amum sim- T R A O £>6I<br />
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' P h u o n g p h a p x a c d i n h h e t o a d p<br />
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v a c a c t h d n g s o d e n a v i t - h a r t e n b e r g c i i a r o b o t<br />
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(*) PHAM DANG PHUYJC<br />
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cac he toa dp da i n dinh cho cac khiu lien ket ciia robot,<br />
cac ma tran A_ dupe xac dinh nhu sau:<br />
Aj = Rot(z,e).Trans(0,0,d).Trans(a,0,0).Rot(x,a)<br />
TOM TAT<br />
Cung theo Denavit, tich ciia cac ma tran A dugc gpi<br />
Khi nghien ciru robot theo mo hinh dong la ma tran T. Ma tran T thuong co hai chi so: tren va dudi<br />
hoc Denavit - Hartenberg (DH), can phai xac ( T ). Chi so tren chi he toa dp tham chieu tdi, bd qua chi so<br />
l<br />
d<br />
<br />
<br />
dinh he toa do gan tren cac khau, sau do, xac tren neu chi sd do bang 0. Chi so dudi thudng dung de chi<br />
djnh cac thong so DH de thiet lap he phi/cfng khiu chip hanh cuoi. Neu mpt robot co 6 khiu ta co:<br />
trinh dong hoc hoac dong Itfc hoc.Thifdng, cac<br />
tai lieu ve robot gidi thieu nguyen tac chung de<br />
gan he toa do va xac dinh cac thong so DH.Tuy<br />
nhien, viec thiic hien theo nguyen tac chung<br />
thudng kho. Bai bao nay gidi thieu mot so<br />
kinh nghiem khi gan he toa do va xac djnh cac<br />
thong so DH cua robot, nham xac djnh chung<br />
mot each nhanh chong, de dang hon.<br />
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I. M O H I N H D O N G H O C DENAVIT-<br />
Hinh 1: Cac vecto dmh vi tri va djnh huong ciia ban kep.<br />
HARTENBERG<br />
<br />
Moi robot co the dugc coi la mot xich dong hgc Ma tiin T md ta moi quan he ve huong va vi tri cua<br />
g<br />
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gom cac khau gan lien vdi nhau bang cac khdp (quay khiu chip hanh cuoi doi vdi he toa dp goc, T cdn duoc 6<br />
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<br />
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hoac tinh tien). De nghien cuu dong hgc robot, ta gin goi la ma tran vecto cuoi. Mpt robot 6 khiu thudng co 6<br />
bic tu do va co the dupe dinh vi tri va dinh hudng trong<br />
tren moi khau ciia robot mdt he toa do. Vi tri va hudng<br />
trudng cong tic cua no. Ba bac tu do diu tien diing de<br />
giua cac he toa do nay cd the dugc mo ta bang cac phep<br />
xac dinh vi tri cua khiu chip harm cuoi va ba bac tu do<br />
bien doi thuan nhat [1][4],<br />
cdn lai dung de xac dinh hudng mong mudn. T se la 6<br />
<br />
J. Denavit (1955) goi phep bien doi thuan nhat, md ma trin mo ta dong thdi ca huong va vi tri he toa dp gan<br />
ta moi quan he giua he toa do ciia hai khau lien ke nhau tren khiu chap hanh cuoi (O ) ciia robot so vdi he toa<br />
n<br />
<br />
la mot ma tran A. Noi each khac, ma tran A la mot mo dp goc (O ). Hinh 1 mo ta moi quan he ciia ban kep doi<br />
0<br />
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t i bien doi thuan nhat gom cac phep quay va phep tinh voi O . Ta dat goc toa dp 0 cua he mo ta tai diem giua<br />
0<br />
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tien tuong doi giua he toa dp cua khau sau doi vdi khau cua cac ngon tay. Gdc toa dp nay duoc mo ta bdi vecto<br />
lien trudc (khau thii i so vdi khau thii i-1). Tren co so diem_p (xac dinh v j tri cua ban kep). Ba vecto' don vi<br />
n, 6, a mo ta hudng cua ban kep. Ma trin vecto cuoi T 6<br />
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(*) Tnrong Dai hoc Pham Van Dong nhu vay se bao gom cac phin tir: cs=<br />
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TAP CHI CO KHI VIET NAM *X* So 4 - Thing 4 nam 2011 » * 1<br />
NGHIEN CUU • TRAO DOI<br />
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<br />
n 0 a Moi true se co hai phap tuven doi voi no. moi phap<br />
Px<br />
X X tuyen diing cho moi khau (trudc va sau mpt khdp). V i<br />
T = n o a Py<br />
6 v<br />
tri tuong doi cua khau thir I so voi khau thu i - l dupe<br />
JX 0^ a. PZ<br />
xac dinh boi hai thong so:<br />
0 0 0 1 - d.: la khoang each giua cac phap tuyen do doc<br />
theo true khdp thu i.<br />
Bp thong so Denavit-Hartenberg (DH)<br />
— 9: la goc giua cac phap tuyen do trong mat phang<br />
Mot robot thuong gom nhieu khau. lien ket noi tiep<br />
nhau thong qua cac khdp (long. Goc (khau co ban) cua vuong goc vdi true khop thu i.<br />
mpt robot dupe gpi la khau so 0 va khong tinh v ao so d. va 9. thuong dupe gpi la khoang each va goc<br />
cac khau. Khau 1 noi vdi khau co ban boi khdp 1 va quay tuong doi giua cac khau.<br />
khong co khdp a dau mut cua khau cuoi cung. tren khau Cac thdng so a., a d. va 9. duac goi la bo thong so<br />
cuoi cimg co gan mpt cong cu. Nhu vay, cac khau. khop Denavit - Hartenberg (Goi tat la bo thong so DH).<br />
dupe danh so tang dan tu khau ca ban. Xet mpt khau<br />
Trudng hop khdp quay thi 9. la cac bien khdp. a,<br />
rieng re thu L bat ky khau nao cung dupe dac trung boi<br />
a. d. la hang so. Trong truong hpp khdp tinh tien thi d,<br />
hai kich thuoc:<br />
la bien khdp. 9 va a bang 0. a = const.<br />
i<br />
<br />
- Dp dai phap tuyen chung a.<br />
- Goc giua cac true khop do trong mat phang II. N GUYEN TAC CHUNG GAN HE TO A<br />
vuong goc voi a.; ky hieu la a.<br />
DO L E N CAC K H A U CUA ROBOT<br />
Thong thuong. ngudi ta gpi a la chieu dai va a la<br />
gdc xoan cua khau (Hinh 2). Nhu noi tren. de mo ta moi quan he giua cac khau<br />
ta gan vao mdi khau mpt he toa dp. Nguyen tac chung<br />
de gan he toa dp len cac khau nhu sau (xem hinh 3):<br />
- Goc cua he toa dp gan len khau thii i (ky hieu<br />
0.) dat tai giao diem cua phap tuyen chung a., vdi tnic<br />
khdp thir i— 1. Truong hpp hai true khdp cat nhau.<br />
goc toa dp se dat tai'chinh diem cat do. Neu cac true<br />
khop song song vdi nhau. goc toa dp dupe chpn tren<br />
true khdp thii i - l . tai diem thich hop, thuong chpn<br />
sao cho d_ = 0.<br />
- Tnic z. cua he toa dp gan len khau thu i dat doc<br />
Hinh 2: Chieu dai va goc xoan ciia khau thu i theo true khdp thu i - l . Chieu cua true z dupe coi la<br />
chieu cua true khdp.<br />
Khi xet moi quan he giua cac khau vdi nhau. trong<br />
thuc te thuong gap hai khau lien ket voi nhau a chinh - True x dupe dat doc theo phap tuyen chung a<br />
true cua khdp (Hinh 3). va hudng tu true khdp thu i den i - l . Trong trudng hpp<br />
cac tnic khdp cat nhau thi true x chpn theo tich vecto<br />
Khopi-1<br />
•(> • ; )•<br />
CD Khau i + True y dupe chpn theo qui tac ban tay phai.<br />
Khau i-<br />
<br />
ni. NHUNG KLNH NGHIEM KHI GAN<br />
HE TOADO V A X A C DINH CAC THONG<br />
Khau i-2 a ;<br />
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d i Zi-I S6 D H CUA ROBOT<br />
\ a,-1 -<br />
'" Q 1. Gan he tog dp<br />
Viec gan he toa dp len cac khau dong vai tro rat<br />
Hrnh 3: Cac mens so DH cua khau : 9 d, a va a<br />
r quan trpng khi thiet lap he phuong trinh dong hpc cua<br />
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<br />
E l TAP CHI CO'KHI VIET NAM *t* So 4 - Thang 4 nam 2011<br />
NGHIEN CUU - TRAO OOl<br />
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robot, thong thuong day cung la budc kho nhat. Khi chon lai vi tri ban dau khac cho robot hoac phdi thay<br />
nghien cuu, hoc tap ve robot cong nghiep, dua vao Rot(y,90°) = Rot(z,90°). Rot(x,90°). Lite nay gid tri ban<br />
nguyen tic chung noi tren, do tinh tong quat nen thuong dau ciia bien khop thir i khdng bang khdng, ma 8. = 90°.<br />
kho co the xac dinh nhanh va chinh xac cac he toa do; Trong tinh toan ta chu y thay 8. = 8 .+ 98° (hay thay sind.<br />
nhieu sinh vien thuong lung tung b budc nay. Trong = - cosd va COS'S. = sind}.<br />
thuc te, ta nhan thay cac true khdp cua robot thudng 2. Xdc dinh ede thdng sd DH (Denavit Hartenberg)<br />
song song hoac vuong goc vdi nhau, dong thoi dua vao<br />
Thong so DH cua cac khau-khbp duoc trinh bay<br />
cac phep bien doi cua ma tran A co the xac dinh cac he<br />
;<br />
thanh mot bang va can cu vao dinh nghia ciia chiing<br />
toa do gan tren cac khau cua robot theo kinh nghiem<br />
de xac dinh. Tuy nhien, viec dua vao dinh nghia la<br />
nhu sau:<br />
kha phuc tap. Sau khi da gan he toa dp len cac khau,<br />
+ Chon mot vj tri ban dau * (Home Position) cua<br />
1<br />
<br />
chung ta cd the xdc dinh cac thdng sd DH cua robot<br />
robot. Vi tri ban dau ciia robot thuong la vi tri duoi theo huong vd vi tri ciia hai he toa dd lien ke nhau se de<br />
thang cac khau, hoac gap lai'90°d cac khau cuoi. Trong ddng hon, each xac dinh nhu sau:<br />
qua trinh gan he toa do, neu vi tri ban dau da chon khong<br />
+ Gdc 8 : niu la khop quay thi 8. Id bien khop (ky<br />
phu hop, neu can ta cd the chon lai vi tri khac.<br />
hieu 8"), neu la khop tinh tien thi 8. = 8.<br />
+ Chon goc toa do O , O ... thuc hien theo cac<br />
0 p<br />
+ Gdc a: i ~~ ( i - l •> D la gdc quay cua z.<br />
a z Z<br />
A<br />
nguyen tac chung. Luu y gdc cua he toa do thu i (O)<br />
thanh z. (gdc cd hudng). Vi du: a la gdc quay ciia z<br />
1 Q<br />
<br />
phai nam tren true khop thu<br />
thanh z r<br />
<br />
+ Chon true z , z,,... Cac true z chon cung phuong<br />
Q ;<br />
+ a.: ta cd a = 0 0, la dd dai tinh tien ciia O<br />
; M iA<br />
<br />
vdi true khdp thir i+1. True z nen huong ve phia cac<br />
din O do doc theo true x. Neu la khdp tinh tien thi<br />
f r<br />
<br />
khau. True z cua he toa do gan tren khau chdp hanh<br />
n<br />
a =0.<br />
cudi khdng nhat thiet phai theo huong tiep can den<br />
+ d.: ta cd d = O 0 la dd dai tinh tien cua 0<br />
ddi tuong. Khi gan cdng cu len khau chap hanh cudi,<br />
; w ; {1<br />
<br />
<br />
din O do doc theo true z._ Niu la khdp tinh tien thi d.<br />
he toa do gdn tren cdng cu se cd huong tiep can ddi<br />
r<br />
<br />
<br />
Id bien khdp.<br />
tuong.<br />
+ Chon true x : Ngoai each xac dinh theo nguyen<br />
IV. KET LUAN<br />
;<br />
<br />
<br />
tac chung, ta nhan thay true x. (hoac x.J chinh la true<br />
quay ciia z thanh z va gdc tao boi (z^Tz;) chinh Vdi nhung kinh nghiem neu tren, viec gan he toa<br />
Id a. (can cic vao phep quay Rot(x,a) trong cac phep dp len cac khau cua robot va xac dinh cac thong so<br />
biin ddi cua ma tran A). Neu z._, va z song song hoac DH tro nen ro rang va nhanh chdng hon. Ket hop vdi<br />
;<br />
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trung nhau thi ta co the can cir nguyen tac chung de viec xay dung phan mem may tinh de tu dong thiet lap<br />
xac dinh. he phuong trinh dong hpc robot [3], thi viec tinh toan,<br />
+ Cac he tog dd Oxyz phdi tuan theo qui tdc ban thiet lap phuong trinh dong hpc robot se thuan tien hon<br />
tay phdi. nhieu. •<br />
<br />
+ Khi gan he toa do len cac khau, ta da xem he toa<br />
T a i lieu t h a m khao:<br />
dp thu i la bien doi cua he toa do thii i - l ma cd. Cac he<br />
toa dp nay phai tuan theo cac phep bien doi co trong ma [1] Paul Richard P. Robot Manipulators: Mathematics,<br />
tran A , do la bon phep bien doi: A. = Rot (z,0).Trans Programming and Control.<br />
;<br />
<br />
The MIT Press - Cambndge, Massachusetts and London, 1981.<br />
(0,0,d).Trans (a,0,0).Rot (x,a). Trong do, khdng cd cac<br />
[2] Giordano Max - Lottrn Jacques. Cours de Robotique -<br />
phep quay hoac tinh tien ddi vdi true y; vi vay, trong Description et Fonctionnement des Robots tndustriels. Armand<br />
qua trinh gan he toa dd len cac khau, neu thay xuat hien Colin Editor, Pans - 1990.<br />
phep quay ciia true z thanh z. quanh true y thi cdn<br />
1<br />
[3] Nguyin Thien Phuc, Pham Phii Ly, Pham Dang Phuoc.<br />
Automatic establish of kinematic equations, modelling and<br />
simulation ofRobots - Proceedings of VJ'ASEM -2000.<br />
[4] Pham Dang Phuoc. Robot cong nghiep. NXB Xay dung,<br />
" VI tri ban dau la vi tri ma cac biin kh&p nhan gid tri ban dau, do<br />
l<br />
<br />
<br />
<br />
ngudi thiet ke chon, thudng bang 0 (dot Mil cd thi khac 0). Ha Noi-2008.<br />
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TAP CHI CO KHI VIET NAM *t* Sd 4 - Thang 4 nam 2011<br />