sun, and X. Li, IEEE Trans. Ind. Electron. 56, 996–

1004 (2009).19K. Kim, X. Liu, Y. Zhang, and Y. Sun, J. Micromech. Microeng. 18, 055013

(2008).20Y. Zhang, B. K. Chen, X. Liu, and Y. Sun, IEEE Trans. Rob. 26, 200–207

(2010).21D. H. Kim, M. G. Lee, B. Kim, and Y. Sun, Smart Mater. Struct. 14, 1265–

1272 (2005).22H. Huang, H. Zhao, Z. Yang, J. Mi, Z. Fan, S. Wan, C. Shi, and Z. Ma, Rev.

Sci. Instrum. 83, 055002 (2012).23B. E. Volland, H. Heerlein, and I. W. Rangelow, Microelectron. Eng. 61–

62, 1015–1023 (2002).24Y. Tian, B. Shirinzadeh, and D. Zhang, Precis. Eng. 33, 160–166

(2009).25K. Rabenorosoa, A. N. Das, R. Murthy, C. Clevy, D. Popa, and P. Lutz, in

Proceedings of the ASME’09 International Design Engineering TechnicalConferences and Computers and Information in Engineering Conference,San Diego, USA, 2009.

26Y. Tian, B. Shirinzadeh, and D. Zhang, Microelectron. Eng. 87, 230–241(2010).

27S. K. Nah and Z. W. Zhong, Sens. Actuators, A 133, 218–224(2007).

28M. N. M. Zubir, B. Shirinzadeh, and Y. Tian, Rev. Sci. Instrum. 80, 065106(2009).

29R. Salim, H. Wurmus, A. Harnisch, and D. Hulsenberg, Microsyst. Tech-nol. 4, 32–34 (1997).

30Y. Haddab, N. Chaillet, and A. Bourjault, in Proceedings of the 2000IEEE/RSJ International Conference on Intelligent Robots and Systems,Takamatsu, 2000 (IEEE, 2000), pp. 659–664.

31N. Lobontiu and J. S. N. Paine, J. Mech. Des. 124, 479–484 (2002).32Y. Tian, B. Shirinzadeh, D. Zhang, and Y. Zhong, Precis. Eng. 34, 92–100

(2010).33N. Lobontiu, Compliant Mechanisms: Design of Flexure Hinges (CRC

Press, 2002).34Y. K. Yong, T. F. Lu, and D. C. Handley, Precis. Eng. 32, 63–70 (2008).35Z. Ni, D. Zhang, Y. Wu, Y. Tian, and M. Hu, Precis. Eng. 34, 133–138

(2010).

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46

085002-10 Sun et al. Rev. Sci. Instrum. 84, 085002 (2013)

36S. Zelenika, M. G. Munteanu, and F. Bona, Mech. Mach. Theory 44, 1826–1839 (2009).

37Y. C. Tsai, S. H. Lei, and H. Sudin, J. Micromech. Microeng. 15, 143–156(2005).

38E. J. C. Bos, J. E. Bullema, F. L. M. Delbressine, P. H. J. Schellekens, andA. Dietzel, Precis. Eng. 32, 100–105 (2008).

39W. Chen and W. Lin, in Proceedings of the 2004 IEEE Conference onRobotics, Automation and Mechatronics, Singapore, 2004 (IEEE, 2004),pp. 83–88.

40L. L. Howell, Compliant Mechanisms (Wiley, New York,2001).

41J. M. Paros and L. Weisbord, Mach. Des. 37, 151–156 (1965).

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

132.174.255.145 On: Fri, 26 Jun 2015 10:15:46