( 7 ) 4>t i ? , p f
TRU'CJNG D AI HOC SU PHAM K Y T HU A T
THA NH PHO HO CHI M IN H
KHOA CO KHI CHE TAO MAY
BO MON C O D IE N TU*
BE THI CUOI HOC KY I NAM HOC 2023-2024
Mon: Ky thuat Robot (Dai Tra)
Ma mon hoc: R 0 B 0 3 3 1129
De so/Ma de: 01 De thi co: 02 trang.
Thai gian: 60 phut.
Dirge phep sir dung 1 to A4 tai lieu.
Cau 1: (3.0 diem) ,
a) Trong toa do cue bo (local frame) thirc hien lan luot phep xoay -25° quay true y,
30° quay true x thi den toa do r2 = [1.7 -2 .7 3.7]7. Tim toa do rx truoc khi
thirc hien cac phep xoay. (1.5d)
b) Trong phep quay Euler, cho toa do diem Ex = [0.15 -0.5 -2.3 ]7 cho xoay
-0.25 [rad] quay true Z, xoay -0.4 [rad] quay true x, xoay -0.15 [rad] quay true
z. Tim toa do diem E2 sau khi thirc hien cac phep xoay tren. (1.5d)
Cau 2: (3.0 diem)
Trong he toa do cue bo (local frame B), cho toa do diem H = [-5 .5 6.6 -8 .8 ]r ,
thirc hien lien tuc cac phep quay -25° quay x, —45° quay z. Sau do, thirc hien phep
tinh tien trong toa do toan cue (global frame G) d = [3 -3 - 1 .2]r .
a) Tim ma tran chuyen vi dong nhat ('T a toa do toan eye, fun diem H sau khi thirc
hien phep chuyen vj tu ma tran 6 T .
b) Tim ma tran nghich dao cua (' T . Xac dinh ma tran xoay 0 R>(4x4) va ma tran
tinh tien 0 D (4x4) cua ma tran nghich dao 0 T .
*e
Hinh 1. Co' cau robot
So hieu: BM1/QT-PBT-RBTV/02 L4n soat xet: 02 Ngay hieu luc: 15/5/2020 Trang: 1/2
Cau 3: (2.0 diem)
Cho ca Cau robot nhir hinh ve ben tren. Ve lai ca cau robot vao bai lam va dat goc toa
do.
a) Xac dinh bang Denavit-Hartenberg (DH).
b) Xac dinh ma tran chuyen vi °T],] T2 cua tirng khau va cua toan bo robot °T2.
Cau 4: (2.0 diem)
Cho l\= 0.7 [m], /2=1.1 [m], d\ = 0.25 [m]. Va diem cuoi P tren khau 2 cua robot dang d
vi tri trong he toa do toan cue co toa do [x0 y 0 z0]' = [0.2 1.2 0.8]/ . Tir “Hinh 1.
Co1 cau robot”, va ket qua ma tran chuyen vi °T2 cua robot tir cau 3. Tim tat ca cac
trudng hop cua goc 9\ va goc Oil
Ghi chu: Can bo coi thi khong dime giai thick de thi. Lam tron chit so thap phan thie
3 sau dau phay
Chuan dau ra cua hoc phan (ve kien thirc) Noi dung kiem tra
[C L 02]: Co kha nang ap dung cac kien thirc ve toan
hoc de xay dung mo hinh toan cho robot noi tiep,
robot song song.
Cau 1
[CL02]: Co kha nang ap dung cac kien thirc ve toan
hoc de xay dung mo hinh toan cho robot noi tiep.
robot song song.
Cau 2
[CL04]: Co kha nang sir dung co so toan hoc cua
phuorng phap ma, tran chuyen vi va Denavit -
Hatenberg de tinh bai toan,dong hoc.
Cau 3
[CL 05]: Co kha nang mo phong bai toan dong hoc vi
tri.
Cau 4
N gay I\- thang (Tnam 20^3
Triro’ng bo mon
(ky va ghi rd ho ten)
Lan soat xet: 02 Ngay hieu lire: 15/5/2020 Trang: 2/2
So hieu: BM1/QT-PDT-RDTV/02
® V i n -f e i
TRUClNG DAI HOC SU' PHAM KY TH U A T DE THI CUOI HOC KY I NAM HOC 2023-2024
t h An h p h o HO CHI m i n h
KHOA CO KHI CHE TAO MAY Mon: Ky thuat Robot (Dai Tra)
BO MON CO DIEN TU M a mon hoc: R 0 B 0 3 3 1 129
B e s o /M a de: 01 B e thi co: 02 trang.
T h d i gian: 60 phut.
D u p e phep su dung 1 to A 4 tai lieu.
DAP AN
Cau 1: (3.0 diem)
a) Trong toa do cue bo (local frame B) thuc hien Ian lupt phep xoay -25° quay true
y, 30° quay true x thi den toa do r2 = [l .7 -2.7 3.7]7 . Tim toa do rf truoc khi
thuc hien cac phep xoay. (1.5d)
Ma tran xoay quanh true y,x tai toa do cue bo (local frame)
0.423'
0 (0.25d)
0.906
(0.25d)
c(-25) 0 -j( - 2 5 ) ' ' 0.906 0
% = 010=0 1
4 - 25) 0 c(-25) -0.423 0
'1 0 0 ' "1 0 0
BR,= 0 c30 ^30 =00.866 0.5
0-s30 c30 0 0.5 0.866
Toa do n truoc khi thuc hien phep xoay
\ = * R \ = ( 'R x*Ry) \
0.757
\ = { " R x"Rvy \ = -4.188
2.399
(Id)
b) Trong phep quay Euler, cho toa do diem £ ,= [0 .15 -0.5 -2.3] cho xoay
-0.25 [rad] quay true Z, xoay -0.4 [rad] quay true x, xoay -0.15 [rad] quay true
z. Tim toa do diem Ei sau khi thuc hien cac phep xoay tren. (1.5d) ~^|T~
S6 hieu: BM1/QT-PDT-RDTV/02 Lan soat xet: 02 Ngay hieu lire: 15/5/2020 Trang: 1/6
Ma tran xoay quanh true Z, x, z cua he toa do Euler
R, =
-025n
180
-0.25;r
180
0
—s -0.25k
180
-0.25;r
180
0
0.969 0.247 0
-0.247 0.969 0
0 0 1
(0.25d)
R, =
0
^ -0 .4 ;^
180
0 -s -0.4;r
180
0
( -OAx'
v 180 ,
f -0.4;rA
180
1 0
0 0.921
0 0.389
0
-0.389
0.921
(0.25d)
X =
-0.15;r
180
-s -0.15;r
180
0
-0.15#
180
-0.15;r
180
0
/
0.989
0.194
0
-0.149 0
0.988
0
(0.25d)
*Neu r,a diroc 3 ma tran xoay thi diroc 0.75d, moi ma tran xoay diro'c 0.25d.
Toa do 8E2 sau khi thirc hien cac phep xoay
8E2 = 8 R 8Ei = bR: hRx[(:Rz Y 8E, =
0.194
0.518
-2.293
(0.75d)
Cau 2: (3.0 diem)
Trong he toa do cue bo (local frame B), cho toa do diem H ] = [-5.5 6.6 -8.8] ,
thuc hien lien tuc cac phep quay -25° quay x, -45° quay z. Sau do, thuc hien phep
tinh tien trong toa do toan cue (global frame G) d = [3 -3 —1.2]7.
a) Tim ma tran chuyen vi dong nhat ('T a toa do toan cue, tim diem H2 sau khi
thuc hien phep chuyen vi tu' ma tran ° T .
b) Tim ma tran nghich dao cua (' T . Xac djnh ma tran xoay R (4x4) va ma tran
tinh tien ° D (4x4) cua ma tran nghich dao 6 T .
Sdhieu: BM1/QT-PBT-RDTV/02 Lan soat xet: 02 Ngay hieu luc: 15/5/2020 Trang: 2/6
Ma tran xoay quanh true x, z tai toa do cue bo (local frame)
"l 0 0 '1 0 0
X = 0 c (-2 5) 5(-25) =0 0.906 -0.423
0 - j( -2 5 ) c(-2 5) 0 0.423 0.906
1
1
L/1
x(-45 ) 0" '0.707 -0.707 O'
X - = -5 (-4 5 ) c (-4 5 ) 0 =0.707 0.707 0
0 0 1 0 0 1
*Neu ra diro'c 2 ma tran xoay thi dirge 0.25d
Ma tran xoay tong hop tai toa do toan cue (global frame)
' 0.707 0.707 0
= > X ; = ( X ; ) ' = ( X X ) ' = ~0-641 0.641 0.423 (0.25d)
0.3 -0.3 0.906
Ma tran chuyen vi T dua tren ma tran xoay tong hop va vector tjnh tien a toa do toan cue
(global frame)
Cirri
_
1B -
0.707
-0.641
0.3
0
0.707
0.641
-0.3
0
0
0.423
0.906
0
3
-3
-1.2 (0.5d)
Toa do H 2, sau khi thuc hien phep chuyen vi
gH2 = % bHx
' 0.707 0.707 0 3 '-5 .5 ' ' 3.778 "
-0.641 0.641 0.423 -3 6.6 1.035
0.3 -0.3 0.906 -1.2 -8.8 -12.791
0 0 0 1 1 1
(Id)
*De bai yeu cau lam phu’Cng phap ma tran chuyen vi T, SV lam khac phu’o’ng phap
chi lay 30% diem.
Ma tran nghich dao T '1 la
% = { c% y = g r t d =
Ma tran xoay: 11R =
0.707 -0.641 0.3 -3.685
0.707 0.641 -0.3 -0.557
z r 1 = 0 0.423 0.906 2.355
00 0 1
0.707 -0.641 0.3 O'
0.707 0.641 -0.3 0 (0.25d)
0 0.423 0.906 0
0 0 0 1
(0.5d)
So hieu: BM l/QT-PDT-RBTV/02 Lan soat xet: 02 Ngay hieu lire: 15/5/2020 Trang: 3/6