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外文翻译--夹具定位规划中完整性评估和修订 英文版.pdf

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外文翻译--夹具定位规划中完整性评估和修订 英文版.pdf

ROBOTICSANDCOMPUTERINTEGRATEDMANUFACTURING212005368–378KEYWORDSFIXTUREDESIGN;GEOMETRYCONSTRAINT;DETERMINISTICLOCATING;UNDERCONSTRAINED;OVERCONSTRAINEDCONSTRAINTSTATUS,AWORKPIECEUNDERANYLOCATINGSCHEMEFALLSINTOONEOFTHEFOLLOWINGTHREECATEGORIESLOCATINGPROBLEMUSINGSCREWTHEORYIN1989ITISCONCLUDEDTHATTHELOCATINGWRENCHESMATRIXNEEDSTOBEFULLRANKTOACHIEVEDETERMINISTICLOCATIONTHISMETHODHASBEENADOPTEDBYNUMEROUSSTUDIESASWELLWANGETAL3CONSIDEREDARTICLEINPRESS07365845/SEEFRONTMATTERR2005ELSEVIERLTDALLRIGHTSRESERVEDDOI101016/JRCIM200411012C3CORRESPONDINGAUTHORTEL15088316092;FAX15088316412EMAILADDRESSHSONGWPIEDUHSONG1WELLCONSTRAINEDDETERMINISTICTHEWORKPIECEISMATEDATAUNIQUEPOSITIONWHENSIXLOCATORSAREMADETOCONTACTTHEWORKPIECESURFACE2UNDERCONSTRAINEDTHESIXDEGREESOFFREEDOMOFWORKPIECEARENOTFULLYCONSTRAINED3OVERCONSTRAINEDTHESIXDEGREESOFFREEDOMOFWORKPIECEARECONSTRAINEDBYMORETHANSIXLOCATORSIN1985,ASADAANDBY1PROPOSEDFULLRANKJACOBIANMATRIXOFCONSTRAINTEQUATIONSASACRITERIONANDFORMEDTHEBASISOFANALYTICALINVESTIGATIONSFORDETERMINISTICLOCATINGTHATFOLLOWEDCHOUETAL2FORMULATEDTHEDETERMINISTIC1INTRODUCTIONAfiXTUREISAMECHANISMUSEDINMANUFACTURINGOPERATIONSTOHOLDAWORKPIECEfiRMLYINPOSITIONBEINGACRUCIALSTEPINPROCESSPLANNINGFORMACHININGPARTS,fiXTUREDESIGNNEEDSTOENSURETHEPOSITIONALACCURACYANDDIMENSIONALACCURACYOFAWORKPIECEINGENERAL,321PRINCIPLEISTHEMOSTWIDELYUSEDGUIDINGPRINCIPLEFORDEVELOPINGALOCATIONSCHEMEVBLOCKANDPINHOLELOCATINGPRINCIPLESAREALSOCOMMONLYUSEDALOCATIONSCHEMEFORAMACHININGfiXTUREMUSTSATISFYANUMBEROFREQUIREMENTSTHEMOSTBASICREQUIREMENTISTHATITMUSTPROVIDEDETERMINISTICLOCATIONFORTHEWORKPIECE1THISNOTIONSTATESTHATALOCATORSCHEMEPRODUCESDETERMINISTICLOCATIONWHENTHEWORKPIECECANNOTMOVEWITHOUTLOSINGCONTACTWITHATLEASTONELOCATORTHISHASBEENONEOFTHEMOSTFUNDAMENTALGUIDELINESFORfiXTUREDESIGNANDSTUDIEDBYMANYRESEARCHERSCONCERNINGGEOMETRYABSTRACTGEOMETRYCONSTRAINTISONEOFTHEMOSTIMPORTANTCONSIDERATIONSINfiXTUREDESIGNANALYTICALFORMULATIONOFDETERMINISTICLOCATIONHASBEENWELLDEVELOPEDHOWEVER,HOWTOANALYZEANDREVISEANONDETERMINISTICLOCATINGSCHEMEDURINGTHEPROCESSOFACTUALfiXTUREDESIGNPRACTICEHASNOTBEENTHOROUGHLYSTUDIEDINTHISPAPER,AMETHODOLOGYTOCHARACTERIZEfiXTURINGSYSTEM’SGEOMETRYCONSTRAINTSTATUSWITHFOCUSONUNDERCONSTRAINTISPROPOSEDANUNDERCONSTRAINTSTATUS,IFITEXISTS,CANBERECOGNIZEDWITHGIVENLOCATINGSCHEMEALLUNCONSTRAINEDMOTIONSOFAWORKPIECEINANUNDERCONSTRAINTSTATUSCANBEAUTOMATICALLYIDENTIfiEDTHISASSISTSTHEDESIGNERTOIMPROVEDEfiCITLOCATINGSCHEMEANDPROVIDESGUIDELINESFORREVISIONTOEVENTUALLYACHIEVEDETERMINISTICLOCATINGR2005ELSEVIERLTDALLRIGHTSRESERVEDCAMLAB,DEPARTMENTOFMECHANICALENGINEERING,WORCESTERPOLYTECHNICINSTITUTE,100INSTITUTERD,WORCESTER,MA01609,USARECEIVED14SEPTEMBER2004;RECEIVEDINREVISEDFORM9NOVEMBER2004;ACCEPTED10NOVEMBER2004LOCATINGCOMPLETENESSEVALUATIONANDREVISIONINfiXTUREPLANHSONGC3,YRONGWWWELSEVIERCOM/LOCATE/RCIMLOCATOR–WORKPIECECONTACTAREAEFFECTSINSTEADOFAPPLYINGPOINTCONTACTTHEYINTRODUCEDACONTACTMATRIXANDPOINTEDOUTTHATTWOCONTACTBODIESSHOULDNOTHAVEEQUALBUTOPPOSITECURVATUREATCONTACTINGPOINTCARLSON4SUGGESTEDTHATALINEARAPPROXIMATIONMAYNOTBESUFfiCIENTFORSOMEAPPLICATIONSSUCHASNONPRISMATICSURFACESORNONSMALLRELATIVEERRORSHEPROPOSEDASECONDORDERTAYLOREXPANSIONWHICHALSOTAKESLOCATORERRORINTERACTIONINTOACCOUNTMARINANDFERREIRA5APPLIEDCHOU’SFORMULATIONON321LOCATIONANDFORMULATEDSEVERALEASYTOFOLLOWPLANNINGRULESDESPITETHENUMEROUSANALYTICALSTUDIESONDETERMINISTICLOCATION,LESSATTENTIONWASPAIDTOANALYZENONDETERMINISTICLOCATIONINTHEASADAANDBY’SFORMULATION,THEYASSUMEDFRICTIONLESSANDPOINTCONTACTBETWEENfiXTURINGELEMENTSANDWORKPIECETHEDESIREDLOCATIONISQ,ATWHICHAWORKPIECEISTOBEPOSITIONEDANDPIECEWISELYDIFFERENTIABLESURFACEFUNCTIONISGIASSHOWNINFIG1THESURFACEFUNCTIONISDEfiNEDASGIQC30TOBEDETERMINISTIC,THERESHOULDBEAUNIQUESOLUTIONFORTHEFOLLOWINGEQUATIONSETFORALLLOCATORSGIQ0;I1;2;;N,1WHERENISTHENUMBEROFLOCATORSANDQX0;Y0;Z0;Y0;F0;C0C138REPRESENTSTHEPOSITIONANDORIENTATIONOFTHEWORKPIECEONLYCONSIDERINGTHEVICINITYOFDESIREDLOCATIONQC3;WHEREQQC3DQ;ASADAANDBYSHOWEDTHATARTICLEINPRESSHSONG,YRONG/ROBOTICSANDCOMPUTERINTEGRATEDMANUFACTURING212005368–378369GIQGIQC3HIDQ,2WHEREHIISTHEJACOBIANMATRIXOFGEOMETRYFUNCTIONS,ASSHOWNBYTHEMATRIXINEQ3THEDETERMINISTICLOCATINGREQUIREMENTCANBESATISfiEDIFTHEJACOBIANMATRIXHASFULLRANK,WHICHMAKESTHEEQ2TOHAVEONLYONESOLUTIONQQC3RANKQG1QX0QG1QY0QG1QZ0QG1QY0QG1QF0QG1QC0QGIQX0QGIQY0QGIQZ0QGIQY0QGIQF0QGIQC0QGNQX0QGNQY0QGNQZ0QGNQY0QGNQF0QGNQC0266666666643777777777589;63UPONGIVENA321LOCATINGSCHEME,THERANKOFAJACOBIANMATRIXFORCONSTRAINTEQUATIONSTELLSTHECONSTRAINTSTATUSASSHOWNINTABLE1IFTHERANKISLESSTHANSIX,THEWORKPIECEISUNDERCONSTRAINED,IE,THEREEXISTSATLEASTONEFREEMOTIONOFTHEWORKPIECETHATISNOTCONSTRAINEDBYLOCATORSIFTHEMATRIXHASFULLRANKBUTTHELOCATINGSCHEMEHASMORETHANSIXLOCATORS,THEWORKPIECEISOVERCONSTRAINED,WHICHINDICATESTHEREEXISTSATLEASTONELOCATORSUCHTHATITCANBEREMOVEDWITHOUTAFFECTINGTHEGEOMETRYCONSTRAINSTATUSOFTHEWORKPIECEFORLOCATINGAMODELOTHERTHAN321,DATUMFRAMECANBEESTABLISHEDTOEXTRACTEQUIVALENTLOCATINGPOINTSHU6HASDEVELOPEDASYSTEMATICAPPROACHFORTHISPURPOSEHENCE,THISCRITERIONCANBEAPPLIEDTOALLLOCATINGSCHEMESXYZOX’Y’Z’O’X0,Y0,Z0GIUCSWCSWORKPIECEFIG1FIXTURINGSYSTEMMODELTHEYFURTHERINTRODUCEDSEVERALINDEXESDERIVEDFROMTHOSEMATRIXESTOEVALUATELOCATORCONfiGURATIONS,FOLLOWEDBYOPTIMIZATIONTHROUGHCONSTRAINEDNONLINEARPROGRAMMINGTHEIRANALYTICALSTUDY,HOWEVER,DOESNOTCONCERNTHEARTICLEINPRESSREVISIONOFNONDETERMINISTICLOCATINGCURRENTLY,THEREISNOSYSTEMATICSTUDYONHOWTODEALWITHAfiXTUREDESIGNTHATFAILEDTOPROVIDEDETERMINISTICLOCATION2LOCATINGCOMPLETENESSEVALUATIONIFDETERMINISTICLOCATIONISNOTACHIEVEDBYDESIGNEDfiXTURINGSYSTEM,ITISASIMPORTANTFORDESIGNERSTOKNOWWHATTHECONSTRAINTSTATUSISANDHOWTOIMPROVETHEDESIGNIFTHEfiXTURINGSYSTEMISOVERCONSTRAINED,INFORMATIONABOUTTHEUNNECESSARYLOCATORSISDESIREDWHILEUNDERCONSTRAINEDOCCURS,THEKNOWLEDGEABOUTALLTHEUNCONSTRAINEDMOTIONSOFAWORKPIECEMAYGUIDEDESIGNERSTOSELECTADDITIONALLOCATORSAND/ORREVISETHELOCATINGSCHEMEMOREEFfiCIENTLYAGENERALSTRATEGYTOCHARACTERIZEGEOMETRYCONSTRAINTSTATUSOFALOCATINGSCHEMEISDESCRIBEDINFIG2INTHISPAPER,THERANKOFLOCATINGMATRIXISEXERTEDTOEVALUATEGEOMETRYCONSTRAINTSTATUSSEEAPPENDIXFORDERIVATIONOFLOCATINGMATRIXTHEDETERMINISTICLOCATINGREQUIRESSIXLOCATORSTHATPROVIDEFULLRANKLOCATINGMATRIXWLASSHOWNINFIG3,FORGIVENLOCATORNUMBERN;LOCATINGNORMALVECTORAI;BI;CIC138ANDLOCATINGPOSITIONXI;YI;ZIC138FOREACHLOCATOR,I1;2;;N;THENC26LOCATINGMATRIXCANBEDETERMINEDASFOLLOWSA1B1C1C1Y1C0B1Z1A1Z1C0C1X1B1X1C0A1Y12637KANGETAL7FOLLOWEDTHESEMETHODSANDIMPLEMENTEDTHEMTODEVELOPAGEOMETRYCONSTRAINTANALYSISMODULEINTHEIRAUTOMATEDCOMPUTERAIDEDfiXTUREDESIGNVERIfiCATIONSYSTEMTHEIRCAFDVSYSTEMCANCALCULATETHEJACOBIANMATRIXANDITSRANKTODETERMINELOCATINGCOMPLETENESSITCANALSOANALYZETHEWORKPIECEDISPLACEMENTANDSENSITIVITYTOLOCATINGERRORXIONGETAL8PRESENTEDANAPPROACHTOCHECKTHERANKOFLOCATINGMATRIXWLSEEAPPENDIXTHEYALSOINTRODUCEDLEFT/RIGHTGENERALIZEDINVERSEOFTHELOCATINGMATRIXTOANALYZETHEGEOMETRICERRORSOFWORKPIECEITHASBEENSHOWNTHATTHEPOSITIONANDORIENTATIONERRORSDXOFTHEWORKPIECEANDTHEPOSITIONERRORSDROFLOCATORSARERELATEDASFOLLOWSWELLCONSTRAINEDDXWLDR,4OVERCONSTRAINEDDXWTLWLC01WTLDR,5UNDERCONSTRAINEDDXWTLWLWTLC01DRI6C26C0WTLWLWTLC01WLL,6WHERELISANARBITRARYVECTORTABLE1RANKNUMBEROFLOCATORSSTATUSO6UNDERCONSTRAINED66WELLCONSTRAINED646OVERCONSTRAINEDHSONG,YRONG/ROBOTICSANDCOMPUTERINTEGRATEDMANUFACTURING212005368–378370WLAIBICICIYIC0BIZIAIZIC0CIXIBIXIC0AIYIANBNCNCNYNC0BNZNANZNC0CNXNBNXNC0ANYN6666647777757WHENRANKWL6ANDN6;THEWORKPIECEISWELLCONSTRAINEDWHENRANKWL6ANDN46;THEWORKPIECEISOVERCONSTRAINEDTHISMEANSTHEREARENC06UNNECESSARYLOCATORSINTHELOCATINGSCHEMETHEWORKPIECEWILLBEWELLCONSTRAINEDWITHOUTTHEPRESENCEOFTHOSENC06LOCATORSTHEMATHEMATICALREPRESENTATIONFORTHISSTATUSISTHATTHEREARENC06ROWVECTORSINLOCATINGMATRIXTHATCANBEEXPRESSEDASLINEARCOMBINATIONSOFTHEOTHERSIXROWVECTORSTHELOCATORSCORRESPONDINGTOTHATSIXROWVECTORSCONSISTONEARTICLEINPRESSLOCATDETERM1234BE3WORKPIHSONG,YRONG/ROBOTICSANDCOMPUTERINTEGRATEDMANUFACTURING212005368–378371INGSCHEMETHATPROVIDESDETERMINISTICLOCATIONTHEDEVELOPEDALGORITHMUSESTHEFOLLOWINGAPPROACHTOINETHEUNNECESSARYLOCATORSFINDALLTHECOMBINATIONOFNC06LOCATORSFOREACHCOMBINATION,REMOVETHATNC06LOCATORSFROMLOCATINGSCHEMERECALCULATETHERANKOFLOCATINGMATRIXFORTHELEFTSIXLOCATORSIFTHERANKREMAINSUNCHANGED,THEREMOVEDNC06LOCATORSARERESPONSIBLEFOROVERCONSTRAINEDSTATUSTHISMETHODMAYYIELDMULTISOLUTIONSANDREQUIREDESIGNERTODETERMINEWHICHSETOFUNNECESSARYLOCATORSSHOULDREMOVEDFORTHEBESTLOCATINGPERFORMANCEWHENRANKWLO6;THEWORKPIECEISUNDERCONSTRAINEDALGORITHMDEVELOPMENTANDIMPLEMENTATIONTHEALGORITHMTOBEDEVELOPEDHEREWILLDEDICATETOPROVIDEINFORMATIONONUNCONSTRAINEDMOTIONSOFTHEECEINUNDERCONSTRAINEDSTATUSSUPPOSETHEREARENLOCATORS,THERELATIONSHIPBETWEENAWORKPIECE’SPOSITION/FIG2GEOMETRYCONSTRAINTSTATUSCHARACTERIZATIONXZYA1,B1,C12,B2,C2X1,Y1,Z1X2,Y2,Z2AI,BI,CIXI,YI,ZIAFIG3ASIMPLIfiEDLOCATINGSCHEME

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