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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 damototheroversofNASA 3 Aplanetaryrovermusthavebehighlyadaptableto uneventerrain 4 Theintroductionofhighlysophisticated multiple degreesoffreedomvehiclemechanismsandthe implementationofadvancedcontrolofthesemechanisms seemstohavebeenacommonmethodtoachievesuch objectives However thereliabilityofthemechanismisofextreme importance andtheresearchapproachofourlaboratoryisto realizeterrainadaptabilitywithasimplemechanism 5 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 Step3 ontheshaft DegreesofFreedom Torealizeasimilarfunctionofamultipledegrees of freedomarm wesuggestthefollowingmethod Bychangingthefrictionalconditionofeachjoint and withthedrivingwheel eachjointcanchangetheirownangle inasimilarfashionsothatthewholejointsperformlikean activerotationalactuator Thismotionmakesthewholeshape ofthearmchangeableattheend Themotionofthis configurationissimilartoexpandablegatesoftenfoundin airports InFig 6 from Step2 to Step3 therotationaldirectionof thewheelchanges Therefore theshapeofthewholearm changessuchasletter S Inthe3 wheeledexpandablerover weadopttheonelink consideringthesimplicityofthe configurationofthearm IV JOINTBRAKINGMECHANISM Inthischapter thedrumtypebrakingmechanismis explainedindetail Asabrakingmechanism thelock pintypemechanism 6 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 M Camr Q f tw J MasterCamA SpringPart C 2 SlaveCamB2 a StructureofBrakingMmPart B 2 a StructureofBrakingMechnism 01020304050607080 master deg 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 differentialmechanism 7 todirectlymeasurethetorque 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 changeofthedisplacementofqbecomessmoothnearO deg f 0 CO2 5 Intheaboveequation C representsaconstantnumber 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 C representsaconstantnumber 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 0 deg 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 chose A7075 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 0 Deg 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 0 Deg 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 05 I15202530 tijme sec 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 ConfOnMobilePl