工業(yè)機(jī)器人第三章歐拉角DH參數(shù)

1、.( , )( , )( ,)( , )RPYRot zRot yRot x .0000100000010000( , )00100000000100010001cscssccsRPYsssc coscsins00( , )00001c cc s ss cc s cs cs s sc cs s cRPYsc sc c .00( , )00001xxxyyyzzznoanoaRPYnoa .22cosxynn22tan2(,)tan2(,)tan2(,)zxyxxyzAnnnAo nAaa.( , )( , )( ,)( , )0000100000010000001000000001000100

2、01EulerRot zRot yRot xcscssccsscsc coscsins00( , )00001c cc s ss cc s cs ss cs s sc cs s cc sEulersc sc c .( , )( , )( ,)( , )00000000010000001000001000010001000100EulerRot zRot yRot zcscscsscscscc c cs sc c ss cc ss c cc ss c sc cs ss cs 00001sc .00( , )00001xxxyyyzzznoanoaEulernoa 22tan2,tan2(,)ta

3、n2(,)xyzzzyxAaaaAo nAaa.601 23456TTT TT TT.600001xxxxyyyyzzzznoapnoapTnoap.601 234560001xxxxyyyyzzzznoapnoapTTT TT TTnoap.連連桿桿變變量量adcossin11 1-90000-122 20a2d21033 39000144 4-900d40-155 59000166 600d610.1122223311222 233123244556445545640000000000,0100001010000010001000100000000,010010000010001cscsa

4、 ccsscsca sscAAAdcscscscscAAAd666600000010000sscdcosiicsiniis.cos()ijijc sin()ijijs5 65 656 55 65 656 5645666000001c cc ssd ss cs scd cTA Asc4 5 64 64 5 64 64 564 54 5 64 64 5 64 64 56 4 5634565 65 656 540001c c cs sc c ss cc sd c ss c cc ss c sc ss sd s sTA A As cs scd cd.111111116236311110001xxxxy

5、yyyzzzznoapnoapTATnoap134 5 64 63 5 6134 5 64 63 5 614 5 64 6134 5 64 63 5 6134 5 64 63 5 614 5 64 613 4 53 513 4 53 514 513 4 563(),(),(),(),(xyzxyzxyzxnc c c cs ss s cns c c cs sc s cns c cc socc c cs cs s cosc c cs cc s sos c cs cac c ss cas c sc cas spc c s ds 56413 4 56356414 56),(),yzc ddps c

6、s dc c ddps s d.22222222612345622220001xxxxyyyyzzzznoapnoapTA A A A Anoap2234 5 64 623 5 62234 5 64 623 5 624 5 64 62234 5 64 623 5 62234 5 64 623 5 624 5 64 6223 4 523 5223 4 523 524 52(),(),(),(),xyzxyzxyzxncc c cs ss s snsc c cs sc s sns c cc socc c cs cs s sosc c cs sc s sos c sc cac c ss cas c

7、sc cas sp 23 4 562356422223 4 56235642 224 562(),(),yzc c s dsc dda cps c s dcc dda sps s dd.61234560001xxxxyyyyzzzznoapnoapTA A A A A Anoap1234 5 64 623 5 614 5 64 61234 5 64 623 5 614 5 64 6234 5 64 623 5 61234 5 64 623 5 614 5 64 61234 5 64 6()(),()(),(),()(),()xyzxync cc c cs ss s cs s c cc sns

8、cc c cs ss s cc s c cc snsc c cs sc s coccc c ss cs s sss c sc coscc c ss cs 23 5 614 5 64 6234 5 64 623 5 6123 4 523 51 4 5123 4 523 51 4 523 4 523 51623 4 523 52342216 4 521623 4 523 5(),(),(),(),()(),()zxyzxys scs c sc cosc c ss cc s sac c c ss cc s sas c c ss cc s sas c sc cpc d c c ss cs da cs

9、d s sdps d c c ss c 2342216 4 52623 523 4 52342 2(),()zs da cc d s sdpd c cs c cc da s.6010149.09001921.1210000001T.連桿連桿 變量變量adcossin11 1-90000-122 2900d20133 300d31044 4-90000-155 59000166 600010.cosiicsiniis1122223311222 233123244556445545640000000000,0100001010000010001000100000000,01001000001000

10、1cscsa ccsscsca sscAAAdcscscscscAAAd666600000010000sscd.61234560001xxxxyyyyzzzynoapnoapTA A A A A Anoap1234 5 64 623 5 614 5 64 61234 5 64 623 5 614 5 64 6234 5 64 623 5 61234 5 64 623 5 614 5 64 61234 5 64 623 5()()()()()()()()xyzxync cc c cs ss s ss s c cc sns cc c cs ss s sc s c cc snsc c cs sc s

11、 soccc c ss cs s sss c sc coscc c ss cs s 614 5 64 6234 5 64 623 5 6123 4 523 51 4 5123 4 523 51 4 523 4 523 51 23121 231223()()()()zxyzxyzscs c sc cosc c ss cc s sac c c ss cs s sas c c ss cc s sas c sc cpc s ds dps s dc dpc d .120001xxxxyyyynzzzznoapnoapA AAnoap.1234560000 xxxxyyyyzzzznoapnoapA A

12、A A A Anoap.11A11623456A TA A A A A1111610000001000010001xxxxyyyyzzzzcsnoapscnoapTnoap.61T112xys pc pdcossinxypp22,tan2(,)xyyxppApp.21221222212sin()cos()1()tan2,1ddddA 222122tan2(,)tan2(,)yxxyAppAdppd.112234 2322xyc ps pa cd sa c2 234232 2xpa sd ca s3 34 34 3a cd sd sk2222222232422xyzpppaaddka.22233

13、434tan2(,)tan2( ,)Aa dAkadk.1132A A1 231 23232 31 231 23232 363112000010001xxxxyyyyzzzzc cs csa cnoapc ss sca snoapTscdnoap1111610000001000010001xxxxyyyyzzzzcsnoapscnoapTnoap4 5 64 64 5 64 64 564 54 5 64 64 5 64 64 56 4 5634565 65 656 540001c c cs sc c ss cc sd c ss c cc ss c sc ss sd s sTA A As cs

14、scd cd.1 231 2323233xyzc c ps c ps pa c a1 231 23232 34xyzc c ps c pc pa sd32 3112 342322112 341132 3232211()()()()()()()()zxyzxyzxyzxyaa cpc ps pa sdspc ps pa cdpc ps paa sspc ps p.232332 31142 32 341132 3tan2()()()()()()xxyzxyAaa cpc ps pda sa sdpc ps paa c2233.1 231 234 5114 5xyxya c ca s cc sa s

15、a cs s 4111 231 2323tan2(,)xyxyzAa sa ca c ca s ca s.111432A A A1111610000001000010001xxxxyyyyzzzzcsnoapscnoapTnoap11114321664A A A A TT1 23 41 41 23 41 423 42 3 42 43 41 23 41 41 23 41 423 42 3 4243 4641 231 23232 340001c c cs ss c cc ss ca c cd sa cc c ss cs c cc ss sa c sd ca sTc ss sca sod.5 65

16、656 55 65 656 5645666000001c cc ssd ss cs scd cTA Asc1 2341 41 2341 422345()()()xya c c cs sas c cc sas cs 1 231 23235()()()xyzac cas sacc555tan2( ,)As c.1111154321665A A A A A TT61 23 41 41 23 41 423 4()()()xyzsn c c ss cns c sc cn s s 61 23 41 451 23 51 23 41 451 23 423 4 523 5()()()xyzcncc cs s c

17、c s sns c cc s cs s cn s c cc s666tan2(,)As c.11121314212223243132333441424344aaaaaaaaTaaaaaaaa13111214232122243132333443414244aaaaxxxxaaaaxxxxdTdxaaaaxxxxaaaaxxxx.(,)( ,)TdTTrans dx dy dz Rot k dT(,)Trans dx dy dz( ,)Rot k d(,)( ,)dTTrans dx dy dz Rot k dI T(,)( ,)Trans ds dy dz Rot k dI .(,)( ,)Tr

18、ans ds dy dz Rot k dI 100010(,)0010001dxdyTrans dx dy dzdz1010( ,)100001zyzxyxk dk dk dk dRot k dk dk d.1001010000101001000011000100001000100010000000zyzxyxzyzxyxdxk dk ddyk dk ddzk dk dk dk ddxk dk ddyk dk ddz 0000000zydxzxdyyxdz 1.00110100501000001A00.5dijk 00.10ijk.000.1100000.1000.50000 0000000z

19、ydxzxdyyxdz 00.5dijk 00.10ijk00.10 xyz100.5dxdydz.000.1100110000010050.1000.501000000000100.1010000000.10.50000dAA .TdTTT 1TTT dTT TdTTT. 這個(gè)變換方程如同前面變這個(gè)變換方程如同前面變換方程一樣，可以用一個(gè)變換換方程一樣，可以用一個(gè)變換圖來(lái)表示，如右圖所示。由圖圖來(lái)表示，如右圖所示。由圖也可以直接得到上式。也可以直接得到上式。 方程方程2 2很重要，因?yàn)樗严嗪苤匾?，因?yàn)樗严鄬?duì)于不同的坐標(biāo)系之間的微分對(duì)于不同的坐標(biāo)系之間的微分變化聯(lián)系起來(lái)了。我們首先展變化聯(lián)

20、系起來(lái)了。我們首先展開(kāi)方程右端的矩陣乘積，展開(kāi)開(kāi)方程右端的矩陣乘積，展開(kāi)過(guò)程中進(jìn)行了簡(jiǎn)化，可得出微過(guò)程中進(jìn)行了簡(jiǎn)化，可得出微分變化向量分變化向量d d和和的元素之間的的元素之間的直接關(guān)系。變換直接關(guān)系。變換T T稱為微分坐標(biāo)稱為微分坐標(biāo)變換。變換。1TTT 2.如果把微分坐標(biāo)變化如果把微分坐標(biāo)變化T T的元素用向量的元素用向量n n、o o、a a和和P P描述為描述為0001xxxxyyyyzzzznoapnoapTnoap()()()()()()()()()()()()0000 xxxxyyyyzzzznoapdnoapdTnoapd.1()()()()()()()()()()()()00

21、00nnnonanpdonoooaopdTTanaoaaapd式中，式中，d d和和就是微分旋轉(zhuǎn)和微分平移。將上式左乘就是微分旋轉(zhuǎn)和微分平移。將上式左乘 可得可得1T.0()()()()0()()()()0()0000Tn oanpnd nn oo ap od oano apad a ()()()ab cbacbca ()0aac.n oaanoo an0()0()0()0000Taopnd nanp od oonpad a 0000000TTTTTTTTTTzydxzxdyyxdx 由于由于n、o、a正交，所以正交，所以34由式由式1定義為：定義為：T. 令式令式3 3和式和式4 4相等，我們就利用相對(duì)基礎(chǔ)坐標(biāo)系來(lái)描述的相等，我們就利用相對(duì)基礎(chǔ)坐標(biāo)系來(lái)描述的微分旋轉(zhuǎn)和平移的向量微分旋轉(zhuǎn)和平移的向量( (和和d)d)，得到相對(duì)于坐標(biāo)系，得到相對(duì)于坐標(biāo)系T T來(lái)描述的來(lái)描述的微分旋轉(zhuǎn)和平移的向量，即微分旋轉(zhuǎn)和平移的向量，即()()()TTTdxpnd ndyp od odzpad aTTTxnyoza65.() ()()()() ()()()().TxyzxyzxyzxyzxxyyzzxxyyzzdxijkPn iPnjPn kd id jd kn in jn kPnPnPnn dn dn d()()(),()()(),.Txxyyzzxxyyz