Performance quantification of conducting polymer actuators for real applications

13 Pages·2017·0.53 MB·English

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Faculty of Engineering and Information
Faculty of Engineering - Papers (Archive)
Sciences
1-2-2007
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Gursel Alici
University of Wollongong, [email protected]
Nam N. Huynh
University of Wollongong, [email protected]
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https://ro.uow.edu.au/engpapers/364
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Alici, Gursel and Huynh, Nam N.: Performance quantification of conducting polymer actuators for real
applications: a microgripping system 2007.
https://ro.uow.edu.au/engpapers/364
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IEEE/ASMETRANSACTIONSONMECHATRONICS,VOL.12,NO.1,FEBRUARY2007 73
Performance Quantification of Conducting Polymer
Actuators for Real Applications: A
Microgripping System
GurselAliciandNamN.Huynh
Abstract—In this paper, we report on modeling, characteriza- electrochemomechanicalpropertiesofthepolymers[10]–[12].
tion,andperformancequantificationofaconductingpolymeractu- Thechangeinthevolumegeneratesabendingdisplacement—
ator,drivingarigidlinktoformeachfingerofatwo-fingergripping
theelectrochemicalenergyisconvertedintomechanicalenergy.
system,whichiswhatwecallamicrogrippingsystem.Theactuator,
Asaresult,considerableamountofresearchhasbeendevoted
whichconsistsoffivelayersofthreedifferentmaterials,operates
in a nonaquatic medium, i.e., air, as opposed to its predecessors. to modeling and understanding their behavior in order to im-
Afterthebendingdisplacementandforceoutputsofasinglefinger provetheirsynthesisconditionsforuseasreliableactuatorsand
aremodeledandcharacterizedincludingtheeffectofthemagni- sensors for new cutting applications ranging from biomedical
tude and frequency of input voltages, the nonlinear behavior of
devicestomicromanipulators[4][7][13].Zhouetal.[4]have
thefingerincludinghysteresisandcreepeffectsisexperimentally
reportedonthreetypesofpolymeractuatorsincludingioniccon-
quantified,andthenaviscoeleasticmodelisemployedtopredict
thecreepbehavior.Theexperimentalandtheoreticalresultspre- ducting polymer film actuator, polyaniline actuator, and pary-
senteddemonstratethatwhilethehysteresisisnegligiblysmall,the lenethermalactuator.Theyhavepresentedtheirfabricationand
creepissignificantenoughsoasnottobeignored.Theresponseof initialperformanceresults.ZhouandLi[14]havereportedon
theactuatorandthefingerunderstepinputvoltagesisevaluated,
theMEMS-basedfabricationofcantilevermicrostructurescon-
andfoundthattheactuatordoesnothaveanytimedelay,butonly
sistingofAu/Nafion/Autrilayersonsiliconsubstratesinorder
a large time constant. Two of the fingers are assembled to form
amicrogrippingsystem,whosepayloadhandlingandpositioning to construct microgrippers operating in aqueous media. Smela
abilityhasbeenexperimentallyevaluated.Itcanliftupto50times etal.[7]havepresentedthedevelopmentandperformanceout-
itsweightunder1.5V.Thepayloadhandledwasasphericalobject comesofpolypyrrole(PPy)andAubilayerconductingpolymer
coveredwithindustrialtypetissuepaper.Thefrictioncoefficient
actuators operating in electrolyte solutions. As an extension
between the object and the carbon fiber rigid link has been de-
of this study, Jager et al. [13] have fabricated a serially con-
termined experimentally and used to estimate the contact force.
All the theoretical and experimental performance quantification nectedmicromanipulatortopick,move,andplace100-μmglass
resultspresenteddemonstratethatconductingpolymeractuators beads.
canbeemployedtomakefunctionalmicrosizedroboticdevices. Thispaperispartofanongoing-projectontheestablishment
Index Terms—Actuators, electroactive polymer actuators, of manipulation systems such as grippers and planar mech-
flexure-based devices, micromanipulation, system identifica- anisms, articulated with the fourth generation PPy actuators
tion/characterisation. fabricated in the Intelligent Polymer Research Institute at the
UniversityofWollongong[2].Conductingpolymershavemany
promising features including low actuation voltage, operation
I. INTRODUCTION
inaquaticmediumsandinair,lowcost,andhighforce–output
ASPOTENTIALelectromechanicalactuatorsandsensors, weightratio.Theirmaindrawbackistheirlowspeedofresponse
which are very suitable for miniaturization, conducting andnonlinearityduetotheactuationprinciple,whichisbasedon
polymer actuators have attracted the attention of many re- masstransfer.Theapplicationofconductingpolymeractuators
searchersinthelastdecade[1]–[9].Acomprehensiveaccountof is an emerging field, as researchers begin to harness the bene-
polymeractuatorsisgivenin[1]and[9].Theyhaveacompos- fits of their material properties, which are greatly enhanced at
itestructurewithpolymerlayersseparatedfromeachotherwith smallerscales[9].Possiblefutureapplicationsincludeartificial
an insulator. When the right stimulus, which is usually a very musclesandawidevarietyofsensorsandactuatorsinbiomed-
smallvoltage,typically1Voracurrent,isappliedtothepoly- icalsystems[6]andmicro/nanomanipulationsystems[15].As
mer layers, a volume expansion and contraction occurs due to theseactuatorsdonotcontainanyrollingandslidingelements,
theyaresuitableformicro/nanomanipulationtasks,whichre-
quiremotionaccuracyoftheorderof0.05–0.1μm(50–100nm).
ManuscriptreceivedNovember20,2005;revisedApril26,2006.Recom-
mendedbyTechnicalEditorJ.P.Desai.Thisworkwasfundedinpartbya In our previous studies [16]–[20], we reported on developing
UniversityResearchCouncil(URC)grant. various mathematical models to predict the bending behavior
G.AliciiswiththeSchoolofMechanical,MaterialsandMechatronicEn-
of the conducting polymer actuators, and employing the mod-
gineering, and the ARC Center of Excellence on Electromaterials Science,
UniversityofWollongong,NSW2522,Australia(e-mail:[email protected]). elstooptimizetheirtopologywithhighforceanddisplacement
N. N. Huynh is with the School of Mechanical, Materials and Mecha- outputs.
tronicEngineering,UniversityofWollongong,NSW2522,Australia(e-mail:
In this paper, we report on the performance quantification
[email protected]).
DigitalObjectIdentifier10.1109/TMECH.2007.886256 of a PPy-based conducting polymer actuator driving a rigid
1083-4435/$25.00©2007IEEE
74 IEEE/ASMETRANSACTIONSONMECHATRONICS,VOL.12,NO.1,FEBRUARY2007
Fig.2. Structureanddimensionsoftheroboticfinger.(a)Frontviewandtop
view.(b)Crosssectionoftheactuatorpart(nottoscale).
Fig. 1. (a) Schematic structure of the conducting polymer actuator.
(b)Schematicrepresentationofthebendingprinciple.
andtheactuatorbends.Fortheactuatoremployedinthisstudy,
theredoxprocessisdescribedby
carbonfiberlink,whichconstituteseachfingerofamicrogrip-
ping system with the dimensions of (5-mm actuator + 5-mm
oxidationreduction
rigidlink)×1mm×0.17mm.Withreferencetothesedimen- P(oPxyid+atPioFn6s−t+atee)− ←−−−−−−−−−−→P(rePduyc0e+dPstaFte6−) . (1)
sions and its fabrication process, the microgripping system is
notMEMS-based.Itmustbenotedthatsurfacemicromachining,
bulk micromachining (i.e., etching), bonding alone, electrode- TheredoxprocessoccurssimultaneouslyonboththePPylay-
position,photolithography,andotherreplicationtechniquesare ers;whileonelayerisoxidized,theotherisreduced,andvice
usedtomakeMEMS-basedmicrodevices/microstructures.The versa.Withreferenceto(1),thedisplacementofPF−ionsinthe
6
performanceevaluationhasbeenrealisedintermsofthebend- PPy layers causes material strain through a number of effects.
ingdisplacementandforceoutput,andtheirnonlinearbehavior Oneistheeffectofthegainorlossofionvolumecausingvol-
including hysteresis and creep. The actuator has been used in umeexpansionorcontractioninthePPylayers.Themovement
arealapplicationtoarticulateatwo-fingergripper.Theexper- of solvent molecules due to osmotic pressure, which accom-
imental and estimated results attest that electroactive polymer pany the ion diffusion, also contributes to the volume change
actuatorsaresuitabletomakemicromanipulationdevicessuch inthePPylayers.Theotherfactoristheresultantelectrostatic
as a gripper, which can handle as much as 50 times its total forces between the displaced ions and the polymer backbone
mass. thatcausethePPylayerstoexpandorcontract.AsthetwoPPy
layersundergoopposingstrains,abendingmomentisinduced,
generatingthedeflectionoftheactuator.
II. POLYMERACTUATORDRIVINGARIGIDLINK
The polymer actuator and the rigid link form a monolithic
composite structure, where the polymer section serves as the B. RoboticFinger
actuatorandaflexurejoint—likeanactiveflexurejoint,andthe
The structure of the robotic finger made up of the polymer
rigidlinkasapayloadcarriedbytheactuator.
actuatorandcarbonfiberisshowninFig.2.
Theconductingpolymerpartofthefingerworksasanactua-
A. ActuationStructureandMechanism
torandaflexurejointcalledactiveflexure(acti-flex)joint,while
ThestructureofthePPy-basedpolymeractuator,considered thecarbonfiberattachedtotheendofthepolymerservesasa
in this paper, is shown in Fig. 1. The actuator has five layers. rigidlinkfortheroboticfinger.
Theoutertwolayers,whicharePPywiththicknessesof30μm, Thefingerisfabricatedasfollows.
aretheelectroactiveelementsprovidingactuation.Themiddle • An already fabricated sheet of conducting polymer is
layer is polyvinylidine fluoride (PVDF), an inert, nonconduc- trimmed into strips of 1 mm×15 mm, and the carbon
tive, porous polymer. It serves as a separator for the two PPy fiberwithathicknessof0.3mmistrimmedintopiecesof
layers and the reservoir for electrolyte (tetrabutylammonium 1mm×5mm.
(cid:2)
hexafluorophosphate) TBA PF 0.05 M in solvent propylene The carbon fiber pieces are cured in an oven for about
6
carbonate.Theelectrolyteandthesolventneedtobestoredin 10minat100 ◦Ctomakeitrigid.
(cid:2)
thePVDFlayerinordertooperatetheactuatorinair.Otherwise, Adouble-sidedstickytapeisputontotherigidcarbonfiber
it has to be operated in an aqueous medium consisting of the pieces.
(cid:2)
electrolyteandthesolvent.Thinlayersofplatinumof10–100A˚ The rigid carbon fiber pieces with the sticky tape on one
are sputter-coated on both sides of PVDF to enhance the con- side are then attached to the polymer strip to make the
ductivitybetweenthePPylayersandtheelectrolyte.Whenan finger.
(cid:2)
electrical potential is applied across the electrodes attached to The samples are replenished in TBA PF 0.05-M elec-
6
thePPylayers,thereduction/oxidation(redox)processoccurs, trolytefor5minbeforeeachtest.
ALICIANDHUYNH:PERFORMANCEQUANTIFICATIONOFCONDUCTINGPOLYMERACTUATORS 75
Fig.5. Schematicrepresentationoftheequipment.
Fig.3. Parametersdefiningthefingertipposition:coordinatesystems,bending
angle,andtheradiusofcurvature.Theradiuswasmeasuredfromtheintersection
oftheperpendicularlinesoftwoadjacentsegments.
Fig.6. Tipdisplacementsfortwoequivalentroboticfingersunderarangeof
constantinputvoltages.
Fig.4. Experimentalsetup.
A. EffectofInputVoltagesonDisplacementOutput
ofaRoboticFinger
Underconstantvoltagesrangingfrom0.2to1V,thetipdis-
III. EXPERIMENTALPERFORMANCEQUANTIFICATIONOF
placements of the robotic finger is measured, and are shown
ROBOTICFINGER
in Fig. 6 for two samples of the same finger. The same exper-
The fabricated finger has the dimensions of (5-mm actuator iments, which were conducted for the polymer actuator with
+5-mmrigidlink)×1mm×0.17mm,asdepictedinFig.3.A the dimensions of 5 mm×1 mm×0.17 mm, had shown the
photographofalltheapparatususedforexperimentsisshownin same trends, i.e., the higher the input voltage, the larger the
Fig.4.eDAQe-corderrecorderunittogetherwitheDAQChart tip displacement. However, it must be noted that the displace-
andeDAQScopesoftwareisusedtorecord,amplify,filter,and ment along the x-axis is much smaller than the displacement
analyse data. Aurora Scientific Inc. dual-mode lever arm sys- along the y-axis. In Section IV, a mathematical model to pre-
tem,model300Bisusedtomeasurethetipforce.Theplatinum dict the bending displacement of the actuator is presented. It
wires on the electrode clamps are connected to the outputs of mustbenotedthatthecorrespondingradiiofcurvaturedepicted
a potentiostat/galvanostat, controlled using Chart 4 Windows in Fig. 7 are needed for the force model provided in the next
software via a Powerlab 4/20 controller. Other equipments in- section. The tip displacement results of our trilayer actuator
clude a PC, a digital video camera, a metal stand and clamps, operatinginairisinagreementwiththeperformancecharacter-
two-electrode clamps and a grid paper. The schematic repre- isationresultspresentedintheliteratureforatrilayerpolymer
sentation of the experimental setup employed to evaluate the actuator (20 mm×15 mm×0.013 mm) operating in a 1-M
performanceofthefingerisshowninFig.5. LiClO aqueoussolutionundercurrentcontrol[12].
4
76 IEEE/ASMETRANSACTIONSONMECHATRONICS,VOL.12,NO.1,FEBRUARY2007
Fig.10. Variationoftheminimumcurrentrecordedduringforcemeasurement
withthefrequency.
Fig.7. Measuredradiiofcurvaturefortwoequivalentroboticfingersundera
rangeofconstantinputvoltages.
Fig.11. Bendingcurveofabendingpolymeractuator.
ventmoleculesrequirescertaintimetomoveinandoutofthe
Fig.8. Experimentdatarecordedunderasquarewavewithamagnitudeof
±1Vwiththefrequencyof1PPM. PPy layers during the redox process. Obviously, with high in-
putfrequencies,thereisnotsufficienttimefortheionsandthe
moleculestoreachdeepintothepolymerlayertogeneratemore
force.Thisislikestoppingtheirmovementinthemiddleoftheir
journeyandaskingthemtogoback.Thisargumentissupported
bythemagnitudeoftheminimumcurrentpassingthroughthe
oxidized layer, i.e., if the minimum current is closer to zero,
the better will be the oxidation, which generates more actua-
tion effect. The minimum current for the input frequencies is
determinedfromtherecordedcurrentdata,asshowninFig.10,
wherethemagnitudeoftheminimumcurrentunderarelatively
highinputfrequencyissignificantlyhigherthanthatofthelow
Fig.9. Variationoftheoutputforcewithinputfrequency.
inputfrequency.
B. EffectofFrequencyoftheInputVoltagesontheForceOutput
ofaRoboticFinger
IV. BENDINGMOTIONANDBENDINGFORCEMODELING
The force output of the robotic finger is measured under a
The mathematical models are needed to provide enhanced
set of square waves with a constant magnitude of ±1 V and
degreesofunderstanding,predictability,control,andefficiency
the frequencies of 10 pulses/min (PPM) or 0.1667 Hz, 6 PPM
inperformanceinordertoimprovethedisplacementandforce
or0.1Hz,4PPMor0.0667Hz,3PPMor0.05Hz,2PPMor
outputsofthepolymeractuatorsbeforeusingtheminrealap-
0.0333Hz,and1PPMor0.0167Hz.Beforeeachtest,aninput
plications[20].
voltage of 0 V is applied to neutralize the finger. The current
passed through the oxidized polymer layer, the input voltage,
andtheoutputforce,dataextractedfromtheeDAQdatalogging
A. BendingMotionModel
system,areshowninthetop,middle,andbottomplotsofFig.8,
respectively.Thesearetypicaldatarecordedforeachfrequency. This mathematical model, which had been reported in our
Themagnitude of theforceforeach frequency isreadfrom previous study [16], is summarized here for the sake of com-
therecordedforcedata,andisshowninFig.9,wheretheforce pleteness.Themodelhasbeenderivedintermsofthetipvertical
decreases linearly with the input frequency. This can be ex- displacementvandthehorizontaldisplacementx,asshownin
plained by the fact that the movement of dopant ions and sol- Fig.11.
ALICIANDHUYNH:PERFORMANCEQUANTIFICATIONOFCONDUCTINGPOLYMERACTUATORS 77
Fig.13. Oneendcantileveredactuatorandtheparametersinthemodel.
Fig.12. Experimentalandtheoreticalbendingcurvesforapolymeractuator
[dimensions:10mm×1mm×0.21mm;β=0.145(F/m2)/(C/m3)][16].
the induced internal bending moment and the moment created
Theresultingmathematicalmodelisasecond-ordernonlinear bytheexternalforceF isalwayszeroatanycrosssectionalong
differentialequationgivenby theactuator[19]
(cid:2) (cid:3) (cid:4) (cid:5)
d2v dv 2 1
− 1+ ⇒ EI+αE bh (h +h )−FL=0 (4)
dx2 dx R 1 1 1 2
3βVC(h +h ) whereEI =E I +E I istheflexuralrigidityofthewhole
(cid:6) (cid:7) (cid:8) 2 1 (cid:7) (cid:8) (cid:9) =0 (2) 1 1 2 2
2bL E 2h1+h2 3+(E −E ) h2 3 actuator. It must be noted that the strain in the PPy layers at a
1 2 2 1 2 distancey fromtheneutralaxisduetothethicknesschangeof
whereV istheinputvoltage,Listhelengthoftheactuator,b thePPylayerduringtheredoxprocessisconstantthroughoutthe
is the width of the actuator, C is the capacitance, E and E PPylayersandisdenotedbyα.Itisreportedintheliteraturethat
are Young’s moduli of PPy and PVDF layers, respec1tively, h2 αisafunctionofthestrain-to-chargeratioandchargedensity
1
and h are described in Fig. 13, and β is the experimentally inthePPylayers[16][19].
2
Equation(4)describestwocasesunderanonzeroinputvolt-
determined proportionality constant relating the internal stress
σtotheexchangedchargedensitygivenby age:1)thetipoftheactuatorisnotblocked(i.e.,F =0)and2)
theactuatortipisblockedtomeasurethetipforce.
ΔQ
σ =β (3) Thefirstcaseisusedtodeterminethevalueofαunderdiffer-
B entinputvoltages,providedthattheradiusofcurvatureR,and
where ΔQ is the exchanged charge, and B is the volume of thenumericalvaluesoftheotherparametersin(4)areknown.
theoxidisedPPylayeroftheactuator.Themodelgivenby(2) Theradiusofcurvatureismeasuredfromtheactuatorbentunder
has been solved for the dimensions and mechanical properties anonzeroinputvoltage,asgiveninFig.7
oftheknownactuators,andthencomparedtotheexperimental
EI
bending results under the voltage step inputs of 0.2, 0.4, 0.8, α=− . (5)
and1.0V,asdepictedinFig.12.Thetheoreticalresultsmatch RE1bh1(h1+h2)
the experimental results quite closely. It should be noted that Thecalculatedvaluesofαarethenemployedtoestimatethe
the model does not account for bending beyond 90◦, which
forceproducedattheactuatortip,fromthesecondcase:
is why the tips of the curves with larger deflections show the
greatestdiscrepancy,whiletherestoftheactuatorshowsabetter E bαh (h +h )
agreement[16]. F = 1 1 1 2 . (6)
L
B. ForceOutputModel In obtaining (6), we assume that the radius of curvature is
It must be noted that many of the modeling approaches re- extremelylarge(1/R≈0).Itcanbeinferredfrom(6)thatthe
portedintheliterature[8],[21]aremainlyforbilayerpolymer tipforceisinverselyproportional totheactuator. Thisfollows
strips, based on the bending modeling of a bimetal thermostat thatpolymeractuatorsarealsosuitableforminiaturisation.The
reportedbyTimoshenko[22].In[19],theTimoshenko’smethod force model described by (6) can be applied to calculate the
has been extended to model force outputs of the trilayer poly- forceatthetipofaroboticfingershowninFig.14.Itisworth
mer actuator and the robotic finger. With reference to Fig. 13, noting that the rigid part apparently does not contribute to the
the force F is the external force needed to block the bending bendingofthefinger.TheequivalentforceFfinger actingatthe
displacementoftheactuatortip.Infact,F istheforcemeasured tipoftherigidpartiscalculatedfrom
bytheforcesensorupontheactivationofthepolymeractuator. L
Under a quasistatic condition, the total moment consisting of Ffinger =FL(cid:7). (7)
78 IEEE/ASMETRANSACTIONSONMECHATRONICS,VOL.12,NO.1,FEBRUARY2007
Fig.14. Demonstrationofparametersintheforcemodelfortheroboticfinger.
Fig.16. Forceresponseofthe5-mmactuatorunderstepinputvoltages.
Fig.15. Theoreticalandexperimentalforceresultsforthe5-mmactuator(top
plot),the10-mmactuator(middleplot),andtheroboticfinger(bottomplot).
V. EXPERIMENTALVERIFICATIONOFFORCEMODEL
Stepresponseexperimentswerecarriedouttoverifytheforce
models described by (6) and (7). The numerical values of the
parametersintheforcemodels[16]are:
1) PPythicknessh =0.03mm;
1
2) PVDFthicknessh =0.11mm; Fig.17. Forceresponsesofthe5-mmactuatorinthefirst10s.
2
3) widthofthefingerb=1mm;
4) Young’smodulusofPPyE =80N/mm2; under a range of step voltages [19]. The results for the 5-mm
1
5) Young’smodulusofPVDFE =440N/mm2. actuatoronlyareshowninFig.16forthesakeofbrevity.
2
To verify the force model of the bending actuator with- Acloseupoftheforceresponsesofthe5-mmactuatorinthe
out the rigid link described by (6), two samples of the ac- first10sisshowninFig.17.Itcanbeseenfromtheseresults
tuator with the dimensions of 5 mm×1 mm×0.17 mm and thatthereisalmostnoinitialdelay(timedelay)intheresponse
10 mm× 1 mm×0.17 mm are experimented with. Similarly, oftheactuator.Achangeintheforcewasrecordedalmostright
toverifytheforcemodelofthebendingactuatorwiththerigid afterachangeintheinputvoltage.However,thesettlingtimeis
link described by (7), a robotic finger with the dimensions of quitesignificantforvoltageinputstoreachasteady-statevalue.
(5+5)mm×1mm×0.17mmisexperimentedwith.Theex- Further,theresultsindicatethattheactuatorshowsacapacitive
perimentalandthepredictedforceresultsusing(6)forthetwo response [5] [23] with a large time constant, which is one of
actuators, and using (7) for the finger are shown in the top, the main disadvantages of electroactive polymer actuators. To
middle,andbottomplotsofFig.15,respectively.Theseresults circumventthisdisadvantage, anewtrilayerpolymeractuator,
demonstratethattheforcemodeliseffectiveenoughtopredict which has been fabricated at our polymer research laboratory,
the force outputs of the actuator without and with a rigid link has a time constant of as small as 0.47 s. These results of the
quitewell.Tothebestofourknowledge,thisisthefirststudy timeconstantsofthetrilayerPPyactuatorsarebetterthanthose
toestablishanexperimentallyverifiedforcemodelforatrilayer of the bilayer PPy actuators presented in the literature [6] [7],
actuatoroperatinginanonliquidenvironment. in which the response time was reported to be of the order of
Experimentswerealsoconductedtocharacterizethetransient seconds.Thesynthesisandperformanceevaluationofthenew
responseofthe5and10mmactuators,andoftheroboticfinger fasteractuatorsarereportedin[24].
ALICIANDHUYNH:PERFORMANCEQUANTIFICATIONOFCONDUCTINGPOLYMERACTUATORS 79
Fig.18. 5-mmactuator(topplot)and10-mmactuator(bottomplot)bending
againsttheforcemeasurementlever.
WithreferencetotheresultsdepictedinFig.15,thereisquite
Fig.19. X andY displacementsoftheroboticfingerundera±1Vcyclic
a good agreement between the experimental and the predicted
triangleinput.(a)Cycle1.(b)Cycle5.
results with the input voltages up to 0.8 V for both actuator
samples and up to 0.4 V for the robotic finger. This is due to
theassumptionofanegligiblysmallreciprocaloftheradiusof
curvature(1/R≈0)onwhichtheforcemodels,(6)and(7),are
based.Infact,forcemeasurementexperimentsshowedthatthe
curvature doesexistwhen theactuator bends againsttheforce
measurement lever. Such bending is more obvious at higher
input voltages and with longer actuators. This phenomenon is
shown in Fig. 18 for the 10- and 5-mm actuators under step
inputvoltagesof1.0V,whenbendingagainsttheforcelever.It
canbeseenthatthecurvatureofsuchbendingisnegligiblefor
the5-mmactuator,butquiteobviousforthe10-mmactuator. Fig.20. Thevoltammetrydiagramfortheroboticfingerundera±1Vcyclic
triangleinput;forthefirst5cycles(A),andforthefirst40cycles(B).
VI. NONLINEARBEHAVIOROFACTUATOR
oftheroboticfingerisdefinedbyX,Y coordinatesofthetipas
Althoughpolymeractuatorshavemanypositivefeatures,they
showninFig.3.TheX,Y coordinatesofthetipdisplacement
suffer from nonlinear problems such as hysteresis and creep,
are provided in Fig. 19, where the hyteresis is not significant.
whichdeserveacomprehensiveinvestigation.Itmustbekeptin
The output current versus the input voltage curve, known as a
mindthat,inthepublishedliterature,therearenoexperimental
voltammetry diagram, which is recorded for the same sample
or theoretical results demonstrating the nonlinear behavior of
tofurtherverifywhetherthehysteresisissignificant,isshown
trilayerpolymeractuatorsoperatinginair.
in Fig. 20. The upper and lower portions of the voltammetry
diagram are known as the oxidation and reduction curves, re-
A. HysteresisEvaluationfortheRoboticFinger
spectively. If the curves are symmetrical about the horizontal
Theinputvoltageintheformofacyclictrianglesignalisap- zero axis, this will indicate no hysteresis [25]. The symmetry
pliedtotheroboticfingeroperatinginthehorizontalplane.The is evident in the curves in Fig. 20, which supports the results
movementoftheactuatorsampleisrecordedafteronecycleand providedinFig.19.Whencomparedtothehysteresisresultspre-
fiveworkingcyclesbyadigitalvideocamera.Thetipposition sentedintheliteratureforabilayerpolymeractuatoroperating
80 IEEE/ASMETRANSACTIONSONMECHATRONICS,VOL.12,NO.1,FEBRUARY2007
Fig.21. Photographsoftheroboticfingershowingthecreepstartinginstant
andtheendofcreeptestfortheinputvoltageof0.6V.
Fig.23. Y coordinateofthetipdisplacementversustime.Thecreepstartsat
A,B,andCforinputvoltagesof0.2,0.4,and0.6V,respectively.
Fig.22. Xcoordinateofthetipdisplacementversustime.Thecreepstartsat
A,B,andCforinputvoltagesof0.2,0.4,and0.6V,respectively.
Fig.24. Bendingangleθversustime.ThecreepstartsatA,B,andCforinput
voltagesof0.2,0.4,and0.6V,respectively.
inanaqueousmedium[7],inwhichthehysteresiswasreported
tobe27◦bendingangle,thehysteresisinourtrilayeractuatoris Theverticallinesacrosstheresponsecurvesof0.2,0.4,and
negligiblysmall.Webelievethatthereasonwhyourtrilayerac- 0.6 in Figs. 22–24 indicate the instant when the creep starts.
tuatorshowsvirtuallynohysteresisbehaviormayhavebeendue The zero current could not be recorded during the experiment
toitssymmetricalstructure.Thereason(s)needtobethoroughly period for the input voltages of 0.8 and 1.0 V, and hence, the
investigated. creepresponseinthesecasescouldnotbefullyrecorded.When
To evaluate the hysteresis repeatability of the actuator, a theexperimentalcreepresultsofourtrilayeractuatoroperating
voltammetrydiagramfor40cycles,thecurvesindicatedby“B” in air is compared to the experimental findings reported for a
wasalsoobtainedandpresentedinFig.20,whereitisobvious trilayer polymer actuator (20 mm×15 mm×0.013 mm) op-
thattherepeatabilityoftheactuatorisacceptable. erating in a 1-M LiClO aqueous solution [26], our actuator
4
showsanonnegligiblecreepbehaviorasopposedtotheresults
providedin[26].WithreferencetoFig.24,whenazerocurrent
B. CreepEvaluationfortheRoboticFinger
was recorded for a constant 0.6 V after 272.5 s, the bending
We describe the creep behavior in the conducting polymer anglewasmeasuredtobe21.96◦.
actuatorasthechangeinthetippositionoftheactuatorafterthe
However, after 1797.5 s the bending angle measured was
polymerlayersarefullyoxidized,i.e.,azero-currentoutputis 27.33◦. This follows that the final position of the actuator did
recordedfromtheoxidizedpolymerlayer.Thecreepobserved
notstayfixedunderazerocurrent.
for a 0.6 V input is presented in Fig. 21. With reference to
the coordinate frame described in Fig. 3, the tip positions are
C. ViscoelasticModelforCreepBehavioroftheRoboticFinger
identified as the robotic finger continuously bends under the
effectofthestepinputvoltagesrangingfrom0.2to1.0V.The The low-frequency creep response of the robotic finger can
variation of the tip coordinates X,Y and the bending angle θ be represented by a system of spring and damper elements,
withtimearedepictedinFigs.22–24. known as Kelvin–Voigt viscoeleastic model shown in Fig. 25.
ALICIANDHUYNH:PERFORMANCEQUANTIFICATIONOFCONDUCTINGPOLYMERACTUATORS 81
Fig.25. Kelvin–Voigtmodelforviscoelasticmaterials.
TABLEI
RMSESTIMATIONERRORSBETWEENTHETHEORETICALANDEXPERIMENTAL
RESULTS
Fig. 26. Experimental and theoretical bending angle results for the finger
Thismodelwasoriginallyproposedtomimictheviscoeleastic operatinginthehorizontalplane.
behavior of polymers [27], and later used to predict the creep
behaviorofpiezoactuators[28],[29].
Thetransferfunctionrepresentationofthismodelisgivenby
θ(t) 1 (cid:10)n 1 (cid:6) (cid:9)
= + 1−e−kit/ci (8)
u(t) k k
x i
0 i=1
where θ(t) and u(t) are the bending angle and the input volt-
Fig.27. Operationofthetwofingersunderdifferentinputvoltages.Theresults
age, respectively. The first term on the right-hand side repre- areobtained5minafterthevoltagesareapplied.
sentselasticbehaviorwhilethesecondterm,whichrepresents
Kelvin–Voigt elements, models creep behavior. The more the
Kelvin–Voigt elements used in the model, the smaller are the
errorsbetweentheestimatedandtheexperimentaldatapoints.
The accuracy of the model is evaluated using the root mean
square (RMS) error (shown in Table I for various numbers of
Kelvin–Voigtelements),whichisgivenby
(cid:11)
(cid:12)
(cid:12) 1 (cid:10)N
(cid:13) Fig.28. Operationofthefingersforadrivingvoltageof1.25Vatdifferent
RMSbendingangle = N (θm−θe)2i. (9) instants.
i=1
Thenumericalvaluesofthespringanddampingparametersin
distributionafterafastmechanicalresponse.”Infact,thecreep
(8) have been estimated for the input voltages of 0.2, 0.4, 0.6,
effectismoreapparentwith0.6Vthanwith0.2Vor0.4V,as
0.8, and 1.0 V using a least-square estimation algorithm. The
seeninFig.26.Futureworkinvolvesusinganionicelectrolyte
estimatedandexperimentalbendingangleresultsareshownin
with larger molecule diameter and different dopant concentra-
Fig.26.
tionssuchthatthecationsandsolventmoleculesdonotspread
The creep behavior of the finger operating in the vertical
around much. Our initial experimental results, which will be
planehasalsobeenevaluatedtobequitesimilar.Thisfollows
reportedinanotherpublication,supportthisexplanation.
that the rigid carbon fiber, which is treated as the uniformly
distributedloadatthetipoftheactuator,doesnothavemuchin-
D. ExperimentalResults
fluenceonthecreepbehavior.Themechanismbehindthecreep
behaviorismainlyduetotheosmoticpressureintheoxidized Thegripperwasfirstsetuptooperateinthehorizontalplane
PPy layer, which is highly populated with the PF− ions and todemonstratethecoordinationofthetwofingers.Fig.27shows
6
solvent molecules, with reference to (1). Under osmotic pres- themeetingpointsoftwofingertipsofthegripperunderinput
sure, the ions and molecules cannot go back to the other PPy voltagesof0.5,0.75,1.0,and1.25V.Exceptfor1.25-Vinput,
layerastheinputpotentialisstillapplied.Hence,theytendto the meeting points in three other cases of driving voltages do
spreadaroundunderthepressure,whichresultsinfurtherbend- not lie on the middle line of the gripper. For a driving voltage
ingofthefullyreducedPPylayer,andhencecausingcreep.This of1.25V,twofingertipsfirstmeteachotheroutsidethemiddle
explanationisinagreementwiththepostulatedexplanationre- line. However, it was observed that one finger was pushing
ported in the literature by Baughman [9] that the creep could the other such that the meeting point was lying on the middle
bedueto“electricalself-dischargeorintraelectrodedopantre- lineafter3min,asdepictedinFig.28.