Robotsgraspandmanipulateobjectswiththeaidofagripper.UsuallytheobjectispresentedCompliancecanbeintroducedtotherobotbyusingacompliantend-eectororgripper.Thiscanbedoneindierentways.Inliteratureavarietyofsubjectsongrippercompliancecanbefound1,3,4,thesearemainlyfocussedoncontroltheoriesforuniversalgrippersandneMechanismandMachineTheory38(2003)15091522*Correspondingauthor.Tel.:+31-15-278-3130；fax:+31-15-278-1397.atapredenedpickuplocationwheretherobotcangraspandmoveittoanotherpredenedlocation.Dicultiesarisewhenthepickuplocationanddestinationarepartofaheavyrigidbodythatcanmoveduetoexternaldisturbances.Iftherobotcannotadapttothismovementduringpickuporrelease,thefullforceofthemovementwillbetransferredintotherobotC213scomponents,whichcanresultindamage.Thereforetherobotshouldbeexibleorcompliantwheretheenvironmentissti3.ComplianceeectsinaparalleljawgripperA.J.G.Nuttall,A.J.KleinBreteler*FacultyofDesign,ConstructionandProduction,DepartmentofTransportationTechnology,UniversityofTechnologyDelft,Mekelweg2,2628CDDelft,TheNetherlandsReceived17April2002；receivedinrevisedform24April2003；accepted30June2003AbstractThispaperdiscussesmechanicalcomplianceeectsinagripperwithparalleljaws.Initacasestudyofadedicatedgripperdesignispresentedtoanalysetwodierentdesignelementsinuencingthecompliantbehaviour:theexibilityintroducedbypreloadedspringsandtheresistancecausedbyfriction.Thegrippermanipulatessemi-automatictwistlocksusedforsecuringseagoingcargocontainers.Thecomplianceeectsareeectivetoreducemisalignmentandoverloadofthegripper.C2112003ElsevierLtd.Allrightsreserved.Keywords:Mechanicalcompliance；Twistlockmanipulator；Preloadedsprings；Frictionforce1.I/locate/mechmtE-mailaddress:a.j.kleinbretelerwbmt.tudelft.nl(A.J.KleinBreteler).0094-114X/$-seefrontmatterC2112003ElsevierLtd.Allrightsreserved.doi:10.1016/S0094-114X(03)00100-9manipulation.In5,6suchacomplianceisinvestigatedusingstinessmodelsandin7aremotecompliancecentreisintroduced.Theseinvestigationsintegratecomplianceintothecontrolsys-tem,withtheaidofspecialsensorsandactuatorsmakingreliableforceandpositioncontrolpossible.Withthisformofelectroniccontroltheuniversalgrippercanmanagemanydierenttasksandobjects.Thisisincontrasttothespecial-purposeend-eectorthatistobedesignedforaspecictaskandobject.Bymakinguseofsimplesensorsandactuatorscombinedwithamechanicalformofcomplianceaneective,reliableandrobustgrippercanresult,whichwillalsobeabletoadapt(allbeitinalimitedmanner)toamovingpickuppoint.Theadaptationofthisformofcomplianceforgrippercongurationshasprovenhardtondinliterature.Thispapergivesaninsightintotheeectsofmechanicalcomplianceinagripper.Acasestudyofagripperdesignwillaidasexampletodiscusstwodierentmodesofmechanicalcompliance.Thisexamplecaseconsistsofaparalleljawgrippercongurationintendedforthemanipulationofsemi-automatictwistlocks.operation.Ifitispulledtheshaftrotatesthatconnectstheconestogether.1510A.J.G.Nuttall,A.J.KleinBreteler/MechanismandMachineTheory38(2003)150915222.BackgroundtothetwistlockmanipulatorAmanipulatorwasrequiredtoautomaticallyconnectandremovesemi-automatictwistlockstoandfromacontainerC213sbottomcornercastings.InFig.1asemi-automatictwistlockisshownontheleft.Thistypeoftwistlockisalashingdevicethatisusedtosecuresea-goingcargocontainerstothedeckofaship.Itconsistsofabody,anupperandlowerrotatingconeandahandleformanualoperationoftheconepositions.TheupperconecanbeinsertedintothebottomcornercastingdepictedontherightsideofFig.1byunlockingitthroughrotatingthelowercone.Thetopcollarxesintotheholeofthecornercasting,becauseitmatchestheshapeofthehole.Whentheconesarerotatedbacktotheiroriginalposition,thetwistlockissecuredtothebottomcornercasting.ThehandleisintendedformanualFig.1.Asemi-automatictwistlockandacornercastingofacontainer.Forautomationofthissecuringprocedureandthereverseoperationagripperhadtobede-signedthatcanholddierenttypesoftwistlocksbytheircollarswithsucientgraspingforce10.Thejawsalsohavetoopenfarenough,topreventcollisionswiththeconeswhilethemanipulatorispositioningoverthetwistlockwithopenjaws.Thecontainercanmoveduringthepickuporreleaseoperationduetoexternaldisturbances,becauseitwillbehoistedupintheairbycablesorrestingonarollingchassiswithpneumatictyres.Thewindisanexampleofadisturbancethatcangenerateuctuatingforcesonthesideofthecontainer,whichcanresultinanoscillatingmovement.Duetothepossiblemovementofthelargecontainermass(30ton)andtherobustconstructionofthetwistlockthegripperwillhavetobecomplianttopreventdamagetoitselforothercomponentsoftherobot.Mechanicalcom-pliancewillalsohelptackletheproblemofthemovingpickuppointonthecontainerandkeeptherequiredcontrolsystemsimple.collarsizeshadtobetakenintoaccountforareliableoperationofthegripper.IngeneratedA.J.G.Nuttall,A.J.KleinBreteler/MechanismandMachineTheory38(2003)150915221511namicforcescreatedonthetwistlock.Thetotalforce(Ftot)thathastobecompensatedinadi-rectionparalleltothecollarsurfaceis200N.Thiswascalculatedbydeterminingthedynamicforcescausedbymovementofthemanipulatorandthestaticgravitationalforce.Withafric-tionalcoecient(l)of0.125thegraspingforceexertedbyeachjaw(Fjaw)canbecalculatedasfollows:Ftot2C1lFjaw)FjawFtot2l800NThisistheminimalforcethathastobeguaranteedduringthemanipulationofatwistlock,forallcollarsizes.Fig.2bshowstheopenandclosedpositionofthejaws.Itshowshowfarthejawshavetoopen,duringthepositioningoftheopengripper.TherehastobeenoughclearancebetweentheconeFig.2atheforcesappliedbythejawsduringagrasparepresented.Thefrictionalforcesonthecollarsideswillhavetobesucientlylargetocompensatethestaticanddy-Thecollarwaschosenascontactsurfaceforthegripper,becauseitisthecommonelementindierenttwistlockdesigns.Ithastotintothestandardisedholeofthecornercasting,sotheshapeandsizewillberoughlythesame.Althoughthewidthoftheholeisonlyallowedatoleranceof1.5mmthecollarwidthsfoundinpracticecanvarybetween57and62mm.This5mmrangeinFig.2.Graspingforcesontwistlockandtherequiredjawtravel.andjawtopreventacollision,becausetheconediameterislargerthenthecollarwidth.Togetaclearanceof15mmthedisplacementofajawhastobe40mm.3.FindingasuitablegrippercongurationAnexistinggripperthatiscapableofproducingaratherlargeclampingforceandlargedis-placementisillustratedinFig.3a2.Itconsistsoftwoparalleljaws,actuatedbyadoubleactingpneumaticcylinder.AttachedtothecylinderC213spistonrodisadualrackgear,whichdrivestwopartialsectorsofpiniongears.Twopairsofthesymmetricalarrangedparallelclosinglinkagesaremounteddirectlyonthepartialsectorsofthepinionsandprovidetheclampingforce.Thisdesignonlyfeaturescompliantbehaviourwithrespecttothewidthofthegraspedobject.Ifthegraspedobjectislargerthenthedistancebetweentheclosedjaws,theywillcomeincontactwiththeobjectbeforetheyarefullyclosed.Thereforethepistonwillnottraveltoitsendpositionduringthisclosingoperation.Thismakesitpossibletograspdierentsizedobjects.Itwillhoweverbemorediculttosensetheclosedpositionofthejaws.Aspecialsensingmethodlikeforcedetectionwillberequiredtomeasuretheclosedposition.1512A.J.G.Nuttall,A.J.KleinBreteler/M