机械手夹持接触力及力封闭分析

406()Vol.40No.6200912JournalofCentralSouthUniversity(ScienceandTechnology)Dec.2009(410083)VVVVTP24A1672−7207(2009)06−1580−07Analysisofgrippingcontactforceandforce-closureofmanipulatorWUYong-hong,LIQun-ming(KeyLaboratoryofDesignforModernComplexEquipmentandExtremeManufacturingMinistryofEducation,CentralSouthUniversity,Changsha410083,China)Abstract:Inordertoreasonablyascertaingraspingforceofmanipulatorwhilestablygrasping,thecontactforcebetweenVstylefingertipandobjectduetothepre-tightenforcewascalculatedbasedonthelinecontacttheory,andthechangeofthecontactforcewiththefingertiponthedifferentpositionswasanalyzed.ThegraspingforceoftheVstylefingertipwascalculatedbasedonthecontactforce.Thecontactmodelofthefingertipandobjectwasestablishedbasedontheforcespiraltheory.Therelationbetweenexternalforceandthecontactforcewithstablygraspingwasanalyzedbyusingforceclosureprinciple,andthemethodforcalculatingthestabilityofgraspingwasfounded.Thecontactforceandgraspingforceofonegraspinginstancewerecalculated.TheresultsshowthatthegraspingforceandthestabilityoftheVstylefingertipcanbeaccuratelycalculated,andthereliablevalueoftheparameterscanbesuppliedforthedesignofthemanipulatoranditscontrolsystem.Keywords:V-stylefinger;contactforce;graspingforce;forcespiral;force-closuregrasp[1−5][6−12]V2VV2009−01−252009−04−09(973)(2006CB705400)(1969−)0731-88877915E-mail:[e-mail]61581VVVVV11.1V12VP1P2P1P2V22V1[15]()2b2ai2biiypoixHertz321)(⎟⎟⎠⎞⎜⎜⎝⎛−=ioiiaxpxp(1)−aixajkoimikifpCK−=∑=δ1(2)1VFig.1Sketch-mapofVstylefingergraspcylindricalobject2VFig.2Pre-tightenforceofVstylefingerandobject3Fig.3Sketch-mapofelementdividingofline-contactareak=1,2,,mmKK=1/4EECkiikpoifkδ[15]21213)(59.6lnπRPRRRllPηηδ+=(3)oimiiipbaKP∑==1π(4)(4)poi02VV2()401582)2(sin11211αPPP==(5)(3)P(2)poiδHertz(1)x1.2V2VVV454VFig.4Sketch-mapofforceapplyonVstylefingertiponhorizontalposition5VFig.5Sketch-mapofforceapplyonVstylefingertiponanyposition2VV1.2.1V2VVP2V11122122011δ012δ021δ022δ111δ112δ121δ122δGGδ022122111011δδδδ−=−(6))2(sin111122αδδδG=−(7)P1P2022021012011δδδδ===(8)112111δδ=(9)122121δδ=(10)(2)(3)(6)~(10)(4)V1.2.2VV4121111δδ=(11)122112δδ=(12))2(cos111122αδδδG=−(13)(2)(11)~(13)(4)VV5P1φP1yP1xϕsinGGx=(14)ϕcosGGy=(15)61583(14)(15)(13)(7)(4)21(6)[12−14]6Fig.6Relationshipbetweenobjectcoordinatesystemandcontactcoordinatesystem6O−xyzCoCi−xyzCiz[16]()⎟⎟⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎜⎜⎝⎛=100000000001000001000001000001ciB⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎝⎛⎟⎟⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎜⎜⎝⎛==zxzyxMMfff100000000001000001000001000001cicicifBF(16)FciFCciFciFCci={fR6:2y2xff+zzff,µ0,|Mx|mx,|Mz|mz}(17)MxMzmymzCiCo(pociRoci)CiCociciociociociocicigofBRRp0RFAdF1oci⎟⎟⎠⎞⎜⎜⎝⎛==−ˆT(18)ciociociociociiBRRp0RG⎟⎟⎠⎞⎜⎜⎝⎛=ˆmCoT1111]][[ckmioioffGGfGFFLLcimimi===∑∑==(19)][1mGGGL=T1][ckcfffcL=(19)TcGfFo=(20)FeR6e1FGffGFciio===∑=mi(21)(21)3K=70.31mm2/N()401584R=10mml=100mmb=1mmE=207GPaVα=90˚0.4P1=P2=2kNV77Vϕ=0˚(2)G1.01.51.8kN2V89V1V22V7Fig.7Contactforceonobjectandfingertipafterapplyingpre-tightenforceonobject/kN:11.0;21.5;31.88φ=0˚V1Fig.8ContactforceonVstylefingertip1withdifferentgravityasφ=0˚/kN:11.0;21.5;31.89φ=0˚V2Fig.9ContactforceonVstylefingertip2withdifferentgravityasφ=0˚10ϕ=30˚G=1.8kNV2V22211V(4)1111;212;321;42210φ=30˚,G=1.8kNVFig.10ContactforceonVstylefingertip1andtip2asφ=30˚,G=1.8kN615851Table1Resultantforceofcontactarea/Nφ=0˚φ=30˚/kNP11P12P21P22P11P12P21P221.01067.21067.21770.31770.3941.31315.61549.81900.11.5894.2894.21950.51950.5703.71230.31618.02144.61.8791.0791.01268.41268.4525.81158.31659.82292.3(16)⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛==zyxfff100010001cicicifBF(18)],,,[22211211GGGGG=⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎝⎛−−−=220220102202211G⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎝⎛−=220220102202212G⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎝⎛−−−=220220102202221G⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎝⎛−=220220102202222G1(20)ϕ=30˚G=1kNCo6πcosGGX==866.02N6πsinGGZ==500NGy=0N(20)F0X=856NF0Z=512NF0Y=0NGX=FOXGY=FOYGZ=FOZ(21)4a.Vb.VVαϕVϕ2V2Vc.Vd.V[1]LIJi-ting,ZHANGYu-ru,ZHANGQi-xian.Calculationofcontactforcesingrashpingbyspacedecomposition[J].ChineseJournalofAeronautics,2001,14(2):112−117.[2],,,.Power[J].,2004,15(7):628−631.LIJian-feng,ZHANGYu-ru,WANGXin-hua,etal.Robustnessanalysisanddeterminationofstabilityloaddomainofmulti-fingeredhandpowergrasps[J].ChinaMechanicalEngineering,2004,15(7):628−631.[3]Al-GallafEA.Multi-fingeredrobothandoptimaltaskforcedistributionNeuralinversekinematicsapproach[J].RoboticsandAutonomousSystems,2006,54(1):34−51.[4]ZHENGYu,QIANWen-han.Limitingandminimizingthecontactforcesinmultifingeredgrasping[J].MechanismandMachineTheory,2006,41(10):1243−1257.[5]XIONGCai-hua,LIYou-fu,XIONGYou-lun,etal.Graspcapabilityanalysisofmultifingeredrobothands[J].RoboticsandAutonomousSystems,1999,27(4):211−224.[6]NahavandiS,JashimUM,SaadatM,etal.Heavytoolsmanipulationbylowpowereddirect-drivefive-barparallelrobot[J].MechanismandMachineTheory,2007,43(11):1450−1461.()401586[7]YashimaM,YamaguchiH.Controlofwholefingermanipulationutilizingfrictionlessslidingcontact-theoryandexperiment[J].MechanismandMachineTheory,1999,34(8):1255−1269.[8]LalibertT,GosselinCM.Simulationanddesignofunderactuatedmechanicalhands[J].MechanismandMachineTheory,1998,33(1/2):39−57.[9]MelchiorriC.Mu