PUMA560型机器人逆运动学问题的解析解

184199412JoJRtNALHARBIUNNIv.SCI.&TECH.Vol.18No.4Dee.1994PUM650A()PUM5A60,.,、、,PUMA560.TP2420241.6,..、、.,、、,.Ll,,:|||J!lweweesJCS||160lseùnùdzaa00-nùcZ0Onù0SrCl0052cZA,=l_!U,C,S,d,1A3C〕SsO0c300--loOùùà10S`CO0ssC`O0c6..rwej.esesLr`i`.…..Jō11`…..J,..es1`1..es,..nànUz55nécsnUOA,A6560llllJ!weeseeeeleseeJ000000100--l000--lo510cl0s’00r.。we:..J..Lwe.ee!weL4A、,=sin;c,=cos(i1,2,…,6),.l,1.IJPUMA560:13204:PUMA506221,s,a,P1PUM(l)i(’)(~)d.()e1PUM{”·}n,A,AZ·’·A`}”’LOaxPxa,P,00431·81~+l149.095~+4520.3245~+5433.07110~+170J.e,,ù4P,00Ico~+1001056252~+2660。ùó`、J`U,:,s,a,p,2.13=A,A。=6TA-6’A’(l),les.lll--JJ.esesJclslslC,J+q0clsl0cl.cac’slsC,ac’+cc-SC0e,d。+a3e.+aZeleZd:sld`+aas.c,a+、c.C,ud`aa2l.rjseeewe.weeeeelL4T5055cs0s`0O0d60l]。|r--l||.Ll5Al`A,...111.``Jē0nU0..00d6l!l“5’5}.}00}A’}。}IJ,c,J[0000Oné,ùù0ǎU00rfee.leese`.J--sA=s+0]),’c`,=cos(0,+),i,j=l,2,…,6,.(l):{p“6“,Ct523“4+a,c!c:,+aZc,c“:,!({p,d6a,s{s:,dJ+a,s.eZ,+aZs.cZ+dZc:}:d`a:。:3d4。。、。,::s:M,=pd。ax,MZ=p,d。a,,M,=d6a::c,:、,=d:881P,=8,:0,:80,(2)M,=peos,M:=plsin-,,,=tg’(MZ/M:)5in(0:)=d:/,:B.,=aresin(dZ/p,),B:2=“(0::),0.2=:+aresin(dZ/l)8.2=“(:0.:),a.2=.+aresin(“2/p:)+:(3)(4)I`M:c:+M:5.=S:3d`+a,CZ,+a:cZ,。23`。,523。:52(5)(M:c:+M:s:)2+Md+a+a;+ZaZd4sino,+Za3a:eoss,=ZaZd`,N:=Za,aZ,N,=(M,c,+MZs.),+M;da;a=N3(6)P:cos2P:5In2Pz=:=tg’(NZ/N,)N、.`,78`、`、83,.=2+aresin(N3/pZ),ó,.....ùù、,é{pZ+“3`·0},2+“】`“=aresin(N,/pZ)2=7raresin(N3/pZ)2i=l,20,8.2.(5)(.:.+25.)c:M3sZ=dosJ+a,e3+a:(9)W.M,,=M.0.+MZ:!,=53c〕+a:=3=w+w;,,=`g’(/)02,,,aresin(/p,)(10)1,“:,,:o”:,,:},,。2`,.、。,+aresin(/p,)“,+aresin(/,)+“,j=1,2,!,。:,111`11...lee11.Joné,lC.1111`eel.!IJ,óA,.…2aU0CUs,ùc353000.1`l.weweesJ,dl1000c,0a300slOs00le:0O01000s3;leseel’lselJ5”OcjaZad3532lAoASA6=0__c’55`s4CSC6c4S60S0d6qssd6s4ssd6csdls’s5c50。--sl’’A’=004:PUM5A06A’A’A「’T=A;A,C,+c,’.sozPaZa3=d,slxP+C.dZ=d、xP+sl+P,s3=dcs6+.d(11)V,=.cuclxP+s:a:2)3)(l(l=s,xP+e,yPd:=cl+5.+C,a:Pa2l`l(11),(12):c,=(ddJ/。,0,,,;,=arccos[(V,d。)/d610,`z,2=85,z、-i,j,k=l,2e:,2.,a:,z:.(11),(12):sVZ/d`,s,0:aresin(VZd/655)(14)8,=o,0:。`:0。8`,,*。:o2,,,:,o0`,z*。2=7r+04`z、:,0`f、::=+o“z、::(15)!、li,j,,=l,20,,z、:,a,`,*:(1)CCZ,S。ss:=nS。+s:c`L.=n,LZ=sx,L3=c.s3。s!d`L56+LZc6=L3(16)p:=+L;,`=gt’(LL.)5in(8。+。)=L,/p。0`,z`:。:=aresin(L3/4)`(17)6,ij`:.2.i,j,k,.m=1,2,::,.e:2·,ili,j3lij,K,L,M.2PUMA560,8.,,.:1018l);)2,.,,,l,32,4.3,:x=22.13,=586·41,z=98·66;03.2461,2.2854,=1.11960.38710.917270.0983400.918670.392220.0457700.07880.06850.99454022.13586.4198.66l:a:=1.2856,=2.3688,8,=0.0766,9。=0.1401,8,=0.7468,0。=0.5854.s[]=l,l,=l..eDantJ.HartenR5.AKinematieontationfor10rPairn`hanist5。」ont~.SAMEJ.APPliedMdn.195:215221FuKCO】ezRC,LeeC5G.Robotics:bCntrol,Sensing.ionandIntellig.MwHillP,17..PLIMSA.,1988.(3):1926TheAnalytieMethodofPUMA560Robot}nverseKinemstiCSProb}em)Bo,Zha,zgOY,zu”,Bixil:AbstnlctUsingilomonenouscooInatcstarnsfonnationtirotPUMA560orbot,thisPaPerdeduanalytiesolutionofistinvcscrkinematiePorblem.ComParedwithohtermehtodswhihCaeroftentised,thismethod15simPle,elearandistcaleulaitngsPdjsquiek.It15valuabieforPUMA560orbotPlanningof」ccrorics.KeyWodsrsubscriPtosrrobot·kinelatics,holonegenocoodrinatcs,analytlemethod