用复矢量法建立机械设计中曲线曲率半径和曲率中心的统一计算式

.2Apr.2009108JOURNALOFSHAANXIUNIVERSITYOFSCIENCE&TECHNOLOGYVol.273:100025811(2009)02201082061,2(1.,710021;2.,450002):,.,,,..:;;;;;;:TH112.2:A0,[129].,,;,;,.,,,.,.111.11,Cxoy,OC,,x,y,C(x,y),OC(x3,y3),OCr-,,OOCr3,3.i-1,OC=r-=rei(1)3:2008-10-24:(1961-),,,,,:2:,OC=x+iyx=rcosy=rsin(2)1.2OCrtr=r(t)=(t)(3)Cv-v-=dOCdt=dr-dt=rei+riei(4)v-=x+iyx=rcos-rsiny=rsin+rcos(5)1.3(4),Ca-=dv-dt=(r-r2)ei+(r+2r)iei(6)a-=x+iyx=(r-r2)cos-(r+2r)siny=(r-r2)sin+(r+2r)cos(7)1.4.,r1-=r1ei1=x1+iy1,r2-=r2ei2=x2+iy2,r1-r2-=r1r2cos(2-1)=x1x2+y1y2.22.1[1],C,COC.,v-a-,=(v-v-)3/2(iv-a-)(8).OCC,;,OCC,,.(8),OCOOC=r3-=r-+iv-|v-|(9)90127.(8)(9),Cr-v-a-OCr-3r-3=r-+(iv-)(v-v-)(iv-)a-(10)(8)(10)Cr-3.,C(8)(10).,(8)(10).2.22.2.1C(x,y)t(x,y)(x,y),(8)=(x2+y2)3/2xy-yx(11)(10)OC(x3,y3)x3=x-y(x2+y2)xy-yxy3=y+x(x2+y2)xy-yx(12)2.2.2Cyxy=y(x)(13),xt,y=y(t)x=t(14)(11)(12)(13)y=dydxy=d2ydx2OC(x3,y3)=(1+y2)3/2y(15)x3=x-y(1+y2)yy3=y+1+y2y(16)2.32.3.1Cr,r=RO+S(17)RO,0112:S=S()(18)S=dSd=drd,S=d2Sd2=d2rd2.,=[(RO+S)2+S2]3/2(RO+S)2+2S2-(RO+S)S(19)OCr-3r-3=(RO+S)ei+[-(RO+S)+S](RO+S)2+S2(RO+S)2+2S2-(RO+S)Sei(20)2.3.2Crtr=RO+S(t)=(t),,=(RO+S)2+S23/2(RO+S)2+2S2-(RO+S)S-S3(21)OCr-3.33.12,r-=ROeio+Reitv-=Rieita=-R2eit(8)(10),=Rr-3=ROeio2343.23,11127x=acosty=bsintx=-asinty=bcostx=-a2costy=-b2sint(11)(12),=(a2sin2t+b2cos2t)3/2abx3=a-(a2sin2t+b2cos2t)acosty3=b-(a2sin2t+b2cos2t)bsint3.34,r-=Reit-Rtieitv-=Rteita-=Reit+Rtieit(8)(10),=Rtr-3=Reit3.45,S=H1-cos2S=Hsin2S=H2cos22(19),=HROH+1-cos22+sin223/2ROH+1-cos22+2sin22-ROH+1-cos22cos223.56(Z=R1R2-R1=5),t,OP=R1,OP=R2,OC=l,2112:56r-=OC=(R2-R1)ei-lei1-R1R2v-=dr-d=(R2-R1)iei-l1-R1R2iei1-R1R2a-=dv-d=-(R2-R1)ei+l1-R1R22ei1-R1R2(8),=(R2-R1)2-2l(R2-R1)1-R1R2cosR1R2+l21-R1R223/2(R2-R1)2-l(R2-R1)1-R1R22-R1R2cosR1R2+l21-R1R234(1),.,,,,.(2),.(3),.[1],.[M].:,2002.[2],.[M].:,1981.[3],.[J].,2004,22(2):72274.[4].[M].:,2001.[5].[M].:,1997.[6],.[M].:,1990.[7]B.H.,.[M].:,1986.[8]H.H.Mabie,F.W.Ocvirk.MechanismsandDynamicsofMachinery[M].NewYork:JohnWileyandSons,1978.[9],.[M].:,1980.(120)31127[1],,.[M].:,2006.[2],.[M].:,2004.[3].[J].MaterialFlow,2006,(4):69276.[4].systemand[J].MaterialFlow,2006,(9):65270.[5],.[M].:,2004.[6].[M].:,2003.[7].[M].:,2002.INTENSITYCALCULATIONANDANALYSISOFCARGOTABLEONSTACKINGCRANEINAUTOMATEDWAREHOUSEANXiao2gang1,KANGXin2(1.Faculty,ShaanxiUniversityofScience&Technology,Xian710021,China;2.JiangsuNovaLogisticsEquipmentCo.,Ltd.,Nanjing211161,China)Abstract:Accordingtothedeficienciesofverticalanalyticalmethodandresearchofhorizontalintensitycalculationofcargotableonstackingcrane,twodirectionanalyticalmethodhasbeenpresetedinthispaper.Itisbetterthanverticalanalyticalmethodandtheimportantdatathatengineeringdesignneedshavebeenobtainedinit.Keywords:automatedwarehouse;stackingcrane;cargotable(113)ANALYTICCALCULATIONFORMULAFORPLANARMOTIONPOINTTRACESRADIUSOFCURVATUREANDCENTERPOINTOFCURVATUREWANGYun2di1,WANGLiang2wen2(1.SchoolofMechanicalandElectricalEngineering,ShaanxiUniversityofScience&Technology,Xian710021,China;2.DepartmentofElectromechanicalEngineering,ZhengzhouLightIndustryInstitute,Zheng2zhou450002,China)Abstract:Thepaperdescribesthedisplacement,velocityandaccelerationofplanarmotionpointbycomplexvector,andextendcomplexvectordotconception.Underthisbase,accord2ingtothetheorythatverticalaccelerationofplanarmotionpointequalstheratiobetweensquareofvelocityandradiusofcurvature,thegeneralcalculationformula,theformulainformofrightanglecoordinatesandtheformulainformofpolaranglecoordinatesforcalcu2latingmotionpointtracesradiusofcurvatureandcenterpointofcurvaturearesubmitted.SometypicalexamplesarediscussedKeywords:planarmotionpoint;tracesradiusofcurvature;centerpointofcurvature;ana2lyticcalculationformula021