球齿轮行星传动结构型式与驱动机构分析Ξ

:1001-2486(2004)03-0093-06X,(,410073):,,,,,,:;;;:TH13214:APlanetaryTransmissionTypeofSphericalGearandItsDrivingMechanismsPANCun2yun,WENXi2sen(CollegeofMechatronicsEngineeringandAutomation,NationalUniv1ofDefenseTechnology,Changsha410073,China)Abstract:Oneofthenewkindofplanetarytranmissioncomposedoftheringinvolutesphericalgearanditsdrivingmechanismisintroduced,andtheconformationofthenewplanetarytranmission,andkinamaticarealsoanalyzed.Thenewplanetarytranmissioniscomposedoftwosphericalgearsandonebracket.Theoutputaxlecanswingtowardalldirections.Synthesizingoneofthespatialdrivingmechanismswhichisusedtocontroltheorientationofthebracket.Themovabilityofthedrivingmechanismisanalysed.Thekinamaticmodelbetweentheorientationangleoftheoutputaxleandthecontrolmotorhasbeenfound,basedonwhichtheorientationanglecanbecontrolledaccurately.Keywords:mechanism;sphericalgear;planetarytranmission;kinamaticanalysis1Fig.1Involutesphericalgear,[1],,,,1,,,,,,,45,,,,(1),(2),,,X:2003-10-10:(59675063,59275159):(1955),,,263JOURNALOFNATIONALUNIVERSITYOFDEFENSETECHNOLOGYVol.26No.32004©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(a),51,2,H,34,EF,EFO1,O11,O22,O1,(2(b)),EF,EF,,1360,2H2,HN1N1,2N2N2212,3,2:iH21=2-1-=2-0-=-r1r2(1=0)(1):2=(1+r1r2)(2)2Fig.2Planetarytranmissionofsphericalgear3Fig.3Sectionview2,EF,EF,4,()2,,H,:,(),,XZ,XZXZ,,,4920043©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:F=6n-[5P+4P+3P]=67-54-43-34=-2(3),,,3,4(34),AB9,,XZ,8,4,4,FG4,,,s,822:F=6n-[5P+4P+3P-p]-F-F=67-(54+43+34-8)-2-2=2(4)67,,,,12,5,421,:F=6n-[2P-P-4P]-F=65-[25+14+43]-2=2(5)59,:©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2)26(a),=0,oxyzo0x0y0z0,BDr,BD260,L:[B0]=[rsin,0,-rcos]T,[D0]=[-rsin,0,-rcos]T(6)[A0]=[rsin,-L,-rcos]T,[C0]=[-rsin,-L,rcos]T(7)6Fig.6Cordinatesystemforkinamaticanalysis,,S:S=l2(8),l[2],KK,:[C]=sin2(1-cos)+cos-cossincossin(1-cos)cossincos-sinsinsincos(1-cos)sinsincos2(1-cos)+cos(9)5(b),BD:[B]=[xb,yb,zb]T=[C][B0]=rsin[sin2(1-cos)+cos]-rcoscossin(1-cos)rsincossin+rcossinsinrsinsincos(1-cos)-rcos[cos2(1-cos)+cos](10)[D]=[xd,yd,zd]T=[C][D0]=-rsin[sin2(1-cos)+cos]+rcoscossin(1-cos)-rsincossin+rcossinsin-rsinsincos(1-cos)+rcos[cos2(1-cos)+cos](11)6920043©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:(x-xb)2+(y-yb)2+(z-zb)2=L2x=rsinz=-rcos(12)(x-xd)2+(y-yd)2+(z-zd)2=L2x=-rsinz=-rcos(13)(12)A:[A]=xAyAzZ=rsinL2-(rsin-xb)2-(rcos+zb)2-yb-rcos(14)(13)C:[C]=xCyCzC=-rsinL2-(rsin+xd)2-(rcos+zd)2-yd-rcos(15)12:S1=L-yA=L+yb-L2-(rsin-xb)2-(rcos+zb)2=L+rsincossin+rcossinsin-1S2=L-yC=L+yd-L2-(rsin+xd)2-(rcos+zd)2=-rsincossin+rcossinsin-2(16):1=L2-r2{sin-sin[sin2(1-cos)+cos]-coscossin(1-cos)}2-r2{cos-sinsincos(1-cos)-cos[cos2(1-cos)+cos]}22=L2-r2{sin-sin[sin2(1-cos)+cos]+coscossin(1-cos)}2-r2{cos-sinsincos(1-cos)+cos[cos2(1-cos)+cos]}2(17),,(9)(17)12S1S2,(8):1=iS12l2=iS22l(18),i,l312,22,12,(18)S1S2,ACBA,LO,r,DC,LO,rS1S2(16),,S1S2,:79,:©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(,)=L-S1+rsincossin-rcossinsin-1=0f2(,)=L-S2-rsincossin-rcossinsin-2=0(19),,=(,),fi()(i=1,2),,:fi((0)+(0))fi((0))+5fi5(0)+5fi5(0)A[aij]22,B(b1,b2)T,ai1=5fi5,ai2=5fi5,bi=-fidetA0,:new=old+new=old+(20),[,]TA=B(16)(17),{,},090,090,{S1,S2},{,180-}{S1,S2},090{S1,S2}20,1,,1Tab.1Calculatingresultofkinamatic()()S1(cm)S2(cm)()()(-)/(100%)(-)/(100%)1000.694664-0.69455210.0002200.0005922.210-3-10300-1.2028579.99999829.99999-210-5-310-51060-0.694552-1.3889019.99999760.00052-310-58.810-41090-1.202857-1.20285710.00014690.001411.4610-31.610-320100.936346-1.75692120.00000110.00000510-6110-520200.475264-2.09339419.99987520.000316.1310-41.5810-32040-0.474994-2.56719720.00000539.999932.510-5-1.710-42080-2.093393-2.56719820.00004880.000322.410-44.0510-440250.448693-4.16708340.00001724.999934.2510-5-2.710-44045-1.326412-4.90415140.00000044.999980-2.810-54075-3.602451-4.90415139.99997974.99993-5.310-5-9.110-54,,,,,,,,,,,,,,:[1]1[A]1,:,19941[2]LiGuixian,LiHuamin,BiZhuming1MechingAnalysisontheQuasi2ellipsoidalGearTransmissionwithinnerToroidalTeethintheFlexibleJointofRobot[J].ChineseJournalofMechanicalEngeering,1992,5.[3]1[M]1:,19841[4]ZhangKun,FengLiqun1TheResearchoftheDesignofSphericalGearTransmissionUsedinFlexibleWristofRobots[J]1JournalofTsinghuaUniversity,1994,34(2)18920043©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.