平面五杆机构运动学和动力学特性分析

39620076JOURNALOFHARBININSTITUTEOFTECHNOLOGYVol139No16Jun.2007于红英,唐德威,王建宇(,150001,E-mai:[e-mail]):对平面五杆机构的运动学特性和动力学特性进行分析.推导了五杆机构的运动学正解和运动学逆解方程.借助Kane动力学分析方程,对五杆机构进行了动力学分析,分析结果表明惯性力对机构的影响很大.:平面五杆机构;运动学;动力学:TH11211:A:0367-6234(2007)06-0940-04Analysisofthekinematicanddynamiccharacteristicsofaplanarfive-barmechanismYUHong-ying,TANGDe-we,iWANGJian-yu(SchoolofMechanicalandElectricalEngineering,HarbinInstituteofTechnology,Harbin150001,China,E-mai:[e-mail])Abstract:Thekinematicanddynamiccharacteristicsofaplanarfive-barmechanismareanalyzed.Equa-tionsofpositivekinematicandinversekinematicarededuced.Kanedynamicequationsareintroducedtoana-lyzethedynamiccharacteristicsofaplanarfive-barmechanism.Theresultsshowthattheinertiaforcesarethemainfactortoaffecttheperformanceofafive-barmechanism.Keywords:planarfive-barmechanism;kinematics;dynamics:2005-08-31.:(1968)),,,.()[1],.,[2].,,.1五杆机构的运动学分析111,.1,A.:14,l1l2l3l4l5,U1U4;X1X4;:A1A4.:C(xC,yC)(ÛxC,ÛyC)(&xC,&yC).111111,[3]:rC=rB+l2=rD+l3.1xy,CxC=xB+l2cosU2=xD+l3cosU3,yC=yB+l2sinU2=yD+l3sinU3.(1)(1),U3A0cosU2+B0sinU2-C0=0.(2):A0=2l2(xD-xB),B0=2l2(yD-yB),C0=l22+l2BD-l23,lBD=(xD-xB)2+(yD-yB)2.(2)U2=2arctanB0+A20+B20-C20A0+C0.(3)(3),/+0/-0BDl2l3,.1/+0,/-0.U2(1)CxCyC,U3=arctanyC-yD/xC-xD.11112(1)tX2=ÛU2=(ÛxD-ÛxB)cosU3+(ÛyD-ÛyB)sinU3l2sin(U3-U2),X3=ÛU3=(ÛxD-ÛxB)cosU2+(ÛyD-ÛyB)sinU2l3sin(U3-U2).(4)CÛxC,ÛyCÛxC=ÛxB-ÛU2l2sinU2=ÛxD-ÛU3l3sinU3ÛyC=ÛyB+ÛU2l2cosU2=ÛyD+ÛU3l3cosU311113(4)tA2=&U2=(&xD-&xB)cosU3+(&yD-&yB)sinU3+l2ÛU22cos(U3-U2)-ÛU23l3l2sin(U3-U2),A3=&U3=(&xD-&xB)cosU2+(&yD-&yB)sinU2-l3ÛU23cos(U3-U2)+ÛU22l2l3sin(U3-U2).C&xC&yC&xC=&xB-&U2l2sinU2-ÛU22l2cosU2,&yC=&yB+&U2l2cosU2-ÛU22l2sinU2.112:14,l1l2l3l4l5,C(xC,yC)(ÛxC,ÛyC)(&xC,&yC).:;X1X4;A1A4.112111,BxB=xA+l1cosU1,yB=yA+l1sinU1.(5)A0=(xC-xA)2+(yC-yA)2+l21-l22,B0=-2(xC-xA)l1,C0=-2(yC-yA)l1.(1)(5)A0+B0cosU1+C0sinU1=0.(6)T=tan(U1/2),(6),T=-C?C2+B2-A2A-B.U1=2arctanT,U1.U2U3U4,BD.,.112.2(1)(5),ÛxC=ÛxA-ÛU1l1sinU1-ÛU2l2sinU2,ÛyC=ÛyA+ÛU1l1cosU1+ÛU2l2cosU2.(7)(7)X1=ÛU1=(ÛyC-ÛyA)sinU2+(ÛxC-ÛxA)cosU2l1sin(U2-U1),X2=ÛU2=(ÛyC-ÛyA)sinU1+(ÛxC-ÛxA)cosU1l1sin(U1-U2)..(7),&xC=&xA-(&U1l1sinU1+ÛU21l1cosU1)-(&U2l2sinU2+ÛU22l2cosU2),&yC=&yA+(&U1l1cosU1-ÛU21l1sinU1)+(&U2l2cosU2-ÛU22l2sinU2).(8)(8)A1=&U1=[(&yA-&yC)sinU2+(&xA-&xC)cosU2-ÛU21l1cos(U1-U2)-ÛU22l2]/[l1sin(U1-U2)]A4X4.2平面五杆机构的动力学分析211Kane,Kane,,[4,5].Kane:urFrF*r0[6],Fr+F*r=0,r=1,2,,,n.n,nqi(i=1,2,,,n),nqi,nÛqi(i=1,2,,,n),n#941#6,:ur(i=1,2,,,n),ur=Eni=1AjrÛqi+ar(r=1,2,,,n).:Ajrar,v=Enr=1vrur+vt,X=Enr=1Xrur+Xt.:vr;Xr.j,.,()Fj.,F*j.Fjj,F*jj,Fjr=Fj#vjr,F*jr=F*j#v*jr.2122,e1e2e33.l1l2l3l4l5,1/2,FC,,C.(),..1234,.21).l1l4U1U4,Kaneu1=ÛU1u2=ÛU4.X1=ÛU1e3=u1e3X11=5X15u1=e3,X12=5X15u2=0.X4=ÛU4e3=u2e3X41=5X45u1=0,X42=5X45u2=e3.1v1=u1l12(e2cosU1-e1sinU1)v11=5v15u1=l12(e2cosU1-e1sinU1),v12=5v15u2=0.v4=u2l42(e2cosU4-e1sinU4)v41=5v45u1=0,v42=5v45u2=l42(e2cosU4-e1sinU4).34.,l1cosU1+l2cosU2=l5+l4cosU4+l3cosU3,l1sinU1+l2sinU2=l4sinU4+l3sinU3.(9)(9)ÛU1l1sinU1+ÛU2l2sinU2=ÛU4l4sinU4+ÛU3l3sinU3,ÛU1l1cosU1+ÛU2l2cosU2=ÛU4l4cosU4+ÛU3l3cosU3.(10)(10)X2=u2l4sin(U4-U3)-u1l1sin(U1-U3)l2sin(U2-U3)e3,X3=u1l1sin(U1-U2)+u2l4sin(U2-U4)l3sin(U3-U2)e3.X21=5X25u1=-l1sin(U1-U3)l2sin(U2-U3)e3,X22=5X25u2=l4sin(U4-U3)l2sin(U2-U3)e3,X31=5X35u1=l1sin(U1-U2)l3sin(U3-U2)e3,X32=5X35u2=l4sin(U2-U4)l3sin(U3-U2)e3.v2=v+X2l22(e2cosU2-e1sinU2),vB=l1X1(e2cosU1-e1sinU1),v21=(l1cosU1+l22X21cosU2)e2-(l1sinU1+l22X21sinU2)e1,#942#39v22=l22X22(e2cosU2-e1sinU2).vC1=(l1cosU1+l2X21cosU2)e2-(l1sinU1+l2X21sinU2)e1,vC2=l2X22(e2cosU2-e1sinU2),v31=l32X31(e2cosU3-e1X21sinU3),v32=l4cosU4+l32X32cosU3e2-l4sinU4+l32X32sinU3e1.(2)Kane.Kane,.,.,,.F,MAME.F1F2F1=F#vC1+MA#X11+ME#X41,F2=F#vC2+MA#X12+ME#X42.(11),.urF*rF*r=E4j=1(F*j#vjr+T*j#Xjr),r=1,2.(12):F*jT*jj.j,mj,Ij,F*j=-mjaj=-mjÛvjem,(j=1,,,4;m=1,2,3).T*j=-IjXj=-IjÛXjem,(j=1,,,4;m=1,2,3).(11)(12)KaneFr+F*r=0,(r=1,2),F#vC1+MA#X11+ME#X41=E4j=1(mjÛvjem#vj1+IjÛXjem#Xj1),F#vC2+MA#X12+ME#X42=E4j=1(mjÛvjem#vj2+IjÛXjem#Xj2).:Kane,.:,,.:(),,.3结语1),.2).参考文献:[1],,.[J]..1999,4(4):82-85.[2],.[J]..2002,18(1):22-24.[3],,.CAD[M]..2000,77-82.[4],,.[J]..1996,29(4):533-537.[5]DJUROVICMD,VUKOBRATOVICMK.AContr-ibutiontodynamicmodelingofcooperatingmanipula-tion[J].MechanismandMachineTheory.1990,25(4):407-415.[6]DIBAKARS,MRUTHYUNJAYATS.Acentro-basedcharacterizationofsingularitiesintheworkspaceofplanarclosed-loopmanipulators[J].MechanismandMachineTheory,1998,33(8):1091-1100.(姚向红)#943#6,: