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外文翻译--三自由度并联机器人精度分析 英文版.pdf

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外文翻译--三自由度并联机器人精度分析 英文版.pdf

ABSTRACTINCREASEINERTIAANDDECREASEOPERATINGSPEED;–ACTIVEJOINTERRORS,COMINGFROMTHEFINITERESOLUTIONOFTHEENCODERS,SENSORERRORS,ANDCONTROLERRORSCORRESPONDINGAUTHOREMAILADDRESSILIANBONEVETSMTLCAIABONEVAVAILABLEONLINEATWWWSCIENCEDIRECTCOMMECHANISMANDMACHINETHEORY432008445–458WWWELSEVIERCOM/LOCATE/MECHMTMECHANISMANDMACHINETHEORY0094114X/SEEFRONTMATTERC2112007ELSEVIERLTDALLRIGHTSRESERVEDPARALLELROBOTSAREINCREASINGLYBEINGUSEDFORPRECISIONPOSITIONING,ANDANUMBEROFTHEMAREUSEDASTHREEDEGREEOFFREEDOM3DOFPLANARALIGNMENTSTAGESCLEARLY,INSUCHINDUSTRIALAPPLICATIONS,ACCURACYISOFTHEUTMOSTIMPORTANCETHEREFORE,SIMPLEANDFASTMETHODSFORCOMPUTINGTHEACCURACYOFAGIVENROBOTDESIGNARENEEDEDINORDERTOUSETHEMINDESIGNOPTIMIZATIONPROCEDURESTHATLOOKFORMAXIMUMACCURACYERRORSINTHEPOSITIONANDORIENTATIONOFAPARALLELROBOTAREDUETOSEVERALFACTORS–MANUFACTURINGERRORS,WHICHCANHOWEVERBETAKENINTOACCOUNTTHROUGHCALIBRATION;–BACKLASH,WHICHCANBEELIMINATEDTHROUGHPROPERCHOICEOFMECHANICALCOMPONENTS;–COMPLIANCE,WHICHCANALSOBEELIMINATEDTHROUGHTHEUSEOFMORERIGIDSTRUCTURESTHOUGHTHISWOULDTHREEDEGREEOFFREEDOMPLANARPARALLELROBOTSAREINCREASINGLYBEINGUSEDINAPPLICATIONSWHEREPRECISIONISOFTHEUTMOSTIMPORTANCECLEARLY,METHODSFOREVALUATINGTHEACCURACYOFTHESEROBOTSARETHEREFORENEEDEDTHEACCURACYOFWELLDESIGNED,MANUFACTURED,ANDCALIBRATEDPARALLELROBOTSDEPENDSMOSTLYONTHEINPUTERRORSSENSORANDCONTROLERRORSDEXTERITYANDOTHERSIMILARPERFORMANCEINDICESHAVEOFTENBEENUSEDTOEVALUATEINDIRECTLYTHEINFLUENCEOFINPUTERRORSHOWEVER,INDUSTRYNEEDSAPRECISEKNOWLEDGEOFTHEMAXIMUMORIENTATIONANDPOSITIONOUTPUTERRORSATAGIVENNOMINALCONFIGURATIONANINTERVALANALYSISMETHODTHATCANBEADAPTEDFORTHISPURPOSEHASBEENPROPOSEDINTHELITERATURE,BUTGIVESNOKINEMATICINSIGHTINTOTHEPROBLEMOFOPTIMALDESIGNINTHISPAPER,ASIMPLERMETHODISPROPOSEDBASEDONADETAILEDERRORANALYSISOF3DOFPLANARPARALLELROBOTSTHATBRINGSVALUABLEUNDERSTANDINGOFTHEPROBLEMOFERRORAMPLIFICATIONC2112007ELSEVIERLTDALLRIGHTSRESERVEDKEYWORDSPARALLELMECHANISMS;ACCURACY;DEXTERITY;PERFORMANCEEVALUATION;ERRORANALYSIS1INTRODUCTIONACCURACYANALYSISOF3DOFPLANARPARALLELROBOTSSEBASTIENBRIOTA,ILIANABONEVB,ADEPARTMENTOFMECHANICALENGINEERINGANDCONTROLSYSTEMS,NATIONALINSTITUTEOFAPPLIEDSCIENCESINSA,RENNES,FRANCEBDEPARTMENTOFAUTOMATEDMANUFACTURINGENGINEERING,ECOLEDETECHNOLOGIESUPERIEUREETS,MONTREAL,CANADARECEIVED21SEPTEMBER2006;RECEIVEDINREVISEDFORM19MARCH2007;ACCEPTED6APRIL2007AVAILABLEONLINE4JUNE2007DOI101016/JMECHMACHTHEORY200704002MOSTONEPASSIVEPRISMATICJOINTINALEGTHEMETHODISILLUSTRATEDONTWOPRACTICALDESIGNS1A3RPRPLANARPARALLELROBOTTHISROBOTISTHEPLANARPROJECTIONOFTHEPAMINSAROBOT6ANDTHE446SBRIOT,IABONEV/MECHANISMANDMACHINETHEORY432008445–458DESIGNPARAMETERSARETHOSEOFTHEPROTOTYPEMANUFACTUREDATINSAOFRENNES,FRANCE2APLANAR3PRRROBOT7APRECISIONPARALLELROBOTBASEDONTHISDESIGNHASBEENDEVELOPEDINTHETECHNICALUNIVERSITYOFBRAUNSCHEIG,INGERMANY8THEREMAINDEROFTHISPAPERISORGANIZEDASFOLLOWSSECTION2BRIEFLYOUTLINESTHEMATHEMATICALTHEOREMSUSEDINTHISPAPERSECTION3PRESENTSTHEMETHODUSEDFORTHEANALYSISOFTHEORIENTATIONANDPOSITIONERRORSFINALLY,SECTION4COVERSSEVERALNUMERICALEXAMPLES,ANDCONCLUSIONSAREGIVENINTHELASTSECTIONTHEREFORE,ASPOINTEDOUTBYMERLET1,ACTIVEJOINTERRORSINPUTERRORSARETHEMOSTSIGNIFICANTSOURCEOFERRORSINAPROPERLYDESIGNED,MANUFACTURED,ANDCALIBRATEDPARALLELROBOTINTHISPAPER,WEADDRESSTHEPROBLEMOFCOMPUTINGTHEACCURACYOFAPARALLELROBOTINTHEPRESENCEOFACTIVEJOINTERRORSONLYINTHEBALANCEOFTHEPAPER,THETERM‘‘ACCURACY’’WILLTHEREFOREREFERTOTHEPOSITIONANDORIENTATIONERRORSOFAPARALLELROBOTTHATISSUBJECTEDTOACTIVEJOINTERRORSONLYTHECLASSICALAPPROACHCONSISTSINCONSIDERINGTHEFIRSTORDERAPPROXIMATIONTHATMAPSTHEINPUTERRORTOTHEOUTPUTERRORDPJDQ;1WHEREDQREPRESENTSTHEVECTOROFTHEACTIVEJOINTINPUTERRORS,DPTHEVECTOROFOUTPUTERRORSANDJISTHEJACOBIANMATRIXOFTHEROBOTHOWEVER,THISMETHODWILLGIVEONLYANAPPROXIMATIONOFTHEOUTPUTMAXIMUMERRORINDEED,ASWEWILLPROVEINTHISPAPER,GIVENANOMINALCONFIGURATIONANDSOMEUNCERTAINTYRANGESFORTHEACTIVEJOINTVARIABLES,ALOCALMAXIMUMPOSITIONERRORANDALOCALMAXIMUMORIENTATIONERRORNOTONLYOCCURATDIffERENTSETSOFACTIVEJOINTVARIABLESINGENERAL,BUTTHESEACTIVEJOINTVARIABLESARENOTNECESSARILYALLATTHELIMITSOFTHEIRUNCERTAINTYRANGESSEVERALPERFORMANCEINDICESHAVEBEENDEVELOPEDANDUSEDTOROUGHLYEVALUATETHEACCURACYOFSERIALANDPARALLELROBOTSARECENTSTUDY2REVIEWEDMOSTOFTHESEPERFORMANCEINDICESANDDISCUSSEDTHEIRINCONSISTENCIESWHENAPPLIEDTOPARALLELROBOTSWITHTRANSLATIONALANDROTATIONALDEGREESOFFREEDOMTHEMOSTCOMMONPERFORMANCEINDICESUSEDTOINDIRECTLYOPTIMIZETHEACCURACYOFPARALLELROBOTSARETHEDEXTERITYINDEX3,THECONDITIONNUMBERS,ANDTHEGLOBALCONDITIONINGINDEX4HOWEVER,INARECENTSTUDYOFTHEACCURACYOFACLASSOF3DOFPLANARPARALLELROBOTS5,ITWASDEMONSTRATEDTHATDEXTERITYHASLITTLETODOWITHROBOTACCURACY,ASWEDEFINEITOBVIOUSLY,THEBESTACCURACYMEASUREFORANINDUSTRIALPARALLELROBOTWOULDBETHEMAXIMUMPOSITIONANDMAXIMUMORIENTATIONERRORSOVERAGIVENPORTIONOFTHEWORKSPACE1,5ORATAGIVENNOMINALCONFIGURATION,GIVENACTUATORINACCURACIESAGENERALMETHODBASEDONINTERVALANALYSISFORCALCULATINGCLOSEAPPROXIMATIONSOFTHEMAXIMUMOUTPUTERROROVERAGIVENPORTIONOFTHEWORKSPACEWASPROPOSEDRECENTLYIN1OBVIOUSLY,THEMAXIMUMOUTPUTERROROVERAGIVENPORTIONOFTHEWORKSPACEISTHEMOSTIMPORTANTINFORMATIONFORADESIGNERHOWEVER,THISMETHODISRELATIVELYDIffiCULTTOIMPLEMENT,GIVESNOINFORMATIONONTHEEVOLUTIONOFTHEACCURACYOFTHEMANIPULATORWITHINITSWORKSPACEANDGIVESNOKINEMATICINSIGHTINTOTHEPROBLEMOFOPTIMALDESIGNINCONTRAST,AVERYSIMPLEGEOMETRICMETHODFORCOMPUTINGTHEEXACTVALUEOFTHEACCURACYOF3DOF3PRPPLANARPARALLELROBOTSWASDESCRIBEDIN5INTHISPAPER,PANDRSTANDFORPASSIVEPRISMATICANDREVOLUTEJOINS,RESPECTIVELY,WHILEPANDRSTANDFORACTUATEDPRISMATICANDREVOLUTEJOINS,RESPECTIVELYTHISMETHODPROPOSESTOREPLACETHEEXISTINGDEXTERITYMAPSBYMAXIMUMPOSITIONERRORMAPSANDMAXIMUMORIENTATIONERRORMAPSWHILETHISMETHODCOVERSTHREEOFTHEMOSTPROMISINGDESIGNSFORPRECISIONPARALLELROBOTSONEOFWHICHISCOMMERCIALIZEDANDTHEOTHERTWOBUILTINTOLABORATORYPROTOTYPES,ITDOESNOTALWAYSWORKFOROTHER3DOFPLANARPARALLELROBOTSTHISPAPERGENERALIZESTHEMETHODPROPOSEDIN5BYFOLLOWINGADETAILEDMATHEMATICALPROOFWHICHGIVESUSIMPORTANTINSIGHTINTOTHEACCURACYOFPLANARPARALLELROBOTSTHEPRESENTSTUDYCONSIDERSONLY3DOFTHREELEGGEDPLANARPARALLELROBOTSWITHPRISMATICAND/ORREVOLUTEJOINTS,ONEACTUATEDJOINTPERLEG,ANDAT2MATHEMATICALBACKGROUNDANALYZINGTHELOCALMAXIMUMPOSITIONERRORANDTHELOCALMAXIMUMORIENTATIONERROROFAPARALLELROBOT,INDUCEDBYBOUNDEDERRORSINTHEACTIVEJOINTVARIABLES,ISBASICALLYSTUDYING,ONASETOFCLOSEDINTERVALS,THEMAXIMAOFFUNCTIONSDXANDD/,DEFINEDASDXffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXC0X02YC0Y02Q;2D/ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi/C0/02Q;3WHEREX0,Y0AND/0ARETHECARTESIANCOORDINATESCORRESPONDINGTOTHENOMINALDESIREDPLATFORMPOSEPOSITIONANDORIENTATIONOFTHESTUDIEDPARALLELROBOT,ANDX,YAND/ARETHEACTUALPLATFORMCOORDINATESINTHECASEOFA3DOFPLANARFULLYPARALLELROBOT,DXANDD/AREFUNCTIONSOFTHREEVARIABLESTHEACTIVEJOINTVARIABLESOFTHEROBOTTHEINPUTS,WHICHWILLBEDENOTEDBYQIINTHISPAPER,I1,2,3THUS,WEHAVETOFINDTHEMAXIMAOFDXANDD/ONTHESETOFINTERVALSQI2QI0C0E;QI0EC138,WHEREQI0ARETHEACTIVEJOINTVARIABLESCORRESPONDINGTOTHENOMINALPOSEX0,Y0,/0OFTHEPLATFORMINTHESELECTEDWORKINGMODE,IE,THESELECTEDSOLUTIONTOTHEINVERSEKINEMATICSANDEISTHEERRORBOUNDONTHEACTIVEJOINTVARIABLESFIG1TOSIMPLIFYOURERRORANALYSIS,WEWILLMAKETHEPRACTICALASSUMPTIONTHATTHENOMINALCONFIGURATIONISSUFSBRIOT,IABONEV/MECHANISMANDMACHINETHEORY432008445–458447FIG1INPUTERRORBOUNDINGBOXFICIENTLYFARFROMTYPE1ANDTYPE2SINGULARITIESTYPE1SINGULARITIES9ARECONFIGURATIONSWHEREAPARALLELROBOTLOSESITSDESIREDFUNCTIONALITY–ITLOSESONEORMOREDEGREESOFFREEDOMTHESEARETHEINTERNALANDTHEEXTERNALBOUNDARIESOFWORKSPACEFORTHISREASON,THEUSABLEWORKSPACEOFANINDUSTRIALPARALLELROBOTWILLBEAWAYFROMTHESESINGULARITIESSIMILARLY,TYPE2SINGULARITIES9AREANOTHERKINDOFCONFIGURATIONSWHEREAPARALLELROBOTLOSESITSDESIREDFUNCTIONALITY–THISTIMEITLOSESCONTROLOFTHEMOBILEPLATFORMFURTHERMORE,NEARTHESECONFIGURATIONS,THEOUTPUTERRORINCREASESEXPONENTIALLYFORTHESEREASONS,INDUSTRIALPARALLELROBOTSAREDESIGNEDTOEXCLUDESUCHSINGULARITIESTHEREFORE,WEWILLOBVIOUSLYPERFORMOURERRORANALYSISONLYFORCONFIGURATIONSTHATARESUffiCIENTLYFARFROMSINGULARITIES,IE,FORNOMINALCONFIGURATIONSFROMWHICHTHEROBOTCANNOTENTERINTOSINGULARITYWHILETHEACTIVEJOINTVARIABLESSTAYWITHINTHEIRERRORBOUNDEDINTERVALSONCEWEHAVEMADETHISPRACTICALASSUMPTION,WEADDRESSTHEPROBLEMOFFINDINGTHEGLOBALMAXIMAOFDXANDD/ITISWELLKNOWNTHATTHEMAXIMUMOFACONTINUOUSMULTIVARIABLEFUNCTION,F,OVERAGIVENSETOFINTERVALSCANBEFOUNDBYANALYSINGTHEHESSIANMATRIX,HH1Q1FQ1;Q20E;Q30E;H7Q2FQ10E;Q2;Q30C0E;IFSUCHFINTHESEFINANDDTHESINGULARITY–THEFIGCOULDDENOTEDCENTRE448SBRIOT,IABONEV/MECHANISMANDMACHINETHEORY432008445–458WITHINTHEINTERVALSTUDIEDTWISTOFTHEMOBILEPLATFORM,WHENLEGSJANDKJ,K1,2,3,I5J5KAREFIXED,ISAPURETRANSLATION2REPRESENTSTHEMOBILEPLATFORMOFAROBOTLINKEDTOTHREEACTUATEDLEGS,THROUGHREVOLUTEJOINTSTHESEBEPRISMATICJOINTSASWELLEACHLEGAPPLIESAWRENCHRIONTHEMOBILEPLATFORM,WHOSECENTERISBYPTHEINTERSECTIONPOINTO3OFTHEWRENCHESR1ANDR2REPRESENTSTHEINSTANTANEOUSROTATIONIITHESEDERIVATIVESAREEQUALTOZEROIFO//OQI0ORIF/C0/00OBVIOUSLY,HOWEVER,AMAXIMUMCANEXISTONLYIFO//OQI0FORA3DOFPLANARPARALLELROBOT,TWODIffERENTSITUATIONSCORRESPONDTOTHECONDITIONO//OQI0–THEROBOTISATATYPE1SINGULARITYHOWEVER,WEALREADYASSUMEDTHATTHEROBOTCANNOTENTERATYPE1PARTIALDERIVATIVESOFD/2AREGIVENASOD/2OQ2O/OQ/C0/053ANALYSISOFTHEORIENTATIONANDPOSITIONERRORS31MAXIMUMORIENTATIONERRORH6Q2FQ10C0E;Q2;Q30E;H12Q3FQ10C0E;Q20C0E;Q3POINTSEXIST,WEWILLCALLTHEMMAXIMAOFTHETHIRDKINDALLY,THEGLOBALMAXIMUMOFFCOULDALSOBEONONEOFTHEEIGHTCORNERSOFTHEINPUTERRORBOUNDINGBOXEIGHTPOINTSWILLBEREFERREDTOASEXTREMAOFTHEFOURTHKINDDINGTHEGLOBALMAXIMAOFFUNCTIONSDXANDD/ISEQUIVALENTTOFINDINGTHEMAXIMAOFFUNCTIONSDX2/2INTHENEXTSECTION,WEWILLSTUDYTHEEXTREMAOFTHEFUNCTIONSDX2ANDD/2H2Q1FQ1;Q20E;Q30C0E;H8Q2FQ10C0E;Q2;Q30C0E;H3Q1FQ1;Q20C0E;Q30E;H9Q3FQ10E;Q20E;Q3;H4Q1FQ1;Q20C0E;Q30C0E;H10Q3FQ10E;Q20C0E;Q3;H5Q2FQ10E;Q2;Q30E;H11Q3FQ10C0E;Q20E;Q3;22310235121230G3Q1;Q3FQ1;Q20E;Q3;G6Q1;Q2FQ1;Q2;Q30C0EIFSUCHPOINTSEXIST,WEWILLCALLTHEMMAXIMAOFTHESECONDKINDTHEGLOBALMAXIMUMOFFCOULDALSOBEONTHEEDGESOFTHEINPUTERRORBOUNDINGBOXTHISTIME,WEHAVETOSTUDYTHEMAXIMAOFTWELVEUNIVARIATEFUNCTIONSG1Q2;Q3FQ10E;Q2;Q3;G4Q1;Q3FQ1;Q20C0E;Q3;GQ;QFQC0E;Q;Q;GQ;QFQ;Q;QE;HO2FOQ21O2FOQ1OQ2O2FOQ1OQ3O2FOQ22O2FOQ2OQ3SYMO2FOQ23266664

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