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Proceedingsofthe2006IEEE/RSJ InternationalConferenceonIntelligentRobotsandSystems October9-15,2006,Beijing,China MechanicalDesignofJointBrakingandUnderactuated Mechanismof“Tri-Star3“;HorizontalPolyarticularArm Equipped3-WheeledExpandableMobileRobot KenjiroTadakuma,MatsumotoMasatsuguandShigeoHirose DepartmentofMechanicalandAerospaceEngneering TokyoInstituteofTechnology 2-12-1Okayama,Meguro-ku,Tokyo152-8552Japan k-damototheroversofNASA3. Aplanetaryrovermusthavebehighlyadaptableto uneventerrain4.Theintroductionofhighlysophisticated multiple-degreesoffreedomvehiclemechanismsandthe implementationofadvancedcontrolofthesemechanisms seemstohavebeenacommonmethodtoachievesuch objectives. However,thereliabilityofthemechanismisofextreme importance,andtheresearchapproachofourlaboratoryisto realizeterrainadaptabilitywithasimplemechanism5.Atthe sametime,specialcarewasalsotakentomaximizethe dimensionsoftheroverasmuchaspossible.Thisisbeneficial becausewhenthesizeoftheroverislarge,terrainobstacles becomescomparativelysmallsothelargerovercanmove aroundonroughterrainwithoutanydelicateoradvanced controllers,asshowninFig.1.Basedonthisconsideration,we developedthehorizontalpolyarticularexpandable3-wheeled planetaryrover,“Tri-Star3“.Thecurrentwheels ofTri-StarIll arenottheexpandabletype,buttheexpandableonewillbe putonthemodelformoreeffectivepropertyofthe expandablemechanismasshowinFig.1. Fig.1ScaleEffectofExpandableMechanism Inthispaper,weshowthemechanicaldesignofthejoint brakingmechanismofthisroverindetail,anddemonstratethe underactuatedperformancebythejointbrakingmechanism. II.CONFIGURATIONOF“TRI-STAR3“ “Tri-Star3“;the3-wheeledexpandablerover,isequipped withthreehorizontalarms,andthereareactivewheelsatthe endofeacharm(Fig.2).Theconfigurationofthearmand wheelmoduleisshowninFig.3.Themostimportantpointof thisroveris,asamainactuator,theroverhasonlythree motorstorotateeachwheel.Therearejointbraking mechanismsineachjoint,drivenbyjustonesmallactuator, withdifferentfunctionsdependingonwhetherthejointis lockedorfree.Whenthejointislocked,thewheelrotatesto producepropellingforcetothebody.Ontheotherhand,when thejointisfreetorotateandthewheelrotates,thewheelcan changeitsownsteeringdirectioninitsyawaxis,orcan changetheangleofthejointofthearmtothebody.Forthis reason,thisroverislightweight,lowcost,andsimpleto control.Thetorqueofthemotoristransmittedby chain(numberltonumber2)andtheinnershaftofthejointrod isrotated.Andbythebevelgearset,therotationaldirectionis changedfromverticaldirectiontohorizontaldirection. Finally,thespurgearrotatestheinnergearfixedto wheels(number3tonumber4),thereforethewheelisrotated. Theoverviewofanactualwholeprototypemodelis showninFig.4.Therotationalmotionistransmittedfromthe motorinthearmtoasprocketbychain,whichrotatesthe bevelgearandfinallythewheel(Fig.3).Thespecificationof thisroverisshowninTable1.Thegearedmotorsofthe wheelsworkin36(W). PassiveJoint Uk.-il|ottd.4- I LVV%*LKD (b)ExpandingMode Fig.2Conceptof3-wheeledexpandablerover 1-4244-0259-X/06/$20.00C)2006IEEE 4252 (a)RetractingMade, C, -,vI 0 ; ArmModule I SpaceforI BatteriesandElectronicdevices i /1/1 I WheelModule SpurGear BrakingMechanizm .1 (a)RetractingMode Fig.4OverviewofActualPrototypeModel )Slope(climbing)(b)Slope(crossing)(c)INarrowchannel Fig.5LocomotionChangingFunctionofRover TABLEI:SpecificationofPrototypeModel WheelRadius192mm Wheel WidthofWheel167.5mm HeightofKnob8.5mm GroundClearance126mm LengthofArm400mm (Distancebetweentwo Armjoints)335mm WidthofArm71mm ThicknessofArm75mm Body LengthofBody 480mm ThicknessofBody91.5mm HeightofVehicle473mm Whole HeightofC.O.G. 21.5cm ExpandableRatio7.24 TotalWeight12.3kg III.CONCEPTOFUNDERACTUATEDFUNCTIONOF3-WHEELED EXPANDABLEROVER Inthisstudy,weproposeanewunderactuatedmethod, consistingofanactivewheelattheendofarm,andvarious jointbrakingmechanisms. 4253 ;J Knobs Step1 ):Untied :Tight Step2 Holes Step3ontheshaft DegreesofFreedom Torealizeasimilarfunctionofamultipledegrees-of- freedomarm,wesuggestthefollowingmethod. Bychangingthefrictionalconditionofeachjoint,and withthedrivingwheel,eachjointcanchangetheirownangle inasimilarfashionsothatthewholejointsperformlikean activerotationalactuator.Thismotionmakesthewholeshape ofthearmchangeableattheend.Themotionofthis configurationissimilartoexpandablegatesoftenfoundin airports. InFig.6,fromStep2toStep3,therotationaldirectionof thewheelchanges.Therefore,theshapeofthewholearm changessuchasletter“S“.Inthe3-wheeledexpandablerover, weadopttheonelink,consideringthesimplicityofthe configurationofthearm. IV.JOINTBRAKINGMECHANISM Inthischapter,thedrumtypebrakingmechanismis explainedindetail. Asabrakingmechanism,thelock-pintypemechanism6 asshowninFig.7havebeendevelopedatthepastresearch. However,inthisdesign,thepinwasnotstrongenoughfor situationssuchasthemobilerobotcollidingwithsomelarge rock,generatinganimpactloadtoeachjoint.Further,the resolutionofthesteeringangledependedonthenumberof holesontheshaftasshowninFig.7. Forabovereasons,inthisresearch,thedrumtypebraking mechanismisadopted.Toimproveuponthisearlierbraking mechanism,thefollowingamendmentswereimplemented. 1)Functionasatorquelimiter 2)Highresolutioncapabilityofthesteeringangleofthe wheel. 3)Abilitytorealizeanunderactuatedmechanism Fig.7:Loi Inadditiontotheabovefunctions,thedrumtypebraking mechanismcanadoptahalfclosedconfiguration,sothe middlestrongbrakingforcecanbeproduced,asmentionedin section3.Torealizeasimilarfunctionofamultipledegreeof freedomactivejoint,asdescribedinsection2,wedeveloped thebrakingmechanismasshowninFig.8. A.ConfigurationofBrakingMechanism Thebrakingmechanismconsistsofacammechanism, specifically,amastercamandslavecam.Whenthemaster camAisrotatedbythegearedmotor,SlavecamB1,B2 accepttheforcefromtherollerofthemastercamA. Therefore,part(B-1)andpart(B-2)rotateeachotherthrough theslavecam.Intheend,part(C-1)andpart(C-2)rotateand griptheshaft.Thetypeofthespringsaretensionspringsthat areusedtoopenthebrakemechanism. B.ProblemofBrakingMechanismthatconsistsofnormal straightshapeofcam Whenconsideringtheshapeoftheslavecam,thereisthe problemthattherotationalspeedsofthetwopartsare differentiftheshapeofthecamisidentical,suchasastraight shape(Fig.9).Therefore,thereisadifferenceofthegripping forcebetweentheclockwiserotationandthecounterclockwise rotationoftheshaft(Fig.10).Thebrakingpropertyshouldbe thesameandnotdependontherotationaldirection, consideringthatthebrakingmechanismwillbeinstalledinthe roverasthejointisbraking.Therefore,wedecidedtodesign theoptimalshapeoftheslavecamB1andB2toenablethe speedoftheangletochangethesamebetweenC1andC2. 4254 Fig.6:SimilarfunctionofMultiple (Topview) (KiD G.iD (KinD (KiintD (KED /% ShaftPalr(-1art(B-1) ,MCamr Qf _ tw % % J MasterCamA SpringPart(C-2)SlaveCamB2 (a)StructureofBrakingMmPart(B-2) (a)StructureofBrakingMechnism 01020304050607080 masterdeg sterCamA Part(C-2) (b)OverviewofBrakingMechnism i)Grippingii)Loosing (c)MotionofBrakingMechnism Fig.8:BrakingMechanismforJointofTri-StarlIl SlaveCamBi I SlaveCamB2 Fig.9:0-0Curve(StraightShapeofCams) Fig.10:0-0Curve(StraightShapeofCams) InFig.8,notethattherotationaldirectionofboth0and01 arecounterclockwise,asapracticalmatter,whenthemaster camrotatescounterclockwisedirection,thepart(B-1)rotates clockwise,inshort01isnegativevalueatthatsituation. Intheexperimentsofthissection,thedatashowninFig. 10wasobtainedbyusingthetestdeviceconsistingofafloat differentialmechanism7todirectlymeasurethetorque appliedtotherotatingshaft. C.Proposalmethodoftheshapeofcamdesignbyusingthe envelopecurve. Consideringtheproblemshownintheprevioussection, weproposethedesignmethodtomaketherotationalangle betweenthepart(B-1)andthepart(B-2)tobethesamewhen themastercammoves. Iftherotationalangleofpart(B)canbechangedarbitrarily bytherotationalangleofthemastercamA,itispossibleto maketherotationalangleofpart(B)match.Inotherwords,if therotationalangleofpart(B-1),(B-2),isanarbitrary functionoftheangleofthemastercamA(Equation1),itis desiredthattheuniqueshapeofthecamisfoundfromthat function. 0=f(0)(1) Wesettherotationalaxisofpart(B)astheoriginofthe coordinatesystem,andconsiderthecalculationinthe coordinatesystemonthepart(B)(Fig.11).Thus,the calculationoftheshapeoftheslavecamisperformedinthe samewayasthecalculationoftheenvelopecurve,whichis drawnwhenthemastercamAisrotated. Theenvelopecurvemeansthecurvethatholdsthetangent lineincommonwiththecurvedlinegroup.Thereisatheorem thatontheequationthatincludestheparametera,inshort, g(x,y,oc)=O,thex(oc),y(oc)complywiththeequation(2),(3) andthereisnoparticularityontheg(x,y,oc)=O,inaddition, (x(oc),y(oc)=(O,0)isrealized,wherethecurvelineis expressedas(x(o),y(o)istheenvelopecurveofthegroupof theg(x,y,oc)=0. 4255 5 0 -5 -10 -15 g(x(a),y(a),a)=O ag(x(a),y(a),a) =O -15r (2) (3) Inshort,wecansaythattheenvelopecurveisthetrajectory thatsomecurvedrawsbychangingitsownparameter. Inthisresearch,tocalculatetheshapeofthecamofthe brakingmechanism,wesetthecoordinateaxisandsome parametersasshowninFig.11,thereforethefunctiong(x,y, a)becomes: g(x,y,)=(x-acos(O+Oi,i)bcos(O+z)2 +(y-asin(O+Oini)bsin(O+)2-r2 InEquation(4),“ini“meanstheinitialvalue,andthe+in frontofbbecomes“+“forBIand“-“forB2. Wesettheqasthequadraticfunctionoffsothatthe changeofthedisplacementofqbecomessmoothnearOdeg. f(0)=CO2(5) Intheaboveequation,Crepresentsaconstantnumber. FromEquation5,theenvelopecurvescanbecalculated.The shapesofthecalculatedenvelopecurvesareshowninFig.12. ThecalculatedshapeofthecamisshowninFig.13.We testedanoptimizedactualmodelbasedonthiscalculated shape.TheexperimentalresultisshowninFig.14.Theangle ofB1andB2isnearlyidenticalbetween0degreesand60 degrees,asshowninFig.14. -20 -25- -25 -30 -30 -35 -40 -50510-10-505 xx (a)SlaveCamB1(b)SlaveCamB2 Fig.12:EnvelopeCurve Intheaboveequation,Crepresentsaconstantnumber. FromEquation5,theenvelopecurvescanbecalculated.The shapesofthecalculatedenvelopecurvesareshowninFig.12. ThecalculatedshapeofthecamisshowninFig.13.We testedanoptimizedactualmodelbasedonthiscalculated shape.TheexperimentalresultisshowninFig.14.Theangle ofB1andB2isnearlyidenticalbetween0degreesand60 degrees,asshowninFig.14. 011i ?0 Fig.11:CoordinateAxis Fig.13:CalculatedShapeofCams 0 -5 -10 -15 -20l 01020304050607080 0deg Fig.14:0-0Curve(CalculatedShapeofCams,) 4256 TheSpecificationofthisbrakingmechanismisas follows.Length:111(mm)xWidth:57(mm)x Thickness:15(mm)andWeightisabout422(g)includingthe servomotorwhichmaximumtorqueis0.98(Nm)madeby Futaba. Wealsocheckedthepropertybetween0andthebraking torqueofthebrakingmechanismontheunoptimized(straight) camandtheoptimizedcam.Theexperimentalresultsare showninFig.15,andFig.16respectively.Observethatin Fig.16thevibrationpropertyoftheoptimizedcamissmaller thanthatofthestraightcam.Therefore,thebrakingmechnism consistsoftheoptimizedcamgripstheshaftmorestablythan unoptimizedone. Inthissection,weproposedawayforoptimaldesignof theshapeofthecamandthroughexperimentwithanactual model,weconfirmedthepropertyoftheoptimizedcamis superior.Wewillcontinuetotestthebrakingmechanismfrom thepointsofdurability,efficiencyandsoon. Oneofthecriteriaforthisbrakingmechanismisacompact design.Materialsofthisbrakingmechanismshouldbe lightweightandhavehightensilestrength.Soweultimately choseA7075;kindofaluminum,whichhasadensityof 3.04(g/cm3)andatensilestrengthof585(N/mm2).Especially onthesurfaceofthecam,whichcontactstherollerofthe mastercam,thesurfacetreatmentwasdonetohardenthe slavecamandfordurability. 4000 4000 3500 a) 0 EH 3000 2500 2000 1500 1000 500 -20020 0Deg. 406080 Fig.16:Propertybetween0andBrakingTorqueof optimizedCam HoweverSUS440;kindofstainlesssteelwasselectedfor theshoeofthebrakingmechanismbecausethatmaterialhas higherdurability.SUS440isheavierthanA7075,butasa brakeshoetheissueofdurabilitybecomesdominant.Aftera fieldtestof300applications,itfunctionsnearlyperfectlyand thereisnobigscarfonthesurfaceofthebrakeshoe. 3500 3000 av 0 EH- 2500 2000 1500 100000 - - -E 500-20 0204060 0Deg. Fig.15:Propertybetween0andBrakingTorqueof StraightCam V.REALIZATIONOFUNDERACTUATEDMOTION Thetestdeviceofonearmandwheelmodulewasbuiltto confirmthebasicfunctionoftheunderactuatedperformances asshowninFig.17.Thedevicehasaslidingguideattheroot ofthearm,soifthefloorisnotperfectlyflat,thewheelcan alwaysmaintaincontactlikeoneoftheactualthreewheel-arm modulesofthismobilerobot,asmentionedinsection3.To simplifytheexperimentandtoconsideronlytheknife-edge model,weremovetheknobsofwheelhere.Eachjointangle 80aremeasuredbythepotentiometerputineachjoint. Weinstalledtheoptimizedbrakingmechanism(shown insectionIV)toeachjointofarm,andconfirmedtheeffectof similarfunctionofthemultipleactivejoints,andalso confirmedthatfunctionasshowninFigs.18and19.InFigs. 18and19,observethatthetwojointschangedtheirown angle.Thisistheunderactuatedmotionasexplainedinsection 3. 4257 (a)SideView(b)TopView Fig.17:TestingDeviceforUnderactuationofOneLeg Module Fig.18:Exampleo0UnderactuatedMlotionofuneLeg Module(SideView) Fig.19:Exampleof Module(TopView) 180 160 140 Firstjoint IN)9X SecondJoint dj 80 60- I 0-IV 0 05I15202530 tijmesec Fig.20:ChangingofEachJointAngleofArm Top Side IIIIIIIV Fig.21:MotionofOneLegTestModel Fig.20showstheoneoftheexampleofmeasured dataofthechangingofeachjointangleintheexperiment.In thisexperiment,whenthemeasuredrotationalspeedissmaller thanthesettingone,themastercamArotatesinthedirection toreducethetorqueofthebrakingmechanism.Ontheother hand,whenthemeasuredrotationalspeedislargerthanthe settingone,theangleofthemastercamArotatesinthe directiontoincreasethetorqueofthebrakingmechanism.As showninthisfigure,bothoftheangleoffirstjointandsecond jointarechangedinmeantime. Inaddition,Fig.21showstheunderactuatedmotioninthis experiment,andfromItoIVcorrespondtoI-IVinFig.20each other.Asaresult,weconfirmedthebasicmotionof underactuatedarm-wheelmoduleontheflatground.And Fig.22showsthemodechangingmotionoftheTri-Star3in thetopview.Thefirstshapeiswidetothemovingdirection, afterthat,theshapechangedtoslimmertothemoving direction.Asshowninthispicture,weconfirmedTri-Star3 canchangeitsownshape. 4258 Gennery,D.,Cooper,B.,Nguyen,T.,Litwin,T.,Mishkin,A.,Stone,H.; 1992.Proceedings.,1992IEEEInternationalConferenceonRobotics andAutomation12-14May1992Page(s):175-180vol.1 l1llllll_5“TheMobilityDesignCocepts/CharacteristicsProc.Int.ConfOnMobilePlanetary Robots Y