玻璃清洁机器人结构设计【全套含CAD图纸、SW三维模型】
收藏
资源目录
压缩包内文档预览:
编号:10079146
类型:共享资源
大小:77.31MB
格式:ZIP
上传时间:2018-05-06
上传人:机****料
认证信息
个人认证
高**(实名认证)
河南
IP属地:河南
100
积分
- 关 键 词:
-
玻璃
清洁
机器人
结构设计
全套
cad
图纸
sw
三维
模型
- 资源描述:
-
- 内容简介:
-
REVERSALSINPARTICULAR,WESHOWTHATREVERSALSAREPRONOUNCEDINMACHININGEVENPLANESURFACESANDSTRAIGHTLINESWITHPARALLELMACHINETOOLSANDAREGENERALLYDICULTTOAVOIDINMULTIAXISFREEFORMMACHININGWITHMOSTTYPESOFMACHINETOOLSMECHANISMANDMACHINETHEORY392004299322CORRESPONDINGAUTHORTEL16172531925FAX161725375491INTRODUCTIONWHENJOINTSINAMACHINETOOLMECHANISMUNDERGOAREVERSALINTHEIRDIRECTIONOFMOTION,SEVERALANOMALIESOCCUR,WHICHMUSTBETAKENCAREOFTOACHIEVEHIGHPRECISIONTHISPAPERDEALSWITHTHEKINEMATICSOFREVERSALSINMACHINETOOLMECHANISMS,CONCENTRATINGMOSTLYONTHETHEORYANDTHEPROPERTIESOFREVERSALSANDREVERSALFREEPATHSTHESEEECTSTENDTOBEIGNOREDDURINGTHEINITIALSTAGESOFMECHANISMDESIGN,ANDOURGOALISTOPRESENTTHETHEORETICALBASISFORPREDICTINGONACTUATORREVERSALMOTIONSOFMACHINETOOLSTAEJUNGKIMA,SEUNGKILSONB,SANJAYESARMAA,ADEPARTMENTOFMECHANICALENGINEERING,MASSACHUSETTSINSTITUTEOFTECHNOLOGY,35010,MIT,CAMBRIDGE,MA02139,USABENGINEERINGDIVISION,LAWRENCEBERKELEYNATIONALLABORATORY,BERKELEY,CA94720,USARECEIVED30AUGUST2002RECEIVEDINREVISEDFORM16JUNE2003ACCEPTED17SEPTEMBER2003ABSTRACTWHENJOINTSINAMACHINETOOLREVERSETHEDIRECTIONOFTHEIRMOTION,NONLINEARITIESTHATAREIGNOREDINMACHINEDESIGNANDCONTROLAREREFLECTEDNOTICEABLYINTHEACCURACYOFMACHINEDSURFACESFOREXAMPLE,FRICTIONCHARACTERISTICSOFAMACHINETOOLBECOMEHIGHLYNONLINEARATLOWOPERATINGSPEEDS,DEMANDINGSOPHISTICATEDCOMPENSATIONWEPRESENTATHEORETICALTREATMENTOFTHEKINEMATICSOFREVERSALSANDREVERSALFREEPATHSOFMACHINETOOLSWEVISUALIZEANDCOMPAREREVERSALCHARACTERISTICSOFACTIVEJOINTSINSERIAL,PARALLEL,ANDHYBRIDMECHANISMSFORVARIOUSTRAJECTORIESANDSWEEPINGPATTERNSREVERSALCHARACTERISTICSHAVEIMPLICATIONSBOTHINTHEDESIGNOFMACHINETOOLSANDINPATHPLANNINGC2112003ELSEVIERLTDALLRIGHTSRESERVEDKEYWORDSREVERSALFRICTIONMACHINETOOLKINEMATICSWWWELSEVIERCOM/LOCATE/MECHMTEMAILADDRESSSESARMAMITEDUSESARMA0094114X/SEEFRONTMATTERC2112003ELSEVIERLTDALLRIGHTSRESERVEDDOI101016/JMECHMACHTHEORY200309002300TKIMETAL/MECHANISMANDMACHINETHEORY392004299322THECOMPLICATIONSASSOCIATEDWITHREVERSALSARISEFROMTHEFACTTHATTHEYEXACERBATENONLINEARITIESINTHEBEHAVIOROFBEARINGSANDDRIVEMECHANISMSACLASSICALEXAMPLEOFAREVERSALRELATEDPROBLEMISBACKLASHINLEADSCREWSBACKLASHARISESWHENAREVERSALINTHELOADINGOFADRIVEMECHANISMCAUSESTHEPOINTOFCONTACTINTHEBEARINGTOCHANGESUDDENLYINPRACTICE,BACKLASHINPRECISIONMECHANISMSCANBEREDUCEDBYPRELOADINGJOINTSTOREDUCEPLAYAMOREFUNDAMENTALNONLINEARITYWHICHISMAGNIFIEDDURINGMOTIONREVERSALSISTHETRANSITIONBETWEENSTATICANDDYNAMICREGIMESOFFRICTIONINJOINTSFIG1ASHOWSTHETYPICALBEHAVIOROFFRICTIONINALUBRICATEDJOINTASITTRANSITIONSFROMLOWVELOCITYTOHIGHVELOCITYMOTIONSTHEFRICTIONMECHANISMCHANGESFROMSTICTIONEECTSTOTHESTRIBECKEECTTOMORELINEARLYVISCOUSBEHAVIOR2THEMAGNITUDEOFTHEFRICTIONFORCEINCREASESANDSWITCHESDIRECTIONASTHEJOINTPASSESTHROUGHTHEZEROSPEEDREGIMESIMPLELINEARCONTROLSTRATEGIES,DESIGNEDFORLINEARVISCOUSFRICTIONMODELS,COMPENSATETHISEECTPOORLY,ANDCANSUERFROMDELAYS,TRACKINGIRREGULARITIESANDLOSSOFMACHININGPRECISION3QUADRANTGLITCHES,ASSHOWNINFIG1B,ARETYPICALEXAMPLESOFFRICTIONINDUCEDERRORSGENERATEDDURINGCIRCULARENDMILLINGONA3AXISMILLINGMACHINE4FIG1ATYPICALFRICTIONCHARACTERISTICINAJOINTANDITSNEGATIVEEECTINPRECISIONARELATIONBETWEENFRICTIONANDVELOCITYBQUADRANTGLITCHESCOURTESYOFEUGENETUNG4BETTERTRACKINGPRECISIONCANBEATTAINEDINTHISREGIMEBYINCREASINGTHEGAININTHECONTROLLEREVERYTIMETHEANOMALYOCCURS,ORBYADOPTINGMORECOMPLEXCONTROLSTRATEGIESHOWEVER,IMPLEMENTINGTHESESTRATEGIESREQUIRESMOREADVANCEDCONTROLLERS,ANDCAREFULEXPERIMENTATIONFORPARAMETERIDENTIFICATION,WHICHAREBOTHNECESSARILYMOREEXPENSIVEITISBEST,THEREFORE,TOAVOIDTHEOCCURRENCEOFREVERSALSDURINGCRITICALMOTIONSTHATTHEDESIGNERCONSIDERSIMPORTANT11REVERSALCHARACTERISTICSASDESCRIBEDABOVE,ITWOULDBEDESIRABLEFORAMACHINETOOLTOBEDESIGNEDINSUCHAWAYTHATREVERSALSDONOTOCCURINSITUATIONSWHERETHEYWOULDHURTPERFORMANCEINCARTESIANMACHINES,FOREXAMPLE,REVERSALSDONOTOCCURWHILETHEMACHINEISEXECUTINGAUNIDIRECTIONALMOTIONINASTRAIGHTLINETRAJECTORYTHISISVERYIMPORTANTBECAUSETHESTRAIGHTLINEHASASPECIALANDFUNDAMENTALROLEINDESIGNANDMANUFACTURINGASADATUMANDASAMATINGSURFACEREVERSALSDOOCCURINCARTESIAN3AXISMACHINES,BUTONLYINPLACESWHERETHEDIRECTIONOFMOTIONISEXPLICITLYREVERSED,SUCHASINMACHININGACIRCLEASSHOWNINFIG1BTHISCONSTITUTESGOODKINEMATICTKIMETAL/MECHANISMANDMACHINETHEORY392004299322301BEHAVIORFROMTHEPOINTOFVIEWOFREVERSALSALLREVERSALSOCCURINANEASILYDESCRIBABLEWAY,ANDREVERSALCHARACTERISTICSAREPOSITIONINDEPENDENTANDCONFIGURATIONINDEPENDENTUNFORTUNATELY,NOTALLMACHINESHAVETHESEDESIRABLEPROPERTIES,ANDREVERSALSAREESPECIALLYDICULTTOPREDICTINPARALLELMACHINESAPARALLELMACHINEMAYSUERAREVERSALWHILEPRESCRIBINGASTRAIGHTLINEMOTIONINITSWORKSPACETHISBEHAVIORCOULDTURNOUTTOBEASEVEREIMPEDIMENTTOTHEUSEOFPARALLELMACHINESINMACHININGAPPLICATIONSSERIALCARTESIANMACHINETOOLSTOOSUERFROMREVERSALSDURINGFREEFORMMACHININGINMACHININGANAERODYNAMICALLYCRITICALSURFACE,FOREXAMPLE,ACURVEDTRAJECTORYMAYRESULTINUNDESIRABLEREVERSALINDUCEDRIDGESUNDERSTANDINGTHESEPROBLEMSISIMPORTANT,ANDWEEXAMINEANUMBEROFISSUESINTHISPAPERWHERETHEREVERSALSOCCURINAPATH,WHATTHENATUREOFREVERSALFREEPATHSIS,WHEREREVERSALSAREINEVITABLEREGARDLESSOFDIRECTIONOFMOTION,HOWTHEREGIONSOFREVERSALFREEREACHABILITYAREDERIVEDANDSOONOURTREATMENTISMOSTLYTHEORETICAL,ANDBASEDONTHEKINEMATICSOFAGIVENMACHINEMUCHOFTHECONTRIBUTIONOFTHISPAPERLIESINDEVELOPINGTHEMATHEMATICALMACHINERYNECESSARYTODESCRIBEREVERSALSANDRELATEDCONCEPTSPRECISELYANDUNAMBIGUOUSLY12BACKGROUNDTHEPROBLEMOFBACKLASHHASBEENANAGEOLDCHALLENGEINMACHINEDESIGN,ANDHASRECEIVEDAGREATDEALOFATTENTIONINTHEMACHINEELEMENTCOMMUNITYADESCRIPTIONOFIDEASANDTECHNIQUESINMACHINEELEMENTSISAVAILABLEIN1THEREHASBEENAGREATDEALOFLITERATUREONFRICTIONMODELS,ANDACOMPREHENSIVESUMMARYISAVAILABLEIN5ANELABORATEMODELOFFRICTIONPRESENTEDBYCANUDASDEWITETAL6CAPTURESTHEDIERENTEECTSTHATMUSTBECONSIDEREDINREVERSALSITUATIONSINCLUDINGTHEEARLYWORKOFCOULOMB,OFDUDLEY7,WHOSHOWEDTHATSTICKSLIPISNOTCAPTUREDBYCOULOMBANDVISCOUSMODELS,OFRABINOWICZ9,WHOSHOWEDTHATTHEREISATIMELAGBETWEENTHEBEGINNINGOFMOTIONANDTHEAPPEARANCEOFAFRICTIONFORCE,ANDOFDAHL8WHOFURTHERINCORPORATEDHYSTERETICEECTSHOWEVER,EVENCANUDASDEWITC213S6PARAMETERMODELDOESNOTCAPTUREALLTHESUBTLETIESOFFRICTION,SUCHASTHEDEPENDENCEOFFRICTIONONTHETIMEDERIVATIVEOFAPPLIEDFORCEINADDITION,FRICTIONPARAMETERSHAVEBEENSHOWNTOBEHIGHLYVARIABLEWITHINTHEWORKSPACE,ANDOVERTIME10NEVERTHELESS,THISMODELFORMSTHEBASISOFANUMBEROFCONTROLMETHODSTHATHAVEBEENPROPOSEDINTHELASTFEWYEARSRESEARCHERSINTHEFIELDOFMOTIONCONTROLHAVEPROPOSEDARICHVARIETYOFCOMPENSATIONMETHODSTOACHIEVESMOOTHMOTIONWITHHIGHACCURACYUNDERTHEACTIONOFFRICTIONNOTBEINGTHEFOCUSOFTHISPAPER,WEPRESENTONLYAROUGHOVERVIEWHERECOMPREHENSIVESUMMARIESAREAVAILABLEIN11,12THETECHNIQUESFORCONTROLOFSYSTEMSUNDERFRICTIONINCLUDEESTIMATIONANDADAPTIVEMETHODS13,14,ROBUSTCOMPENSATIONSCHEMES15,REPETITIVECONTROL4,MULTILOOPCONTROL16,NONLINEARCOMPENSATIONSIMILARTOSLIDINGMODE17,NONLINEARPIDWHICHCHANGESTHEGAINDEPENDINGONPLANTSTATE18ANDABROADCLASSOFPULSECODEMODULATIONTECHNIQUESWHICHARESUMMARIZEDIN12THEREISAGREATDEALOFLITERATUREONPARALLELMACHINES,ANDTHEREAREDOZENSOFMILLINGMACHINESWHICHUSEPARALLELKINEMATICSTRUCTURESASUMMARYISAVAILABLEIN19THEPUTATIVEADVANTAGEOFPARALLELMACHINESOVERTHEIRSERIALCOUNTERPARTSISTHATTHELOADCANBEDISTRIBUTEDMOREEVENLYTOTHEIRKINEMATICLINKSAND,ASARESULT,AHIGHERSTINESSCANBEACHIEVEDUSINGLIGHTERSTRUCTURALELEMENTSANDLESSEXPENSIVEACTUATORSHOWEVERWEWILLSHOWTHATTHECOUPLEDKINEMATICSOF302TKIMETAL/MECHANISMANDMACHINETHEORY392004299322PARALLELMECHANISMSCANCAUSEREVERSALSINTHEIRJOINTSFORSEEMINGLYSIMPLEANDSTRAIGHTTRAJECTORIESFURTHERMORE,STUDIESHAVESHOWNTHATTHEERRORSINANACTUATORPROPAGATESINTOALLTHECOORDINATEAXES19,ANDTHISCANBEPROBLEMATICWHENITISIMPORTANTTOMAINTAINPLANARITYORSTRAIGHTNESSINADDITION,THEREISLITERATURETHATSHOWSTHATFREQUENTACTUATORREVERSALSCANEXCITEHIGHERHARMONICCOMPONENTSINTHEMACHINETOOLSTRUCTURE20,21THISINCREASESTHENECESSARYSTRUCTURALSTINESSOFPARALLELMACHINESAND,TOSOMEEXTENT,UNDERMINESTHEVERYBASISFORWHICHPARALLELMECHANISMSAREPREFERREDINTHEFIRSTPLACEBEYONDTHIS,HOWEVER,THEREAPPEARSTOBELITTLEPRIORWORKINTHESTUDYOFREVERSALSINSERIALORPARALLELMACHINETOOLS13OUTLINEANABSOLUTELYFAIRCOMPARISONAMONGSTDIERENTMACHINETOOLMECHANISMSISNOTEASYTOESTABLISHFORREVERSALBEHAVIORBECAUSEPERFORMANCEDEPENDSONTHETRAJECTORIESCONSIDEREDANDONTHETASKSATHANDIFFOREXAMPLE,THEMACHINEISNOTREQUIREDTOCUTFLATSURFACES,BUT,SAY,SPHERESFIG2THEMACHINESWECONSIDERAASERIAL,BHYBRIDANDCPARALLELMACHINETOOLINSTEAD,APARALLELMACHINEOFACERTAINCONFIGURATIONMAYBEMORENATURALTHANACARTESIANSERIALMACHINEINSTEADOFMAKINGASSUMPTIONSABOUTTHETASKTHATTHEMACHINEISCONSIDEREDFOR,WEWILLDEFINETHECONCEPTOFATASKSPACEWHICHPROVIDESTHECAPABILITYOFCAPTURINGANYTASKSURFACE,ANDWEWILLASKHOWMANYREVERSALSCANOCCURINATYPICALPATHANDWHETHERITISPOSSIBLETOACHIEVETHESAMEOBJECTIVEWITHAREDUCEDNUMBEROFREVERSALSINSECTION2,WESETAMATHEMATICALFRAMEWORKUPONWHICHTHERESTOFTHISPAPERISBASEDINSECTION3,WEANSWERFUNDAMENTALQUESTIONSABOUTTHEBEHAVIOROFREVERSALSANDDEVELOPMETHODSOFANALYSISINSECTION4,WEPRESENTSOMEEXAMPLESWITHTHREETYPESOFMACHINETOOLSASERIAL,AHYBRIDANDAPARALLELMACHINEASSHOWNINFIG2WECONCLUDEINSECTION52AFRAMEWORKFORANALYSISINTHISSECTION,WELAYDOWNAMATHEMATICALFRAMEWORKUPONWHICHTHERESTOFTHISPAPERISBASEDITISASSUMEDTHATWHATWEWILLCALLARESTRICTEDINVERSEKINEMATICSMAPISKNOWNTHISSECTIONSIMPLYDEFINESTHETERMANDJUSTIFIESTHENEEDFORTHISASSUMPTIONTODESCRIBETHEMOTIONOFACUTTINGTOOL,WEATTACHAFIDUCIALPOINTONTHECENTERLINEOFTHECUTTINGTOOLNEARTHETOOLTIP13TUPLESOFTHECARTESIANCOORDINATESOFTHEFIDUCIALPOINTCONSTITUTEWHATWEREFERTOASTHEWORKSPACEOFTHEMACHINETOOLINGENERAL,ACUTTINGTOOL,ASARIGIDBODY,HAS6DEGREESOFFREEDOMTHREEFORTHETRANSLATIONOFTHEFIDUCIALPOINTANDANOTHERTHREEFORINTERESTIDENTICALTKIMETAL/MECHANISMANDMACHINETHEORY392004299322303WECANPERFORM5AXISMACHININGUSING6AXISMACHINESTHEADDITIONALONEDEGREEOFFREEDOMISREDUNDANTIN3AXISMACHINING,ONLYTRANSLATIONOFACUTTINGTOOLISALLOWEDANDTHETASKSPACEDIMENSIONIS3INTHEPATHPLANNINGSTAGE,THEDIMENSIONCANBEFURTHERREDUCEDBYINTRODUCINGTASKCONSTRAINTSFOREXAMPLEIN3AXISROUGHING,ITISCOMMONTOREMOVEMATERIALFROMTHESTOCKLAYERBYLAYERINTHISCASE,THETASKCONSTRAINTISTHATTHEFIDUCIALPOINTSHOULDSTAYONAPLANEWHILEALAYEROFMATERIALISREMOVED,ANDTHETASKSPACEDIMENSIONOFMACHININGEACHLAYERIS2INFINISHINGTHESURFACEOFAFREEFORMPARTUSING5AXISMACHINING,THETOOLTIPISCONSTRAINEDTOCONTACTTHEREQUIREDSURFACE,ANDTHETASKSPACEDIMENSIONOFFINISHINGISREDUCEDTO4WHENPLANNINGFINISHINGPATHS,COLLISIONFREEORIENTATIONSOFACUTTINGTOOLATEACHPOINTONTHEDESIGNEDSURFACECANBEDETERMINEDBYACOLLISIONDETECTIONPREPROCESSOR,ANDTHEREMAININGPLANNINGTASKCANBEPERFORMEDONA2DIMENSIONALSPACEINTHISCASE,THETASKSPACEDIMENSIONIS2CONSIDERAMACHINETOOLPOSSESSINGNDEGREESOFFREEDOMANDAMACHININGSTRATEGYWHOSETASKSPACEDIMENSIONISM6NTHEMOTIONOFACUTTINGTOOLRESTRICTEDTOTHESTRATEGYCANBECAPTUREDBYAHISTORYOFMTUPLESOFREALNUMBERSWEREFERTOTHETOTALITYOFTHEMTUPLESREPRESENTINGTHERESTRICTEDPOSTURESASTHETASKSPACEUNDERTHESTRATEGYTHETOTALITYOFTHENTUPLESOFDISPLACEMENTSOFACTUATORSINTHEMACHINEISREFERREDTOASTHEACTUATIONSPACEWEASSUMETHATTHEKINEMATICSOFAMACHINETOOLANDTHECONSTRAINTSINTRODUCEDBYAMACHININGSTRATEGYDETERMINEASMOOTHMAPFFROMTHETASKSPACEUC26RMOFTHESTRATEGYTOTHEACTUATIONSPACEHC26RNOFTHEMACHINETOOL,FUHUHFUWHICHWEREFERTOASTHERESTRICTEDINVERSEKINEMATICMAPANYREDUNDANCYMUSTBERESOLVEDINAPOINTWISEMANNERORHOLONOMICALLYBASEDONOURASSUMPTIONWEASSUMETHATTHETASKSPACEUISSIMPLYCONNECTEDANDTHATITAVOIDSSINGULARITIESBYCHOICETHERANGEFUOFTHEMAPISANMDIMENSIONALSUBSPACEOFTHENDIMENSIONALACTUATIONSPACETHEACTUATORDISPLACEMENTHCANBETHOUGHTOFASONEOFTHELOCALCOORDINATESOFTHECONFIGURATIONSPACEOFTHEMACHINETOOLTHISSETTINGISGENERALENOUGHFOROURPURPOSE,EVENTHOUGHCOMPLETEGENERALITYCANBEACHIEVEDBY1SINCEACUTTINGTOOLHASANONZERODIAMETER,THECONTACTPOINTBETWEENTHETOOLANDTHESURFACEISNOTNECESSARILYONTHELINEOFSYMMETRYOFTHETOOL22HOWEVER,ALOOSEDEFINITIONOFTHELOCATIONOFTHEFIDUCIALPOINTSUCESFOROURCURRENTASTHETASKSPACEDIMENSIONOFTHEAPPLICATIONTHETASKSPACEDIMENSIONISNOTNECESSARILYTOTHEDEGREESOFFREEDOMOFTHEMACHINEINVOLVEDINTHEMACHININGTASKFOREXAMPLE,THEROTATIONOFTHECUTTINGTOOLSINCEWEARECONSIDERINGMILLINGMACHINES,ANDBECAUSECUTTINGTOOLSCANBECONSIDEREDTOBEAXISYMMETRIC,THESIXTHFREEDOMOFMOTION,WHICHISTHESPINABOUTTHECENTERLINEOFACUTTINGTOOL,ISTYPICALLYUNNECESSARYANDREDUNDANTTHEREFORE,TWOADDITIONALCOORDINATESAREENOUGHTODESCRIBETHEORIENTATIONOFA5AXISMACHINEINTHECONTEXTOFMILLINGALLTHREEDEGREESOFFREEDOMOFROTATIONMAYBENECESSARYINOTHERAPPLICATIONSWEREFERTOTHENUMBEROFDEGREESOFFREEDOMOFTHECUTTINGTOOLRESTRICTEDTOOURSUBJECTIVEANALYSISDISPLACEMENTSARIGOROUSSTATEMENTOFTHEABOVEASSUMPTIONEXCEEDSTHESCOPEOFOURCURRENTTREATMENT,DESCRIBED3REVERSALANALYSISREVERSINGMOTIONCOMPARE311AREVERSALCONDITIONONATRAJECTORYFORATRACKINGTASKANYI,WEREFERTOTHEPOINTUT0ASAREVERSALPOINTIFTHEREISNOREVERSALPOINTALONGATRAJECTORY,312REVERSALSINGULARPOINTSANDSTRONGREVERSALSINGULARPOINTSATAPOINTU2UINTHETASKSPACEU,IFTHEREISANINTEGERK2F12NGSUCHTHAT304TKIMETAL/MECHANISMANDMACHINETHEORY392004299322RFKC17OFKOU1OFKOU2OFKOUMC20C210WEREFERTOTHEPOINTUASAREVERSALSINGULARPOINTWITHRESPECTTOTHEKTHACTUATOR,WHEREFKISTHEWESAYTHATTHETRAJECTORYISREVERSALFREEFORTHEITHACTUATORTOBEREVERSEDATT20TC138ALONGAREGULARTRAJECTORY,ITISSUCIENTTHAT_HITC17DDTFIUTXMJ1OFIOUJC1DUJDTC18C190ANDHITC17D2DT2FIUT60THISCONDITIONITSELFSUGGESTSASTRAIGHTFORWARDPROCEDUREFORFINDINGTHEREVERSALPOINTSALONGAGIVENREGULARTRAJECTORYINTHETASKSPACEPLOTTINGANDCOUNTINGREVERSALPOINTSALONGSPECIFIEDTRAJECTORIESISAONEWAYTOVISUALIZEORTOCOMPARETHEREVERSALCHARACTERISTICSOFMACHINETOOLSAFUNDAMENTALFUNCTIONOFAMACHINETOOLISTHEABILITYTOTRACKATRAJECTORYSPECIFIEDFORITSENDEECTORWECONSIDERAMACHINETOOLMOVINGALONGAPIECEWISEREGULARTRAJECTORYUT20TC138UT2UINTHETASKSPACEUIFHITC17FIUTHASALOCALEXTREMUMATTT0FORMOSTOFOURPROPOSITIONSCANBEUNDERSTOODINTUITIVELYWEOMITSOMEPROOFSBUTPROVIDETHEIRRATIONALEINTHEMAINBODYOFTEXT31REVERSALCONDITIONSINTHISSECTION,WESHOWVARIOUSWAYSTOINTERPRETREVERSALSOFACTUATORSKTHCOMPONENTPATHSWEALSOASKATWHICHPOINTINATRAJECTORYTHEACTUATORSREVERSETHEIRDIRECTIONOFFINALLY,WEANALYZETHEREVERSALCHARACTERISTICSOFSURFACEMACHININGORSWEEPINGWETHETHREETYPESOFMACHINETOOLSINSECTION4USINGTHECONCEPTSDEVELOPEDINTHISSECTIONINTHISSECTION,WEDEVELOPSEVERALCONCEPTSWHICHAREUSEFULINJUDGINGTHEREVERSALCHARACTERISTICSOFMACHINETOOLSWEWILLASKWHETHERAPOINTTOPOINTTASKCANBECOMPLETEDWITHOUTANYACTUATORREVERSALSORWHETHERTHEREISACONDITIONTHATGUARANTEESREVERSALFREEORCERTAINLYBUTMOREDETAILSAREAVAILABLEIN23,24INTHISPAPER,WEWILLSHOWHOWTHESETTINGABOVECANCAPTURETHEREVERSALCHARACTERISTICSOFMOSTMACHINESCONSIDERINGTHECONFIGURATIONSPACEOFMACHINETOOLSINCLUDINGBOTHACTIVEANDPASSIVEJOINTOFTHEINVERSEKINEMATICSFAREVERSALSINGULARPOINTWITHRESPECTTOTHEKTHOUOUPLACEMENTFKISEITHERALOCALMAXIMUMORMINIMUMTHEREFORE,THEKTHACTUATORMUSTREVERSEITSACTUATORSANDTHEVELOCITY_UINTHETASKSPACEHAVETHEFOLLOWINGLINEARRELATIONTKIMETAL/MECHANISMANDMACHINETHEORY392004299322305WHERECISTHEJACOBIANMATRIXOFTHERESTRICTEDINVERSEKINEMATICSFTHEMTUPLE_UISANELEMENTOFTHETANGENTSPACEOFTHETASKSPACETHETANGENTSPACEATAPOINTU2UISDENOTEDBYTUUTHEUNION_HC_U1DIRECTIONOFMOTIONATTHESTRONGREVERSALSINGULARPOINT,WHICHLEADSTOTHEFOLLOWINGPROPOSITIONPROPOSITION1WHENTHEFIDUCIALPOINTOFAMACHINETOOLPASSESASTRONGREVERSALSINGULARPOINTWITHRESPECTTOTHEKTHACTUATOR,REVERSALOFTHEKTHACTUATORISUNAVOIDABLEMEREREVERSALSINGULARPOINTSWHICH,FOREMPHASIS,WEWILLSOMETIMESREFERTOASNONSTRONGREVERSALSINGULARPOINTS,ALSOIMPLYAHIGHCHANCEOFREVERSALSBECAUSETHETRAJECTORIESPASSINGAREVERSALSINGULARPOINTMUSTSATISFYAVERYSPECIALCONDITIONTOCONSTITUTEREVERSALFREEMOTIONSTHISISESPECIALLYEASYTOUNDERSTANDFORA2DIMENSIONALTASKSPACEIFANONDEGENERATEREVERSALSINGULARPOINTINA2DIMENSIONALTASKSPACEWITHRESPECTTOTHEKTHACTUATORISNOTSTRONG,THEKTHCOMPONENTFKOFTHEINVERSEKINEMATICSHASASADDLEPOINTATTHEREVERSALSINGULARPOINTTHISIMPLIESPROPOSITION2ATANONDEGENERATE,NONSTRONGREVERSALSINGULARPOINTINA2DIMENSIONALTASKSPACE,AREGULARTRAJECTORYMUSTBETANGENTIALTOONEOFTHESEPARATRICESOFTHEFUNCTIONFKIFITISREVERSALFREETHEPROOFCANBEEASILYESTABLISHEDTHROUGHTHEMORSELEMMATHECONDITIONSTATEDABOVEISARATHERSPECIALCONDITIONWHICHISRARELYSATISFIED,ESPECIALLYINSWEEPINGTASKS,WHICHWEDISCUSSINSECTION33APLOTOFTHEREVERSALSINGULARPOINTSISACANONICALWAYTOVISUALIZETHEREVERSALCHARACTERISTICSOFMACHINETOOLSBECAUSEITSAPPEARANCEDOESNOTDEPENDONAPARTICULARTRAJECTORYWEMAYHAVECHOSEN313REVERSALFREEDIRECTIONSINTHETANGENTSPACESOFTHETASKSPACEWECANSPECIFYAREVERSALCONDITIONINTERMSOFTANGENTVECTORSOFTRAJECTORIESWEALSODEFINERELATEDTERMSFORFUTUREUSEINTHISSECTIONIFACUTTINGTOOLMOVESINATRAJECTORYOBEYINGTHEGIVENTASKCONSTRAINTS,THEVELOCITY_HOFTHEIJAREVERSALSINGULARPOINTISSAIDTOBEDEGENERATEIFITSCORRESPONDINGHESSIANMATRIXISSINGULARDEGENERATEREVERSALSINGULARPOINTSAREUNCOMMONINTHATASLIGHTPERTURBATIONOFKINEMATICPARAMETERSCANREMOVETHEMATASTRONGREVERSALSINGULARPOINTWITHRESPECTTOTHEKTHACTUATOR,THEKTHACTUATORDISHKIJC17O2FKACTUATORISSAIDTOBESTRONGIFTHEHESSIANMATRIXHKIJC138OFTHEKTHCOMPONENTFKOFTHEINVERSEKINEMATICSFISDEFINITEATTHEPOINT,WHEREOFTANGENTSPACESISREFERREDTOASTHETANGENTBUNDLE,ANDSYMBOLICALLYASTUATEVERYPOINTINTHETASKSPACEATANINSTANT,EACHACTUATORHASTWOALTERNATIVES,EITHERINCREASINGORDECREASINGITSDISPLACEMENTINOTHERWORDS,EITHER_HIP0OR_HI602INPARTICULAR,IFATRAJECTORYISREVERSALFREE,ONLYONEOFTHETWOINEQUALITIESMUSTHOLDDURINGITSENTIREINTERVALOFMOTION,EXCEPTFOR_HI0INOTHERWORDS,EACHACTUATORDISPLACEMENTMUSTBEMONOTONICALONGA306TKIMETAL/MECHANISMANDMACHINETHEORY392004299322REVERSALFREETRAJECTORYTHEPERMUTATIONSOFTHESEBINARYALTERNATIVESOVERALLTHEACTUATORSCANBEENCODEDUSINGABINARYSYSTEMUSINGTHESYMBOLSIANDDASTHEBASICDIGITS,WHERETHESYMBOLSREPRESENTTHEWORDSINCREASINGANDDECREASINGFOREXAMPLE,INA5AXISMACHINETOOL,IFTHEFIRSTANDTHELASTACTUATORDISPLACEMENTSAREINCREASINGANDTHEOTHERDISPLACEMENTSAREDECREASING,WEDENOTETHECASEBYIDDDI,WHICHWEREFERTOASANACTUATORPERMUTATIONTHENUMBEROFPOSSIBLEACTUATORPERMUTATIONSIS2N,WHERENISTHENUMBEROFACTUATORSCONVERSELY,ANACTUATORPERMUTATIONPIMPOSESNINEQUALITIESINTHETANGENTSPACETUUATAGIVENPOINTU2UEACHINEQUALITY,_HIP0OR_HI60,CANBETHOUGHTOFASAHALFSPACEINTHETANGENTSPACEDUETOTHELINEARRELATIONSHOWNINEQ1THEINTERSECTIONOFSUCHHALFSPACESFORMSASIMPLYCONNECTEDCONEINTHETANGENTSPACEWEREFERTOTHERESULTINGCONEASTHEPTHREVERSALFREECONEOFAGIVENPOINTU2U,ANDSYMBOLICALLYASCPUUWESAYTHATCPUUISVOIDIFCPUUF0G,A
- 温馨提示:
1: 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
2: 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
3.本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
人人文库网所有资源均是用户自行上传分享,仅供网友学习交流,未经上传用户书面授权,请勿作他用。