de cuong thi robot cong nghiep
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Cu hi n tp ch-ng i
Cu 1: nh ngha robot cng nghip? Nu cc ng dng carobot cng nghip?
Hin nay c nhiu nh ngha v Robot, c th im qua mt
s nh ngha nh sau :nh ngha theo tiu chun AFNOR (Php) :
Robot cng nghip l mt c cu chuyn ng t ng c th
lp trnh, lp li cc chng trnh, tng hp cc chng
trnh t ra trn cc trc to ; c kh nng nh v,
nh hng, di chuyn cc i tng vt cht : chi tit,
dao c, g lp . . . theo nhng hnh trnh thay i
chng trnh ho nhm thc hin cc nhim v cng ngh
khc nhau.
nh ngha theo RIA (Robot institute of America) :
Robot l mt tay my vn nng c th lp li cc chng
trnh c thit k di chuyn vt liu, chi tit, dng
c hoc cc thit b chuyn dng thng qua cc chng
trnh chuyn ng c th thay i hon thnh cc nhim
v khc nhau.
nh ngha theo OCT 25686-85 (Nga) :Robot cng nghip l mt my t ng, c t c nh
hoc di ng c, lin kt gia mt tay my v mt hthng iu khin theo chng trnh, c th lp trnh li
hon thnh cc chc nng vn ng v iu khin trong
qu trnh sn xut.
C th ni Robot cng nghip l mt my t ng linh hot
thay th tng phn hoc ton b cc hot ng c bp v
hot ng tr tu ca con ngi trong nhiu kh nng thch
nghi khc nhau.
Robot cng nghip c kh nng chng trnh ho linh hottrn nhiu trc chuyn ng, biu th cho s bc t do ca
chng. Robot cng nghip c trang b nhng bn tay my
hoc cc c cu chp hnh, gii quyt nhng nhim v xc
nh trong cc qu trnh cng ngh : hoc trc tip tham
gia thc hin cc nguyn cng (sn, hn, phun ph, rt kim
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loi vo khun c, lp rp my . . .) hoc phc v cc
qu trnh cng ngh (tho lp chi tit gia cng, dao c,
g . . .) vi nhng thao tc cm nm, vn chuyn v
trao i cc i tng vi cc trm cng ngh, trong mt
h thng my t ng linh hot, -c gi l H thng tng linh hot robot ho cho php thch ng nhanh v thao
tc n gin khi nhim v sn xut thay i.
Cc ng dng ca robot cng nghip:
T khi mi ra i robot cng nghip c p dng trong
nhiu lnh vc di gc thay th sc ngi. Nh vy cc
dy chuyn sn xut c t chc li, nng sut v hiu
qu sn xut tng ln r rt.
Mc tiu ng dng robot cng nghip nhm gp phn nng
cao nng sut dy chuyn cng ngh, gim gi thnh, nng
cao cht lng v kh nng cnh tranh ca sn phm ng
thi ci thin iu kin lao ng. t c cc mc tiu
trn l nh vo nhng kh nng to ln ca robot nh : lm
vic khng bit mt mi, rt d dng chuyn ngh mt cch
thnh tho, chu c phng x v cc mi trng lm vic
c hi, nhit cao, cm thy -c c t tr-ng v
nghe -c c siu m ... Robot -c dng thay th con
ngi trong cc trng hp trn hoc thc hin cc cngvic tuy khng nng nhc nhng n iu, d gy mt mi,
nhm ln.
Trong ngnh c kh, robot c s dng nhiu trong cng
ngh c, cng ngh hn, ct kim loi, sn, phun ph kim
loi, tho lp vn chuyn phi, lp rp sn phm . . .
Ngy nay xut hin nhiu dy chuyn sn xut t
ng gm cc my CNC vi Robot cng nghip, cc dy chuyn
t mc t ng ho cao, mc linh hot cao . . . y cc my v robot c iu khin bng cng mt h
thng chng trnh.
Ngoi cc phn xng, nh my, k thut robot cng c s
dng trong vic khai thc thm lc a v i dng, trong
y hc, s dng trong quc phng, trong chinh phc v tr,
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trong cng nghip nguyn t, trong cc lnh vc x hi . .
.
R rng l kh nng lm vic ca robot trong mt s iu
kin vt hn kh nng ca con ngi; do n l phng
tin hu hiu t ng ho, nng cao nng sut lao ng,gim nh cho con ngi nhng cng vic nng nhc v c
hi. Nhc im ln nht ca robot l cha linh hot nh
con ngi, trong dy chuyn t ng, nu c mt robot b
hng c th lm ngng hot ng ca c dy chuyn, cho nn
robot vn lun hot ng di s gim st ca con ngi.
Cc ng dng c th ca robot:
ng dng robot trong cng nghip: Robot gp vt liu
hn im, phun sn, phc v my cng c lm khun trong
cng nghip nha.
ng dng robot trong phng th nghim: dng thc
hin cc cng vic th cng, thc hin cc cng vic lp
i lp li.
ng dng robot trong thao tc cn khuch i lc: Dng
trong nhng khu vc nguy him(phng x ) bc d hng ha,
vt liu, phi c trng lng ln cng knh trong cc
nghnh cng nghip nng
ng dng robot trong nng nghip: Robot ct lng cu,
m x tht heoTrong lnh vc ny robot m nhim c ngay
cc cng vic mang tnh lp li, nhiu thao tc i hi s
phi hp tay ngh cao v s lanh li ca i mt.
ng dng robot trong khng gian: Tay my c ch to
nhm tng cng kh nng bc d hng ha tip t, lp ghp
vi cc trm khng gian khc nhau. Cc xe t hnh trang b
tay my linh hot, cc robot cng dng chung trong cc
trm khng gian, bo tr v tinh, xy dng trong khnggian
ng dng robot trong tu ln: Pht trin cc tu ln
khng ngi li trong cng tc kim tra, d tm, bo tr
thm him di y i dng.
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ng dng robot trong gio dc: Robot c s dng lm
phng tin ging dy trong cc chng trnh gio dc.
Robot c kt hp vi ngn ng LOGO ging dy v nhn
thc my tnh, to ra phng hc robot.
ng dng robot trong h tr ngi tn tt: thng quaxung no iu khin cc tay my lm nhng thao tc mong
mun, nhng b phn thay th c th.
ng dng robot trong sinh hot v gii tr: Cc loi
chi tr em, robot htoong minh s dng trong nh v vn
phng
Cu 2: Nu khi nim min lm vic, bc t do? C nhngloi khp no? Bc t do ca mi loi?
Khi nim min lm vic ca robot:
Min lm vic (hay vng lm vic, trng cng tc,khng gian cng tc) ca robot l ton b th tch c
qut bi khu chp hnh cui khi robot thc hin tt c
cc chuyn ng c th. Min lm vic b rng buc bi ccthng s hnh hc ca robot cng nh cc rng buc c hc
ca cc khp; v d, mt khp quay c chuyn ng nh hn
mt gc 360
0
. Ngi ta thng dng hai hnh chiu m tmin lm vic ca mt robot.
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Bc t do ca robot (DOF : Degrees Of Freedom) :
Bc t do l s kh nng chuyn ng ca mt c
cu (chuyn ng quay hoc tnh tin) trong khng gian
hot ng. dch chuyn c mt vt th trong khng
gian, c cu chp hnh ca robot phi t c mt s
bc t do. Ni chung c h ca robot l mt c cu h,
do bc t do ca n c th tnh theo cng thc :
5
1
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y: w - S bc t do ca tay my.n - S khp ca tay my;
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pi- S khp loi i (i = 1,2,. . .,5 : S bc t do b
hn ch hay loi khp).
i vi cc c cu c cc khu c ni vi nhau bng
khp quay hoc tnh tin (khp ng loi 5) th s bc t
do bng vi s khu ng . i vi c cu h, s bc t dobng tng s bc t do ca cc khp ng.
nh v v nh hng khu chp hnh cui mt cch
tu trong khng gian 3 chiu robot cn c 6 bc t do,
trong 3 bc t do nh v v 3 bc t do nh
hng. Mt s cng vic n gin nng h, sp xp... c
th yu cu s bc t do t hn. Cc robot hn, sn...
thng yu cu 6 bc t do. Trong mt s trng hp cn s
kho lo, linh hot hoc khi cn phi ti u ho qu
o,... ngi ta dng robot vi s bc t do ln hn 6.
Cc bc chuyn ng c phn ra bc chuyn ng c bn
(chuyn ng nh v) v bc chuyn ng b xung (chuyn
ng nh hng).
Chuyn ng c bn thng l chuyn ng tnh tin
hoc l chuyn ng quay, mi bc chuyn ng c ngun dn
ng ring.
Chuyn ng b xung thng l cc chuyn ng quay
nhm tng kh nng linh hot, m bo cho khu chp hnhcui hon thnh nhim v.
Khp v bc t do ca mi loi:
Ty theo cu trc, mi khp hn ch mt s chuyn ng
gia 2 khu. B mt tip xc ca mi khu ti khp gi l
mt thnh phn khp. Hai thnh phn khp to thnh mt
khp ng. Khp ng c th phn thnh khp thp v khp
cao ty thuc vo dng tip xc.
Khp thp : nu hai thnh phn tip xc l mt.Khp cao : nu hai thnh phn tip xc l im hoc
ng.
C 6 loi khp thp v hai loi khp cao c bn thng
dng trong cc c cu my v cc robot l:
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Khp quay (Revolute Joint - R): khp li chuyn ng
quay ca khu ny i vi khu khc quanh 1 trc quay.
Ngha l khp quay hn ch 5 kh nng chuyn ng tng
i gia hai thnh phn khp v c 1 bc t do. Khp quay
thng c gi l khp bn l.Khp lng tr (Prismatic Joint - P): Cho php hai khu
trt trn nhau theo 1 trc. Do khp lng tr hn ch 5
kh nng chuyn ng tng i gia hai khu v c 1 bc
t do. Ngi ta cn gi khp lng tr l khp tnh tin
(Join - T).
Khp tr (Cylindrical Joint - C): Cho php 2 chuyn ng
c lp gm 1 chuyn ng quay quanh trc v chuyn ng
tnh tin dc trc quay. Do khp tr hn ch 4 kh nng
chuyn ng gia 2 khu v c 2 bc t do.
Khp ren (Helical Joint - H): Cho php chuyn ng quay
quanh trc ng thi tnh tin theo trc quay. Tuy nhin
chuyn ng tnh tin ph thuc vo chuyn ng quay bi
bc ca ren vt. Do khp ren hn ch 5 kh nng chuyn
ng tng i gia hai khu v cn lai 1 bc t do.
Khp cu (Spherical Joint - S): Cho php thc hin chuyn
ng quay gia 2 thnh phn khp quanh tm cu theo tt c
cc hng , nhng khng c chuyn ng tnh tin gia 2thnh phn khp ny. Do khp cu hn ch 3 kh nng
chuyn ng v cn li 3 bc t do.
Khp phng (Plane Joint - E): Cho 2 kh nng chuyn ng
tnh tin theo 2 trc trong mt phng tip xc v mt kh
nng quay quanh trc vung gc vi mt phng tip xc. Do
khp cu hn ch 3 kh nng chuyn ng v cn li 3
bc t do.
Khp bnh rng (Geat Pair - G): Cho hai bnh rng n khpvi nhau cc mt rng tip xc y nhau chng thng trt
trn nhau. Do khp bnh rng phng hn ch 4 kh nng
chuyn ng tng i gia 2 thnh phn khp cn li 2 bc
t do.
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Khp cam phng (Cam Pi - Cp): Tng t nh khp bnh rng
hai thnh phn khp lun tip xc vi nhau. Do , khp
cam phng c 2 bc t do.
Cu 3: Cng thc tnh bc t do ca tay my? Tnh bc tdo ca nhng tay my sau:
Cng thc tnh bc t do ca tay my:
5
1
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ipinw
Trong : w - S bc t do ca tay my.
n - S khp ca tay my;
pi- S khp loi i (i = 1,2,. . .,5 : S bc t do b
hn ch hay loi khp).Tnh bc t do ca nhng tay my sau:
Hnh a Hnh b Hnh c
Hnh a: S khp n = 4
i 1 2 3 4 5pi 0 0 0 2 2
Vy: S bc t do ca tay my l:
ADCT:
5
1
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ipinw
Thay s: 6)2.52.4(4.6 w
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Hnh b: S khp n = 4
i 1 2 3 4 5pi 0 0 1 1 2
Vy: S bc t do ca tay my l:
ADCT:
5
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ipinw
Thay s: 7)2.51.41.3(4.6 w
Hnh c: S khp n = 4
i 1 2 3 4 5pi 0 0 0 1 3
Vy: S bc t do ca tay my l:
ADCT:
5
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ipinw
Thay s: 5)3.51.4(4.6 w
Hnh d Hnh eHnh f
Hnh d: S khp n = 4
i 1 2 3 4 5
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pi 0 0 1 1 2
Vy: S bc t do ca tay my l:
ADCT:
5
1
.6i
i
pinw
Thay s: 7)2.51.41.3(4.6 w
Hnh e: S khp n = 4
i 1 2 3 4 5pi 0 0 2 0 2
Vy: S bc t do ca tay my l:
ADCT:
5
1
.6i
ipinw
Thay s: 8)2.52.3(4.6 w
Hnh f: S khp n = 4
i 1 2 3 4 5pi 0 0 1 0 3
Vy: S bc t do ca tay my l:
ADCT:
5
1
.6i
ipinw
Thay s: 6)3.51.3(4.6 w
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Hnh g Hnh h
Hnh i
Hnh g: S khp n = 3
i 1 2 3 4 5
pi 0 0 0 1 2
Vy: S bc t do ca tay my l:
ADCT:
5
1
.6i
ipinw
Thay s: 4)2.51.4(3.6 w
Hnh h: S khp n = 3
i 1 2 3 4 5pi 0 0 0 0 3
Vy: S bc t do ca tay my l:
ADCT:
5
1
.6i
ipinw
Thay s: 33.53.6w
Hnh i: S khp n = 4
i 1 2 3 4 5pi 0 0 0 1 3
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Vy: S bc t do ca tay my l:
ADCT:
5
1
.6i
ipinw
Thay s: 5)3.51.4(4.6 w
Cu 4: Phn loi robot cng nghip theo h thng dn ng
v khng gian lm vic?
Phn loi theo h thng truyn ng :
C cc dng truyn ng ph bin l :
H truyn ng in : Thng dng cc ng c in 1
chiu (DC : Direct Current) hoc cc ng c bc (step
motor). Loi truyn ng ny d iu khin, tc ng nhanhv chnh xc, kt cu gn, gi thnh khng cao, mmen quay
cao, trng lng gim v p ng nhanh, p dng c k
thut iu khin phc tp. Tuy nhin, bn cht l tc
cao, khe h bnh rng lm gim chnh xc, gy qu
nhit khi qu ti, cn s dng phanh ghim v tr v
khp.
H truyn ng thu lc : c th t c cng sut
cao, p ng nhng iu kin lm vic nng, tc chym, c th kha cng khp ti v tr xc nh (khng nn
c), an ton p sut chy n. Tuy nhin h thng thu
lc thng c kt cu cng knh, chi ph cao, khng thch
hp cho c cu quay vi tc nhanh, cn c ng hi
du, tn ti phi tuyn ln kh x l khi iu khin.
H truyn ng kh nn : c kt cu gn nh hn do
khng cn dn ngc, gi thnh khng cao, kh thi khng
gy nhim mi trng nhng li phi gn lin vi trung
tm ta ra kh nn, gy n kh iu chnh tc , phi s
dng b lc. H ny lm vic vi cng sut trung bnh v
nh, km chnh xc, thng ch thch hp vi cc robot
hot ng theo chng trnh nh sn vi cc thao tc n
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gin nhc ln - t xung (Pick and Place or PTP :
Point To Point).
Phn loi theo dng khng gian lm vic:
Khng gian lm vic ca c cu chp hnh c xc
nh l th tch khng gian tc ng c th vi ti.Thng s dng hai nh ngha v khng gian lm vic.
Th nht l khng gian c th vi ti, th tch khng
gian trong c cu tc ng c th vi ti tng im
theo t nht 1 chiu. Th hai l khng gian linh hot,
th tch khng gian trong c cu tc ng c th
vi ti tng im theo mi chiu c th. Khng gian
linh hot l mt phn ca khng gian c th vi ti.
Mt s robot cu trc ni tip in hnh:
Robot kiu to cc (Robot ta vung gc):
l tay my c 3 chuyn ng c
bn tnh tin theo phng ca
cc trc h to gc (cu
hnh T.T.T). Trng cng tc c
dng khi ch nht. Do kt cu
n gin, loi tay my ny c
cng vng cao, chnh xc
c kh d m bo v vy nthung dng vn chuyn phi
liu, lp rp, hn trong mt phng
Robot kiu to tr : Vng
lm vic ca robot c dng hnh
tr rng. Thng khp th nhtchuyn ng quay, cc khp cn
li chuyn ng tnh tin hoc
c mt trc tnh tin v 2 trc
quay. V d robot 3 bc t do,
cu hnh R.T.T nh hnh v. C
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nhiu robot kiu to tr nh : robot Versatran ca hng
AMF (Hoa K).
Robot kiu to cu : Vng lm vic ca robot c dnghnh cu, thng cng vng ca loi robot ny thp hn
so vi hai loi trn. V d robot 3 bc t do, cu hnh
R.R.R hoc R.R.T lm vic theo kiu to cu (hnh).
Robot kiu ta gc (H ta phng sinh) : y l kiu
robot c dng nhiu hn c. Ba chuyn ng u tin lcc chuyn ng quay, trc quay th nht vung gc vi haitrc kia. Cc chuyn ng nh hng khc cng l ccchuyn ng quay. Vng lm vic ca tay my ny gn gingmt phn khi cu. Tt c cc khu u nm trong mt phngthng ng nn cc tnh ton c bn l bi ton phng. uim ni bt ca cc loi robot hot ng theo h to gc l gn nh, tc l c vng lm vic tng i ln sovi kch c ca bn thn robot, linh hot cao.Cc robot hot ng theo h to gc nh : Robot PUMA
ca hng Unimation - Nokia (Hoa K - Phn Lan), IRb-6,IRb-60 (Thu in), Toshiba, Mitsubishi, Mazak (Nht Bn).V.V...V d mt robot hot ng theo h to gc (H to phng sinh), c cu hnh RRR.RRR :
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Robot kiu SCARA : Robot SCARA
ra i vo nm 1979 ti trng
i hc Yamanashi (Nht Bn) l
mt kiu robot mi nhm p ng
s a dng ca cc qu trnh sn
xut. Tn gi SCARA l vit tt
ca "Selective Compliant
Articulated Robot Arm" : Tay my
mm do tu . Loi robot nythng dng trong cng vic lp
rp nn SCARA i khi c gii
thch l t vit tt ca "Selective Compliance Assembly
Robot Arm". Ba khp u tin ca kiu Robot ny c cu
hnh R.R.T, cc trc khp u theo phng thng ng. S
ca robot SCARA nh hnh. Vng lm vic ca tay my
SCARA l mt phn ca hnh tr rng.
CU HI N TP CHNG 2Cu 1:Trnh by cng thc ma trn cosin chhng? Nu v chng minh nhng tnh
cht c bn ca ma trn cosin chhng.Cng thc ma trn cosin chhng:
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Cho vt rn B v h quy chiu R0 = )0(3)0(2)0(1 ,, eee
trong )0(
3
)0(
2
)0(
1,, eee
lba vc t n v trn cc trc Ox0, Oy0, Oz0 . Ta gn cht vt rn vo mt h quy chiu
R1 = )1(3)1(2)1(1 ,, eee
vi)1(
3
)1(
2
)1(
1,, eee
l ba vc t n v trn cc trc Ax, Ay,Az (Hnh).
Ma trn vung cp ba:
)1(
3
)0(
3
)1(
2
)0(
3
)1(
1
)0(
3
)1(
3
)0(
2
)1(
2
)0(
2
)1(
1
)0(
2
)1(
3
)0(
1
)1(
2
)0(
1
)1(
1
)0(
1
...
...
...
eeeeee
eeeeee
eeeeee
A
c gi l ma trn cosin chhng ca vt rn B i vi h quy chiu R0.
Nu ta a vo k hiu: ).cos(.)1()0()1()0(
jijiij eeeea
, (i,j = 1,2,3)
th ma trn cosin chhng c dng:
333231
232221
131211
aaa
aaa
aaa
A
Tnh ngha trn, trong h quy chiu R0 ta c cc h thc hin h:)0(331
)0(
221
)0(
1111... eaeaeae
)0(
332
)0(
222
)0(
1122... eaeaeae
)0(
333
)0(
223
)0(
1133... eaeaeae
Nu ta k hiu ie l ma trn ct gm cc phn t ca vc t ie
trong h qui chiu R0.
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Ta c:
31
21
11
1
a
a
a
e
,
32
22
12
2
a
a
a
e
,
33
23
13
1
a
a
a
e
Th ma trn cosin chhng c dng:
321eeeA
Ma trn cosin chhng A cn c gi l ma trn quay ca vt rn.
Nhng tnh cht c bn ca ma trn cosin chhng:nh l 1:Ma trn cosin chhng l ma trn trc giao.Chng minh:Tcc phng trnh :
Ta suy ra:
0
11
21
31
(1)
1
R
a
a
a
e
, 012
22
32
(1)
2
R
a
a
a
e
,0
13
23
33
(1)
3
R
a
a
a
e
T ma trn cosin chhng c th vit di dng :
A= 0 (1)1R e 0 (1)2R e 0 (1)3R e (1.12)Ta thy ma trn cosin chhng Al ma trn c ba ct l ba vec t trc chun. do Al mt ma trn trc giao. T tnh cht ca ma trn trc giao ta suy ra A-1 =AT. Do , tcng thc (1.11) ta c th bin i ngc :
u(1)=A-1.u(0)=AT.u(0)
nh l 2: nh thc ca ma trn csin chhng bng 1, detA= 1.Chng minh: theo biu thc tnh tch hn hp ca ba vct
1 1 1
2 2 2
3 3 3
.( )
a b c
a b c a b c
a b c
=
| |
V cng thc (1.12) ta suy ra:
detA= (1) (1) (1)1 2 3, ,e e e = 2 3 1, ;Do R1 l h quy chiu thun nn ta c:
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BI TP LN: RBT CNG NGHIP
Trang:18LP : CTK8LC1
GVHD: Trn Xun Tin
(1) (1) (1)
2 3 1e e e
Th(2) vo (1) ta c :
detA= 2(1) (1)
1. 1e e
inh l 3: Ma trn csin chhng c t nht mt tr s ring bng 1Chng minh: trc ht ta chng minh cc tr ring ca ma trn csin chhng A u ctr tuyt i l 1. Ga s l tr ring ca ma trn A, u l vc t ringtng ng. Theobi ton tr s ring ta c:
A. u = u T ta suy ra :
2
( ).( ) ( ) .( ) . . .T T T T
Au Au Au Au u A Au u u u .
Vy : . 1Au u u
By gita chng minh trong ba tr ring ca ma trn A c mt tr ring l 1 .Theo trn ta c || || || . Do A l ma trn vung cp ba vi cc phn t lcc s thc nn phng trnh c trng ca n l phng trnh i s bc ba vi h sthc : Do cc tr s ring ca ma trn A c th c hai khnng: l cc s thc . c mt tr s ring thc v mt cp tr ring lin hp.Ga s
l tr ring ca A. Theo (3) ta thy c hai khnng xy ra hoc
hoc
. Nu , nh l c chng minh. Nu , ta c :detA= Ta thy c hai khnng xy ra: hoc l hai s thc , hoc l hai s phclin hp. Nu v l hai s phc lin hp ( ta c h thc : 2 22 Hthc (6) mu thun vi h thc (5) . Vy phi l hai s thc , do 2 3 1, nn ta suy ra:Hoc 2 1 , 3 1 hoc 2 1 , 3 1
Nh th ma trn csin chhng A lun c mt tr ring bng 1.Cu 2: Trnh by nhng ma trn quay c bn, cc gc euler, cc gc Roll- Pitch-Yaw.Trnh by nhng ma trn quay c bn:Trc ht ta quy c hng quay dng quanh mt trc l hng quay ngc chiu kimng hnh hnh v:
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BI TP LN: RBT CNG NGHIP
Trang:19LP : CTK8LC1
GVHD: Trn Xun Tin
Cc php quay quanh trc x,y,z ca h tovung gc Oxyz c l php quay cbn. Ta tm ra ma trn quay ca php quay quanh trc mt gc . Hnh:
Theo cng thc nh ngha ma trn csin chhng:
)1(
3
)0(
3
)1(
2
)0(
3
)1(
1
)0(
3
)1(
3
)0(
2
)1(
2
)0(
2
)1(
1
)0(
2
)1(
3
)0(
1
)1(
2
)0(
1
)1(
1
)0(
1
...
...
...
eeeeee
eeeeee
eeeeee
A
Ta ddng xc nh c ma trn csin chhng:
cossin0
sincos0
001
xA
Ma trn trn c gi l ma trn quay caphp quay c bn quanh trc x0. Bng cchtng tta xc nh c cc ma trn quay c bn quanh cc trc y0 v z0.
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BI TP LN: RBT CNG NGHIP
Trang:20LP : CTK8LC1
GVHD: Trn Xun Tin
cos0sin
010
sin0cos
yA
100
0cossin
0sincos
zA
Cc gc Euler:
V tr ca vt rn B quay xung quanh im O cnh xc nh bi v tr ca h quy chiung Oxyz (gn cht vo vt rn B) i vi h quy chiu cnh Ox0y0z0 .Ga s giaoca mt phng quy chiu ) v mt phng Oxy (mt phng ng ) l ng OK. Trc OKny c gi l ng nt .Ta a cc k hiu sau:-Gc gia trc Ox0 v OK l ,-Gc gia trc Oz0 v Oz l ,-Gc gia trc OK v Ox l
Ba gc , , c gi l ba gc Euler. S dng cc gc Euler ta c th quay h quychiu Ox0y0z0 sang h quy chiu Oxyz bng php quay nh sau:
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BI TP LN: RBT CNG NGHIP
Trang:21LP : CTK8LC1
GVHD: Trn Xun Tin
Quay h quy chiu R0 = Ox0y0z0 quanh trc Oz0 mt gc trc Ox0 chuyn ti ngOK. Vi php quay ny, h quy chiu Ox0y0x0 chuyn sang h quy chiu R1 = Ox1y1z1vi Oz0 Oz1.
Quay h quy chiu R1 = Ox1y1z1 quanh trc Ox1 OKmt gc trc Oz1 chuyn titrc Oz2 Oz h quy chiu Ox1y1z1 chuyn thnh h quy chiu Ox2y2z2 vi Ox1 Ox2 OK.Quay h quy chiu R2 = Ox2y2z2 quanh trc Oz2 Oz mt gc trc Ox2 OKchuyn ti trc Ox.Vi php quay ny, h quy chiu Ox2y2x2 chuyn sang h quy chiuOxyzvi Oz2 Oz.
Nh th , bng ba php quay Euler quanh trc Oz0 mt gc , quanh trc OK mt gc ,quanh trc Oz mt gc , h quy chiu Ox0y0z0 chuyn sang h quy chiu Oxyz. Th tcc php quay l z-x-z. cc ma trn ng vi cc php quay Euler c dng:
Cc gc Roll - PitchYawCc php quay Roll - PitchYaw ln lt quanh cc trc zyx. Ta c th quay hquy chiu cnh Ox0y0z0 sang h quy chiu ng Oxyz bng ba php quay Roll - Pitch
Yaw nh hnh:
z2 z
z1 z
y 2
y1
x
x 2
z0 z1
x1 K
x0
y0
y1
x1 x 2
z0 z
1
y 0
y1
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BI TP LN: RBT CNG NGHIP
Trang:22LP : CTK8LC1
GVHD: Trn Xun Tin
Quay h Ox0y0z0 quanh trc Oz0 mt gc ty (gc Roll). H Ox0y0z0 chuyn thnh hOx1y1z1 vi Oz0 Oz1.Quay h Ox1y1z1 quanh trc Oy1 mt gc ty (gc Pitch) sao cho trc Ox1 chuyn
n trc Ox. H Ox1y1z1 chuyn thnh h Ox2y2z2 vi Oy1 Oy2.Quay h Ox2y2z2 quanh trc Ox2 Ox mt gc ty (gc Yaw) sao cho trc Oz2chuyn n trc Oz. H Ox2y2z2 chuyn thnh h Oxyz.Cc ma trn quay tng ng vi cc php quay Roll, Pitch, v Yaw c dng nh sau:
z
x
y
Rol l
Pitch
Y aw
z0 z1
x1
x 0
y 0
y1
z1 z0
x 2 xx1
z2
y1
x 2 x
z
y 2
z2
O O O
y
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BI TP LN: RBT CNG NGHIP
Trang:23LP : CTK8LC1
GVHD: Trn Xun Tin
Cu 3: Trnh by v chng minh cc nh l v vn tc gc v gia tc gc ca vt rn.
nh v vn tc c ca vt rnXc nh vn tc gc ca vt rn qua cc vc tn v ca h quy chiu gn lin vovt rn.nh l 1: Trong c svung gc R1 = { , , }gn lin vo vt rn B,
vn tc gc ca vt rn B i vi h quy chiu R0 c xc nh bi cng thc :
0 0 00
(1) (1) (1)
(1) (1) (1) (1) (1) (1)2 3 1
1 3 2 1 3 2. . .
R R RR B de de de
e e e e e edt dt dt
Chng minh:Trong h qui chiu R1 ={ , , } vc t vn tc gc ca vt rn B c th vitdi dng:
0 0 0 0(1) (1) (1) (1) (1) (1)
1 1 2 2 3 3( . ). ( . ). ( . ).R B R B R B R B
e e e e e e (1)Do , , l ba vc t n v trn ba trc ca h ta vung gc nn ta ccng thc quen bit:
=
.
,
=
.
,
=
.
(2)
Th cc biu thc 2 vo 1 ta c :0 0 0 0(1) (1) (1) (1) (1) (1) (1) (1) (1)
3 1 1 2 2 31 3 1[ .( ]. [ .( ]. [ .( ].
R B R B R B R B
e e e e e e e e e (3)Da vo tnh cht ca tch hn hp ba vc t
.( ) .( ) .( )a b c b c a c a b V nh ngha vn tc gc ca vt rn , h thc (3) c dng
0 0 0 0(1) (1) (1) (1) (1) (1) (1) (1) (1)
3 2 1 1 3 2 2 1 3[ .( )]. [ .( )]. [ .( )].R B R B R B R B
e e e e e e e e e
0 0 0(1) (1) (1)
(1) (1) (1) (1) (1) (1)2 3 1
3 1 2 2 2 3. . . . . .
R R Rde de d e
e e e e e edt dt dt
(4)
Do tch v hng ca hai vc t c tnh cht giao hon, t (4) ta suy ra cng thc
0 0 00
(1) (1) (1)
(1) (1) (1) (1) (1) (1)2 3 1
1 3 2 1 3 2. . .
R R RR B d e d e d e
e e e e e edt dt dt
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BI TP LN: RBT CNG NGHIP
Trang:24LP : CTK8LC1
GVHD: Trn Xun Tin
nh l c chng minh.
Xc nh vn tc c ca vt rn t a trn csn ch hnnh l 2: cho A l ma trn cosin chhng ca vt rn B trong h quy chiuR0={x0y0z0}. Khi ton t sng ca vc t vn tc gc ca vt rn trong h quy chiu
cnh R0 c xc nh bi cng thc: Trong : 0 0 0
0 0 0
(0), ,
TR R RB B B
B x y z , = 0R dAdt
Chng minh: chn P l mt im ty thuc vt rn B. Ta c:
pp Ar r u
(1)
o hm phng trnh (1) theo thi gian trong h quy chiu c nh 0 ta c:
0 0
R Rp A
p p A pd r d r u v v udt dt
(2)
Trong 0R B l vn tc gc ca vt rn.Nu s dng k hiu ma trn th phng trnh (2) c dng (4)Cn phng trnh (1) c dng: T cng thc u(0) =Au(1) ta c
(5)
Trong l ma trn ct gm c ba thnh phn l hnh chiu ca vct pu trong hOx0y0z0 cn
(1)
pu l ma trn ct gm ba thnh phn l cc hnh chiu ca vct pu trongh Ax1y1z1 .Th (5) vo (4) ta c: (6)o hm phng trnh (6) theo thi gian trong h 0 ta c:
(0) (0) (1)Ap pAv v u (7)
Do ma trn cosin ch hng la ma trn trc giao nn t h thc (5) ta suy ra(1) 1 (0) (0)
T
p p pu A u A u (8)
Th (8) vo (7) ta c(0) (0) (0)
AAT
p pAv v u (9)
o snh (9) vi (3) ta suy ra cng thc
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BI TP LN: RBT CNG NGHIP
Trang:25LP : CTK8LC1
GVHD: Trn Xun Tin
a tc c ca vt rn
nh nha a tc c ca vt rn v h ta 0 t n vect
hu
0R B
bn h the th an trn h quy chu 0 ca vc t vn tcc 0
0 0
( )
RR B R Bd
dt nh trn h quy chu 1n n v vt nu vct vn tc c ca vt rn
c bu dn d dn 0 (1) (1) (1)1 1 1
1 2 31 2 3. . .
R B
e e e
Th biu thc tnh gia tc gc ca vt rn c dng nh sau:
0 (1) (1) (1)(1) (1) (1)1 2 31 2 3
R B
e e e hn nh theo nh ngha gia tc gc ta c :
0 0
0 0 (1) (1) (1)1 1 11 2 31 2 3
( ) ( . . . )
R RR B R Bd d
e e edt dt
0 0 0
(1) (1) (1)
(1) (1) (1) 1 2 31 1 1(1) (1) (1)1 2 31 2 3 1 2 3
R R Rde de de
e e edt dt dt
(1)
Do0
(1)
(1)R Bii
dee
dt (i 1,2,3) nn ta c
0 0 0
0
(1) (1) (1)
(1) (1) (1)1 2 31 1 1 1 1 11 2 31 2 3 1 2 3
( . . . )
R R RR Bd e de d e
e e edt dt dt
0 0
0R B R B
(2)Th (2) vo (1) ta c
0 (1) (1) (1)(1) (1) (1)1 2 31 2 3
R B
e e e
Cu 4:Trnh by cng thc cng vn tc gc v cng thc cng gia tc gc ca vtrn.
Cng thc cng vn tc gc:
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BI TP LN: RBT CNG NGHIP
Trang:26LP : CTK8LC1
GVHD: Trn Xun Tin
Xt mt vct ty ca vt rn B. Vt rn B chuyn n i vi h quychiu , h quy chiu li chuyn n i vi h quy chiu . The nh nhavn tc gc ta c cng thc:
Hnh 1
0
0
RR Bd c
cdt
(1)
1
1
RR Bd c
cdt
(2)
Mt khc t cng thc:0 1
0 1
R RR Rd c d c
adt dt
(.)
Ta c phng trnh:0 1
0 1
R RR Rd c d c
cdt dt
(3)
Th cc h thc (1) v (2) vo phng trnh (3) c0 0 01 1 1 1( )
R R RR R R RB B Bc c c c (4)T (4) suy ra
0 0 1 1R R R RB B (3.1)Cng thc (3.1) l cng thc cng vn tc vt rn.
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BI TP LN: RBT CNG NGHIP
Trang:27LP : CTK8LC1
GVHD: Trn Xun Tin
Hnh 2Chuyn ng ca vt rn B i vi h quy chiu 1 c gi l chuyn ng tngi, chuyn ng ca vt rn B i vi h quy chiu 0 c gi l chuyn ng tuyt
i. Chuyn ng ca h quy chiu ng 1 i vi h quy chiu cnh 0 c gi
l chuyn ng theo. K hiu 0R B
a , (vn tc gc tuyt i ca vt rn B),
1R B
r , (vn tc gc tng i ca vt rn B), 0 1R R e ,(vn tc gc theo).
Khi biu thc (3.1) c dng
a r e (3.2)
nh l 2.4. Ti mi thi im, vn tc gc tuyt i ca vt rn B bng tng hnh hcvn tc gc tng i v vn tc gc theo ca n.Ap dng lin tip cng thc (3.1) i vi n+1 h quy chiu nh hnh 2 ta c
0 0 11 1 2 ... n n n BR R R R RR R R RB
(3.3)
Cng thc cng vn tc gc:o hm theo thi gian cng thc (3.1) h quy chiu 0 ta c
0 0 0
0 0 1 1( ) ( ) ( )
R R RR R R RB Bd d d
dt dt dt (1)
Ch n cng thc (.) ta c0
0 0 01 1 1 1( )
RR R RR R R RB B Bd
dt (2)
Tnh ngha chuyn ng tuyt i, tng i v theo ca vt rn suy ra
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BI TP LN: RBT CNG NGHIP
Trang:28LP : CTK8LC1
GVHD: Trn Xun Tin
0R B
a , 1
R B
r , 0 1
R R
e (3)
Th(3) vo (2) ta c
a e r e r (3.4)
nh l 2.5. mi thi im gia tc gc tuyt i ca vt rn B bng tng hnh hc giatc gc tng i, gia tc gc theo, v gia tc gc ph p e r ca vt rn.
Gia tc ph p e r cn c gi l gia tc gc Resal.
Cu 5:Xc nh vn tc, gia tc mt im bt k thuc vt rn.Vn tc 1 m bt k thuc vt rn:
xt chuyn ng ca vt rn B trong h quy chiu 0 0 0 0R ox y z , ta ly im A bt
k thuc vt rn lm im nh v(im cc). Dng h quy chiu 1 1 1 1R Ax y z
gn linvo vt rn B.
V tr ca im P c xc nh bi vc t sau
P A Pr r u (1)
o hm 2 v theo thi gian ca phng trnh (1) trong h quy chiu o ta c0 0 0R R R
P A Pd r d r du
dt dt dt
(2)Theo nh ngha vn tc gc ca vt rn ta c
0R
R BPP P
d uu u
dt (3)
Th(3) vo phng trnh (2) ta c
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BI TP LN: RBT CNG NGHIP
Trang:29LP : CTK8LC1
GVHD: Trn Xun Tin
0 0R R
P AP
d r d r u
dt dt ==> P A Pv v u (4.1)
Chiu phng trnh vc t (4.1) ln h quy chiu Ro ta c:(0) (0) (0) (0)
P A Pv v u (4.2)Chiu phng trnh vc t (4.1) ln h quy chiu 1 ta c(1) (1) (1) (1)
P A Pv v u (4.3)
Ch rng:(0) (1)
P Pu Au
Gia tc 1 m bt k thuc vt rn:o hm theo thi gian biu thc (4.1) trong h quy chiu ota c
0 0 00R R RR
P A PP
d v d v d udu
dt dt dt dt
T suy ra
).~.(~.~PPAP
uuaa (4.4)Chiu phng trnh (4.4) ln h quy chiu o ta c phng trnh ma trn
)0()0()0()0()0()0(
)0()0()0()0()0()0()0(
).~.~~(
).~.(~.~
PAP
PPAP
uaa
uuaa
(4.5)
Chiuphng trnh vc t (4.4) ln h quy chiu R1
)1()1()1()1()1()1(
)1()1()1()1()1()1()1(
).~.~~(
).~.(~.~
PAP
PPAP
uaa
uuaa
(4.6)
Cu 6:Cho c cu nh hnh v.
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BI TP LN: RBT CNG NGHIP
Trang:30LP : CTK8LC1
GVHD: Trn Xun Tin
Da vo cc h ta gn ln cc khu, cc thng skch thc v gc quay , hytnh:
Cc ma trn cosin chhng gia cc h ta lin tip (R0 R1 R2 R3 R4 R5): A1, A2,A3,A2,A3,A4,A5:
100
0cossin
0sincos
11
11
1
A
;
100
0cossin
0sincos
22
22
2
A
100
0cossin
0sincos
33
33
3
A
;
100
0cossin
0sincos
44
44
4
A
100
0cossin
0sincos
55
55
5
A
Vn tc gc, gia tc gc cc khu trong h ta R0(O0x0y0z0)Gi i l vn tc gc ca khu th i.
p dng cng thc: V cng thc cng vn tc gc ta c: BRRRRRRRBR n ...3221100 Vn tc gc khu 1:
Ta c: Vi:
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BI TP LN: RBT CNG NGHIP
Trang:31LP : CTK8LC1
GVHD: Trn Xun Tin
100
0cossin
0sincos
11
11
1
A
=
000
0sincos
0cossin
11
11
.
100
0cossin
0sincos
11
11
1
T
A
= Tng t ta c:Vn tc gc khu 2:
=
Vn tc gc khu 3:
=
Vn tc gc khu 4:
=
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BI TP LN: RBT CNG NGHIP
Trang:32LP : CTK8LC1
GVHD: Trn Xun Tin
Vn tc gc khu 5:
Do R5 tnh tin so vi R0 nn ma trn cosin chhng ca h ta R5 so vi R0 l:
100
010
001
05A
;
=
;
Gia tc gc cc khu:
Vn tc, gia tc ti trng tm cc khu(trn t c m chnh gia ca cc khu)trong h ta R0(O0x0y0z0):
Vn tc cc gc ta :
vO1 =
; vO2 =
vO3 =
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BI TP LN: RBT CNG NGHIP
Trang:33LP : CTK8LC1
GVHD: Trn Xun Tin
vO4=
vO5 = Vn tc ti trng tm cc khu:
vG1 =
; vG2 =
vG3 =
vG4 =
[ 0 ]vG5 =
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BI TP LN: RBT CNG NGHIP
Trang:34LP : CTK8LC1
GVHD: Trn Xun Tin
[ 0]
Gia tc ti trng tm cc khu:
aG1 =
aG2 = ( ) ( ) ( ) ( ) ( ) ( ) aG3 =
[
.l2.S(2.1 + 2.2 + 3) - (
.l3.S(2.1 + 2.2 + 3))/2 -
.l1.S(2.1 + 2) -
.l2.C(2.1 + 2.2 + 3) - (.l3.C(2.1 + 2.2 + 3))/2 - .l1.C(2.1 + 2) -2. .l2.C(2.1 + 2.2 + 3) - 2. .l2.C(2.1 + 2.2 + 3) - .l3.C(2.1 +2.2 + 3) - .l3.C(2.1 + 2.2 + 3) - 2. .l1.C(2.1 + 2)][ .l2.C(2.1 + 2.2 + 3) + (.l3.C(2.1 + 2.2 + 3))/2 + .l1.C(2.1 + 2) -.l2.S(2.1 + 2.2 + 3) - (.l3.S(2.1 + 2.2 + 3))/2 - .l1.S(2.1 + 2) -2. .l2.S(2.1 + 2.2 + 3) - 2. .l2.S(2.1 + 2.2 + 3) - .l3.S(2.1 +2.2 + 3) -
.l3.S(2.1 + 2.2 + 3) - 2.
.l1.S(2.1 + 2)]
[ 0]
aG4 =
[- .l2S(2. + 2. + ) - (.l3.C(2. + 2. + + ))/2 - (.l4.C(2. +2. + + ))/2 - .l1.S(2. + ) - .l2.C(2. + 2. + ) - .l1.C(2. + ) - (.l3.S( + + + ))/2 - (.l4.S( + + + ))/2 -
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:35LP : CTK8LC1
GVHD: Trn Xun Tin
. .l3.C( + + + ) - . .l3.C( + + + ) - . .l3.C(+ + + ) - . .l4.C( + + + ) - . .l4.C( + + +) - . .l4.C( + + + - 2. . .l2.C(2. + 2. + ) -2.
.
.l2.C(2.
+ 2.
+
) - 2.
.
.l2.C(2.
+ 2.
+
)]
.l2C(2. + 2. + )+ .l1C(2. + )-(.l3.S(2. + 2. + + ))/2 -(.l4.S(2. + 2. + + ))/2 - .l2.S(2. + 2. + ) - .l1.S(2. + )+( l3.C(2. + 2. + + ))/2 + ( l4.C(2. + 2. + +))/2 - . .l3.S( + + + ) - . .l3.S( + + + ) -. .l3.S( + + + ) - . .l4.S( + + + ) - . .l4.S(+ + + ) - . .l4.S( + + + - 2. . .l2.S(2. + 2. + )- 2.
.
.l2.S(2.
+ 2.
+
) - 2.
.
.l2.S(2.
+ 2.
+
)]
[ 0]
aG5 =
[- .l1S(2. + 2. + ) - (.l3.C(2. + 2. + + ))/2 - .l1.S(2. + ) - .l2.C(2. + 2. + ) - .l1.C(2. + ) - .l4.S( + + + ) -(.l3.S( + + +2 ))/2 - . .l4.C( + + + ) - . .l4.C( + + + ) - . .l4.C( + + + ) - . .l4.C( + + + ) -
.
.l3.C(2.
+ 2.
+
+
) -
.
.l3.C(2.
+ 2.
+
+
) -
. .l3.C(2. + 2. + + ) - 2. . .l2.C(2. + 2. + ) -2. . .l2.C(2. + 2. + ) - 2. . .l1.C(2. + 2. + )][ .l2S(2. + 2. + ) + .l1.C(2. + ) - (.l3.S(2. + 2. + + ))/2
- .l2.S(2. + 2. + ) - .l1.S(2. + ) + .l4.C( + + + ) +(.l3.C( + + +2 ))/2 - . .l4.S( + + + ) - . .l4.S( + + + ) - . .l4.S( + + + ) - . .l4.S( + + + ) -
.
.l3.S(2.
+ 2.
+
+
) -
.
.l3.S(2.
+ 2.
+
+
) -
. .l3.S(2. + 2. + + ) - 2. . .l2.S(2. + 2. + ) -2. . .l2.S(2. + 2. + ) - 2. . .l1.S(2. + 2. + )][ 0]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:36LP : CTK8LC1
GVHD: Trn Xun Tin
BI TP CHNG III V IV
L
1
L2
L3
x1z1
x0
z0Z3
X3
Z2
X2
-
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BI TP LN: RBT CNG NGHIP
Trang:37LP : CTK8LC1
GVHD: Trn Xun Tin
H2
di ai i Khp1 1 L1 0 90 R2 2 0 L2 -90 R3 3 0 L3 0 R
Bng D-H:
Vit cc ma trn H1, H2, H3
;
Vit phng trnh th hin v tr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
aE =
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:38LP : CTK8LC1
GVHD: Trn Xun Tin
. - . - . + - . - . . - . - . - . - . - . - 2. . . + 2. . . - . -
.
.
-
.
+ 2.
.
.
+ 2.
.
.
+
2. . . . - . - . - . - . + . - . - .L3.S1.S3 - . - . - . - 2. . . - 2. . . + . - . - . - 2. . . . - 2. . . +2. . .
.
-
.
-
.
-
.
+
.
-
.
-
2. . . ; ;
;
;
Vit biu thc vn tc gc, gia tc gc a phngv tuyt i ca tng khu
; ;
;
;
;
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
39/114
BI TP LN: RBT CNG NGHIP
Trang:39LP : CTK8LC1
GVHD: Trn Xun Tin
Xy dng v tnh ton cc phn t trong ma trn Jacobi:
JR=
[
]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:40LP : CTK8LC1
GVHD: Trn Xun Tin
H3Bng D-H:
di ai i Khp
1 1 0 L1 90 R2 2 0 L2 0 R3 3 0 L3 0 R
Vit cc ma trn H1, H2, H3
-
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BI TP LN: RBT CNG NGHIP
Trang:41LP : CTK8LC1
GVHD: Trn Xun Tin
D3 =
[ C1.C2.C3 - C1.S2.S3, - C1.C2.S3 - C1.C3.S2, S1, l1.C1 + l2.C1.C2 + l3.C1.C2.C3 -
l3.C1.S2.S3][ C2.C3.S1 - S1.S2.S3, - C2.S1.S3 - C3.S1.S2, -C1, l1.S1 + l2.C2.S1 + l3.C2.C3.S1 -l3.S1.S2.S3][ C2.S3 + C3.S2, C2.C3 - S2.S3, 0,l2.S2 + l3.C2.S3 + l3.C3.S2][ 0, 0, 0,1]
Vit phng trnh th hin v tr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
vE =
- .( + . + . - ) - .( . + . + . ) -.( . + . ).( . + . +. - . . ) - .( + . . +. . ) - . . . + . . ).( .cos(2 + 3) + . ) + . .cos(2 + 3)
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:42LP : CTK8LC1
GVHD: Trn Xun Tin
aE =
. . . . - . . - . . . - .. - . . . - . . . . - . . . . - . . . . - . . . . - . . + . . . . + . . . . + 2. . . . . . - .l3. . . - . . . - . . . . - . . . . - . . . . +. . . . - 2. .. . . . + 2. . . . . +2. . . . . . .+ 2. . . . . . + 2. . . . . . + 2. .. . . .
.
.
-
.
.
-
.
.
.
-
.
.
.
+
.
.
.
-
.
.
.
-
. . . . - . . . . - . . . . + . . . . + . . . . + . . . . - 2. . . . . . + . . . . -. . . . - . . . . - . . . . - . . . - . . . . - 2. . . . . . - 2. . .l3. . . -2. . . . . . - 2. . . l3. . . - 2. . . . . . + 2. .. . . . . . - .l3.sin(2 + 3) - . .sin(2 + 3) - . + . .cos(2 + 3) +
.
.cos(2 + 3) - 2.
.
.
.sin(2 + 3)
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:43LP : CTK8LC1
GVHD: Trn Xun Tin
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:44LP : CTK8LC1
GVHD: Trn Xun Tin
( ) ( )
Xy dng v tnh ton cc phn t trong ma trn Jacobi
JR=
[
]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:45LP : CTK8LC1
GVHD: Trn Xun Tin
H4
ng hc thun:
Tnh bc tdo ca tay my.
S khp n = 3
i 1 2 3 4 5
pi 0 0 0 0 3
Vy s bc t do ca tay my l:ADCT:
5
1
.6i
ipinw
Trong : w s bc t do ca tay my
ns khp ca tay my.
pis khp loi i (i 1,2,,5 s khp hay s bc t do b hn ch )Thay s: 33.53.6 w (bc t do)
Xy dng cc h ta cho cc khu:
-
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BI TP LN: RBT CNG NGHIP
Trang:46LP : CTK8LC1
GVHD: Trn Xun Tin
Bng D-H:
di ai i Khp1 1 0 l1 0 R2 2 0 l2 0 R3 3 0 l3 0 R
Vt cc a trn H1 H2 H3
=
D3 =
[
(
-
) -
(
+
), -
(
+
) -
(
-
), 0,
+ ( - ) - ( + ) + - ][( + ) + ( - ), ( - ) - ( + ), 0, + ( + ) + ( - ) + - ][ 0 0 1 0][ 0 0 0 1]
Vt phn trnh th hn v tr chp hnh cu
X0
Z0
X1
Z1
X2
Z2
X3
Z3
L3
L2
L1
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:47LP : CTK8LC1
GVHD: Trn Xun Tin
rE = + ( - ) - ( + ) + -
+
(
+
) +
(
-
) +
+ -
0Vt bu thc vn tc a tc tuyt ca chp hnh cu
vE =- ( + + ) - ( + ) - )( + + ) + ( + ) +
0
aE =[ -
-
-
-
) -
-
-
-
- - - - - 2 - 2 -2 - 2 ][ - - + + + - - - - + + - 2 -2 - 2 - 2 ][ 0]
; ;
Vt bu thc vn tc c a tc c a phn v tuyt ca tn hu
-
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BI TP LN: RBT CNG NGHIP
Trang:48LP : CTK8LC1
GVHD: Trn Xun Tin
; ;
ng hc ngc
Xy dn v tnh tn cc phn t trn a trn Jacb
; JR=
[
]
H5Bng D-H:
di ai i Khp1 1 0 l1 0 R2 2 0 l2 -90 R3 3 0 l3 0 R
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
49/114
BI TP LN: RBT CNG NGHIP
Trang:49LP : CTK8LC1
GVHD: Trn Xun Tin
Vit cc ma trn H1, H2, H3
Vit phng trnh th hin v tr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
50/114
BI TP LN: RBT CNG NGHIP
Trang:50LP : CTK8LC1
GVHD: Trn Xun Tin
aE =2. . . - . - - . - . - . - . - . - . - 2 - . - . - . . - 2
-
.
.
+ 2
.
. - . - . - . + . . - + . . -. - . - . . - 2. . + . . + . . - . . - 2. . - 2. . . . - 2. . .(- - . )
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
-
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51/114
BI TP LN: RBT CNG NGHIP
Trang:51LP : CTK8LC1
GVHD: Trn Xun Tin
Xy dng v tnh ton cc phn t trong ma trn Jacobi
-
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BI TP LN: RBT CNG NGHIP
Trang:52LP : CTK8LC1
GVHD: Trn Xun Tin
JR=
[
]
H6
di ai i Khp1 1 0 L1 -90 R2 2 0 L2 0 R3 3 0 L3 0 R
Bng D-H:
DH =
[ q1, 0, l1, -pi/2][ q2, 0, l2, 0]
-
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53/114
BI TP LN: RBT CNG NGHIP
Trang:53LP : CTK8LC1
GVHD: Trn Xun Tin
[ q3, 0, l3, 0]
Vit cc ma trn H1, H2, H3
H1 =
[ C1, 0, -S1, l1.C1][ S1, 0, C1, l1.S1][ 0, -1, 0, 0][ 0, 0, 0, 1]
H2 =
[ C2, -S2, 0, l2.C2][ S2, C2, 0, l2.S2][ 0, 0, 1, 0][ 0, 0, 0, 1]
H3 =
[ C3, -S3, 0, l3.C3][ S3, C3, 0, l3.S3][ 0, 0, 1, 0][ 0, 0, 0, 1]
D3 =
[ C1.C2.C3 - C1.S2.S3, - C1.C2.S3 - C1.C3.S2, -S1, l1.C1 + l2.C1.C2 + l3.C1.C2.C3 -l3.C1.S2.S3][ C2.C3.S1 - S1.S2.S3, - C2.S1.S3 - C3.S1.S2, C1, l1.S1 + l2.C2.S1 + l3.C2.C3.S1 -
l3.S1.S2.S3][ - C2.S3 - C3.S2, S2.S3 - C2.C3, 0, -l2.S2 - l3.C2.S3 - l3.C3.S2][ 0, 0, 0,1]
Vit phng trnh th hin v tr im chp hnh cui
-
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BI TP LN: RBT CNG NGHIP
Trang:54LP : CTK8LC1
GVHD: Trn Xun Tin
rE =
l1.C1 + l2.C1.C2 + l3.C1.C2.C3 - l3.C1.S2.S3l1.S1 + l2.C2.S1 + l3.C2.C3.S1 - l3.S1.S2.S3
- l2.S2 - l3.C2.S3 - l3.C3.S2
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
vE =
- dq1.(l1.S1 + l2.C2.S1 + l3.C2.C3.S1 - l3.S1.S2.S3) - dq2.(l2.C1.S2 + l3.C1.C2.S3 +l3.C1.C3.S2) - dq3.(l3.C1.C2.S3 + l3.C1.C3.S2)
dq1.(l1.C1 + l2.C1.C2 + l3.C1.C2.C3 - l3.C1.S2.S3) - dq2.(l2.S1.S2 + l3.C2.S1.S3 +
l3.C3.S1.S2) - dq3.(l3.C2.S1.S3 + l3.C3.S1.S2)
- dq2.(l3.cos(q2 + q3) + l2.C2) - dq3.l3.cos(q2 + q3)
aE =
dq1^2.l3.C1.S2.S3 - dq1^2.l1.C1 - dq1^2.l2.C1.C2 - dq2^2.l2.C1.C2 - ddq1.l2.C2.S1 -ddq2.l2.C1.S2 - dq1^2.l3.C1.C2.C3 - dq2^2.l3.C1.C2.C3 - dq3^2.l3.C1.C2.C3 -ddq1.l1.S1 + dq2^2.l3.C1.S2.S3 + dq3^2.l3.C1.S2.S3 + 2.dq1.dq2.l2.S1.S2 -ddq1.l3.C2.C3.S1 - ddq2.l3.C1.C2.S3 - ddq2.l3.C1.C3.S2 - ddq3.l3.C1.C2.S3 -ddq3.l3.C1.C3.S2 + ddq1.l3.S1.S2.S3 - 2.dq2.dq3.l3.C1.C2.C3 +2.dq1.dq2.l3.C2.S1.S3 + 2.dq1.dq2.l3.C3.S1.S2 + 2.dq1.dq3.l3.C2.S1.S3 +2.dq1.dq3.l3.C3.S1.S2 + 2.dq2.dq3.l3.C1.S2.S3ddq1.l1.C1 - dq1^2.l1.S1 - dq1^2.l2.C2.S1 - dq2^2.l2.C2.S1 + ddq1.l2.C1.C2 -ddq2.l2.S1.S2 - dq1^2.l3.C2.C3.S1 - dq2^2.l3.C2.C3.S1 - dq3^2.l3.C2.C3.S1 +dq1^2.l3.S1.S2.S3 + dq2^2.l3.S1.S2.S3 + dq3^2.l3.S1.S2.S3 - 2.dq1.dq2.l2.C1.S2 +ddq1.l3.C1.C2.C3 - ddq1.l3.C1.S2.S3 - ddq2.l3.C2.S1.S3 - ddq2.l3.C3.S1.S2 -ddq3.l3.C2.S1.S3 - ddq3.l3.C3.S1.S2 - 2.dq1.dq2.l3.C1.C2.S3 - 2.dq1.dq2.l3.C1.C3.S2
- 2.dq1.dq3.l3.C1.C2.S3 - 2.dq1.dq3.l3.C1.C3.S2 - 2.dq2.dq3.l3.C2.C3.S1 +2.dq2.dq3.l3.S1.S2.S3
dq2^2.l3.sin(q2 + q3) - ddq2.l2.C2 + dq3^2.l3.sin(q2 + q3) + dq2^2.l2.S2 -ddq2.l3.cos(q2 + q3) - ddq3.l3.cos(q2 + q3) + 2.dq2.dq3.l3.sin(q2 + q3)
-
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BI TP LN: RBT CNG NGHIP
Trang:55LP : CTK8LC1
GVHD: Trn Xun Tin
A1 =
[ C1, 0, -S1][ S1, 0, C1][ 0, -1, 0]
A2 =
[ C2, -S2, 0][ S2, C2, 0][ 0, 0, 1]
A3 =
[ C3, -S3, 0][ S3, C3, 0][ 0, 0, 1]
W10 =
[ 0, -dq1, 0][ dq1, 0, 0][ 0, 0, 0]
W21 =
[ 0, -dq2, 0][ dq2, 0, 0][ 0, 0, 0]
W32 =
[ 0, -dq3, 0][ dq3, 0, 0][ 0, 0, 0]
-
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BI TP LN: RBT CNG NGHIP
Trang:56LP : CTK8LC1
GVHD: Trn Xun Tin
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
w10 =
00
dq1
w21 =
00
dq2
w32 =
00
dq3
w1 =
00
dq1
w2 =
-dq2.S1dq2.C1dq1
w3 =
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
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BI TP LN: RBT CNG NGHIP
Trang:57LP : CTK8LC1
GVHD: Trn Xun Tin
- dq2.S1 - dq3.S1dq2.C1 + dq3.C1
dq1
a1 =
00
ddq1
a2 =
- ddq2.S1 - dq1.dq2.C1ddq2.C1 - dq1.dq2.S1ddq1
a3 =
- dq1.(dq2.C1 + dq3.C1) - ddq2.S1 - ddq3.S1ddq2.C1 - dq1.(dq2.S1 + dq3.S1) + ddq3.C1
ddq1
Xy dng v tnh ton cc phn t trong ma trn Jacobi
JT =
[ -S1.(l1 + l3.cos(q2 + q3) + l2.C2), -C1.(l3.sin(q2 + q3) + l2.S2), -l3.sin(q2 + q3).C1][ C1.(l1 + l3.cos(q2 + q3) + l2.C2), -S1.(l3.sin(q2 + q3) + l2.S2), -l3.sin(q2 + q3).S1][ 0, - l3.cos(q2 + q3) - l2.C2, -l3.cos(q2 + q3)]
JR =
[ 0, -S1, -S1][ 0, C1, C1][ 1, 0, 0]
-
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BI TP LN: RBT CNG NGHIP
Trang:58LP : CTK8LC1
GVHD: Trn Xun Tin
Jb =
[ -S1.(l1 + l3.cos(q2 + q3) + l2.C2), -C1.(l3.sin(q2 + q3) + l2.S2), -l3.sin(q2 + q3).C1][ C1.(l1 + l3.cos(q2 + q3) + l2.C2), -S1.(l3.sin(q2 + q3) + l2.S2), -l3.sin(q2 + q3).S1][ 0, - l3.cos(q2 + q3) - l2.C2, -l3.cos(q2 + q3)][ 0, -S1, -S1][ 0, C1, C1][ 1, 0, 0]
H7
Bng D-H: di ai i Khp
1 1 L1 0 90 R2
20 L2 0 R
3 3 0 L3 0 R
Vit cc ma trn H1, H2, H3
-
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BI TP LN: RBT CNG NGHIP
Trang:59LP : CTK8LC1
GVHD: Trn Xun Tin
H1 =
; H2 =
H3 =
D3 =
[
]
Vit phng trnh th hin v tr im chp hnh cui
rE=
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
vE=
[
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
60/114
BI TP LN: RBT CNG NGHIP
Trang:60LP : CTK8LC1
GVHD: Trn Xun Tin
aE=
[
A1 = ; A2 =
; A3 =
=
; =
; =
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
61/114
BI TP LN: RBT CNG NGHIP
Trang:61LP : CTK8LC1
GVHD: Trn Xun Tin
= ; =
; =
; =
; =
=
=
; =
=
Xy dng v tnh ton cc phn t trong ma trn Jacobi
JT=
[ ]
; JR =
-
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BI TP LN: RBT CNG NGHIP
Trang:62LP : CTK8LC1
GVHD: Trn Xun Tin
H8Bng D-H:
di ai i Khp1 1 L1 0 90 R2 2 0 L2 -90 R3 3 0 L3 0 R
Vit cc ma trn H1, H2, H3 :
[c1.c2.c3 - s1.s3, - c3.s1 - c1.c2.s3, -c1.s2, l2.c1.c2 - l3.s1.s3 + l3.c1.c2.c3]D3=[ c1.s3 + c2.c3.s1,c1.c3 - c2.s1.s3, -s1.s2, l2.c2.s1 + l3.c1.s3 + l3.c2.c3.s1 ]
[ c3.s2, -s2.s3, c2, l1 + l2.s2 + l3.c3.s2 ][ 0, 0, 0, 1 ]
Vit phng trnh th hin vtr im chp hnh cui
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
63/114
BI TP LN: RBT CNG NGHIP
Trang:63LP : CTK8LC1
GVHD: Trn Xun Tin
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cuivE =- .( + . ) - .( +. ) -.( . + . . ).( . - . ) - .( . + . ) +. . + . . )
.(
.
+
) -
.
.
aE =
. . . - . . . - . . . 2 + . . . - . . . - . . . - . . . - . . . - . . . . - . . + . . . . + . . . . + 2. . . . . . - .l3. . . - . . . -. . . . - . . . . - . . . . + . . . . -2. .. . . . + 2. . . . . + 2. . . . . . .+2.
.
.
.
.
.
+ 2.
.
.
.
.
.
+ 2.
.
.
.
.
.
. . - . . - . . . - . . . + . . . - . . . -. . . . - . . . . - . . . . + . . . . + . . . . + . . . . - 2. . . . . . + . . . . -. . . . - . . . . - . . . . - . . . - . . . . - 2. . . . . . - 2. . .l3. . . -2. . . . . . - 2. . . l3. . . - 2. . . . . . + 2. .. . . .
.
.
-
.l3.sin(2 + 3) -
.
.sin(2 + 3) -
.
+
.
.cos(2 + 3) +
. .cos(2 + 3) - 2. . . .sin(2 + 3)
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
64/114
BI TP LN: RBT CNG NGHIP
Trang:64LP : CTK8LC1
GVHD: Trn Xun Tin
;
;
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
; ;
; ;
;
;
Xy dng v tnh ton cc phn t trong ma trn Jacobi
JR=
[
]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
65/114
BI TP LN: RBT CNG NGHIP
Trang:65LP : CTK8LC1
GVHD: Trn Xun Tin
H9
Bng D-H:
di ai i Khp
1 1 L1 0 0 R2 2 0 L2 0 R3 3 0 L3 0 R
Vit cc ma trn H1, H2, H3
L1
L2
L3
1
2 3
z 0
x 0
z1
x1
z 2
x 2
z 3
x 3
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
66/114
BI TP LN: RBT CNG NGHIP
Trang:66LP : CTK8LC1
GVHD: Trn Xun Tin
Vit phng trnh th hin v tr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
- 2 - 2 ( )1 2 2
2 2 2 2 2- ( )- ( )- ( - )- ( )2 12 1 2 3 123 1 2 3 3 123 1 2 3 2 12 1 2
2 2 2- ( ( )- (
1 3 123 2 12 2
12 3 123 1 2 1
1 3 123 2 3 3 12 1
3
3
3 2
)
l Cl C l S l C l S
l C l S l C S a l
l C
E
2 2 ) ( )-2 -2 ( )
2 3 2 12 1 2 1 2 2 12 3 123 1 2 1 3 2 3
0
l C l S l S
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
67/114
BI TP LN: RBT CNG NGHIP
Trang:67LP : CTK8LC1
GVHD: Trn Xun Tin
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
68/114
BI TP LN: RBT CNG NGHIP
Trang:68LP : CTK8LC1
GVHD: Trn Xun Tin
Xy dng v tnh ton cc phn t trong ma trn Jacobi
[
]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
69/114
BI TP LN: RBT CNG NGHIP
Trang:69LP : CTK8LC1
GVHD: Trn Xun Tin
H10
Bng D-H:
di ai i Khp1 1 0 L1 -90 R2 2 0 L2 -90 R3 3 0 L3 0 R
Vit cc ma trn H1, H2, H3
; ;
Vit phng trnh th hin v tr im chp hnh cui
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
70/114
BI TP LN: RBT CNG NGHIP
Trang:70LP : CTK8LC1
GVHD: Trn Xun Tin
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
( )
aE =
[
.l3.C1.S3
.l1.C1 -
.l2.C12 -
.l2.C12 -
.l3.S13 -
.l3.S13 -
.l2.C2.S1 - .l2.C1.S2 - .l1.S1 + .l3.C3.S1 - ..l3.C123 - .l3.C123 - .l3.C123 + 2. . .l3.C13 + 2. . .l2.S12 - .l3.C23.S1 - .l3.C13.S2 -.l3.C12.S3 + 2. . .l3.C3.S12 + 2. . .l3.C2.S13 + 2. . .l3.C1.S23][.l1.C1 - .l1.S1 - .l2.C2.S1 - .l2.C2.S1 + .l3.C1.S3 + .l3.C1.S3 +.l2.C12 - .l3.C13 - .l2.S12 + .l3.S13 - .l3.C23.S1 - ..l3.C23.S1 - ..l3.C23.S1 - 2. . .l2.C1.S2 + 2. . .l3.C3.S1 + .l3.C123 - .l3.C3.S12 -.l3.C2.S13 - 2. . .l3.C13.S2 - 2. . .l3.C12.S3 + 2. . .l3.S123][ .l2.S2 - .l2.C2 + .l3.C3.S2 + .l3.C3.S2 - .l3.C23 + .l3.S23 +2. . .l3.C2.S3]
; ;
;
;
;
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
; ;
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
71/114
BI TP LN: RBT CNG NGHIP
Trang:71LP : CTK8LC1
GVHD: Trn Xun Tin
;
;
;
; - .( .C1 - .S12) - .S1 - .C1.S2 - ..C12 ][ .C1 - .( .S1 + .C1.S2) - .S12 - ..C2.S1][ - .C2 + ..S2 ]
Xy dng v tnh ton cc phn t trong ma trn Jacobi
[
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
72/114
BI TP LN: RBT CNG NGHIP
Trang:72LP : CTK8LC1
GVHD: Trn Xun Tin
H11 di ai i Khp
1 1 0 0 -90 R2 -90 L1 L2 -90 P3 3 0 L3 0 R
Bng D-H:
Vit cc ma trn H1, H2, H3
L1
L2
L3
x0
z1
x1
z0
Z2
X2
Z3
X3
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
73/114
BI TP LN: RBT CNG NGHIP
Trang:73LP : CTK8LC1
GVHD: Trn Xun Tin
Vit phng trnh th hin v tr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
aE =. - . - . - 2. . . - . - . +. + . + 2. . . . - 2. . . - . - . + . + . - . + . + 2. . .
.(
.
+
.
)
; ;
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
74/114
BI TP LN: RBT CNG NGHIP
Trang:74LP : CTK8LC1
GVHD: Trn Xun Tin
;
;
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
; ;
; ;
;
;
;
;
Xy dng v tnh ton cc phn t trong ma trn Jacobi
; JR=
[
]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
75/114
BI TP LN: RBT CNG NGHIP
Trang:75LP : CTK8LC1
GVHD: Trn Xun Tin
l1
l3
1
3
o2
o1
o0
o3
Z2
Z3
X3
Z1
Z0
X0
X1X2
Z1
l2
H12
Bng D-H:
di ai i Khp1 1 0 0 0 R2 L1 L2 -90 P3 3 0 L3 0 R
Vit cc ma trn H1, H2, H3
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
76/114
BI TP LN: RBT CNG NGHIP
Trang:76LP : CTK8LC1
GVHD: Trn Xun Tin
Vit phng trnh th hin v tr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
[
1 3
1 3
1l 3
]
aE =
1 .l2.C1 -2
1
.l2.S1 -
2
1
.l3.C3.S1 -
2
3
.l3.C3.S1 + 1 .l3.C1.C3 -
3
.l3.S13 - 2. 1 .
3 .l3.C1.S3
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
77/114
BI TP LN: RBT CNG NGHIP
Trang:77LP : CTK8LC1
GVHD: Trn Xun Tin
1 .l2.S1 +2
1
.l2.C1 +
2
1
.l3.C1.C3 +
2
3
.l3.C13 + 1 .l3.C3.S1 +
3
.l3.C1.S3 - 2. 1 .
3 .l3.S13. l3.S3.2
3
+ 1l - 3 .l3.C3
A3 =
=
Vitbiu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
78/114
BI TP LN: RBT CNG NGHIP
Trang:78LP : CTK8LC1
GVHD: Trn Xun Tin
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
79/114
BI TP LN: RBT CNG NGHIP
Trang:79LP : CTK8LC1
GVHD: Trn Xun Tin
1
Xy dng v tnh ton cc phn t trong ma trn Jacobi
;
[
]
H13Bng D-H:
di ai i Khp1 1 0 L1 0 R2 L2 0 90 P3 3 0 L3 0 R
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
80/114
BI TP LN: RBT CNG NGHIP
Trang:80LP : CTK8LC1
GVHD: Trn Xun Tin
Vit cc ma trn H1, H2, H3
;
;
Vit phng trnh thhin v tr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
aE =
. - . - . + . - . + + . +2. . . . - . - . - . - . - . +2. . . . . . + .
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
81/114
BI TP LN: RBT CNG NGHIP
Trang:81LP : CTK8LC1
GVHD: Trn Xun Tin
;
;
; ;
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
;
;
; ;
;
;
Xy dng v tnh ton cc phn t trong ma trn Jacobi
; JR=
[
]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
82/114
BI TP LN: RBT CNG NGHIP
Trang:82LP : CTK8LC1
GVHD: Trn Xun Tin
H14
Bng D-H: di ai i Khp
1 1 0 L1 0 R2 2 0 0 -90 R3 L2 L3 0 P
Vit cc ma trn H1, H2, H3:
Vit phng trnh th hin v tr im chp hnh cui:
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
83/114
BI TP LN: RBT CNG NGHIP
Trang:83LP : CTK8LC1
GVHD: Trn Xun Tin
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui:
aE =[ - - - - + - -2 -2 - - - - - 2 - 2 ][ + - - - - - + +
- 2
- 2
-
-
- 2
- 2
]
[ 0 ]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
84/114
BI TP LN: RBT CNG NGHIP
Trang:84LP : CTK8LC1
GVHD: Trn Xun Tin
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu:
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
85/114
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
86/114
BI TP LN: RBT CNG NGHIP
Trang:86LP : CTK8LC1
GVHD: Trn Xun Tin
S khp n = 3
i 1 2 3 4 5pi 0 0 0 0 3
Vy s bc t do ca tay my l:ADCT:
5
1
.6i
ipinw
Trong : w s bc t do ca tay myns khp ca tay my.pis khp loi i (i 1,2,,5 s khp hay s bc t do b hn ch )
Thay s: 33.53.6 w (bc t do)
Xy dng cc h ta cho cc khu
Lp bng DH:
di ai i Khp1 1 0 0 -90 R2 l1 l2 0 P3 3 0 l3 0 R
Vt cc a trnH1, H2, H3
X0, X1
Z1
X2
Z2
Z0
L
1
L2 L3
Z3
X3
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
87/114
BI TP LN: RBT CNG NGHIP
Trang:87LP : CTK8LC1
GVHD: Trn Xun Tin
=
Vt phn trnh th hn v tr chp hnh cu
Vt bu thc vn tc a tc tuyt ca chp hnh cu
aE =[ l1 - l1 - l2 - l2 - 2 - l3 - l3 -
l3
-
l3
+ 2
]
[
+
l2
- 2
-
l1
-
l1
-
l2
-
l3
-
l3
+
l3 - l3 - 2 2l3 ][l3( - )]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
88/114
BI TP LN: RBT CNG NGHIP
Trang:88LP : CTK8LC1
GVHD: Trn Xun Tin
Vt bu thc vn tc c a tc c a phn v tuyt ca tn hu
ng hc ngc:
Xy dn v tnh tn cc phn t trn a trn Jacb
JR=
[
]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
89/114
BI TP LN: RBT CNG NGHIP
Trang:89LP : CTK8LC1
GVHD: Trn Xun Tin
H16Bng D-H:
di ai i Khp1 1 0 L1 -90 R2 2 0 0 90 R3 L2+L3 0 0 P
Vit cc ma trn H1, H2, H3
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
90/114
BI TP LN: RBT CNG NGHIP
Trang:90LP : CTK8LC1
GVHD: Trn Xun Tin
Vit phng trnh th hin v tr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
( ) aE =
.( . - . ) - .( + ) - .( .( + )+ . + . ) - .( . . - . + . . )+
.
+
.
)
.( . + . - . . )) + .( + ) + .( . + . ) + .( . - .( + . )) + . . .( +)) + . + . . - .( . + . )) - . . - .
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
91/114
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
92/114
BI TP LN: RBT CNG NGHIP
Trang:92LP : CTK8LC1
GVHD: Trn Xun Tin
Xy dng v tnh ton cc phn t trong ma trn Jacobi
JR=
[
]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
93/114
BI TP LN: RBT CNG NGHIP
Trang:93LP : CTK8LC1
GVHD: Trn Xun Tin
H17
Bng D-H:
di ai i Khp1 L1 0 -90 P2 L2 0 90 R3 3 0 L3 0 R
Vit cc ma trn H1, H2, H3
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
94/114
BI TP LN: RBT CNG NGHIP
Trang:94LP : CTK8LC1
GVHD: Trn Xun Tin
Vit phng trnh th hin vtr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
95/114
BI TP LN: RBT CNG NGHIP
Trang:95LP : CTK8LC1
GVHD: Trn Xun Tin
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
96/114
BI TP LN: RBT CNG NGHIP
Trang:96LP : CTK8LC1
GVHD: Trn Xun Tin
Xy dng v tnh ton cc phn t trong ma trn Jacobi
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
97/114
BI TP LN: RBT CNG NGHIP
Trang:97LP : CTK8LC1
GVHD: Trn Xun Tin
[
]
H18
Bng D-H:
di ai i Khp1 1 L1 0 -90 R2 L2 0 90 P
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
98/114
BI TP LN: RBT CNG NGHIP
Trang:98LP : CTK8LC1
GVHD: Trn Xun Tin
3 3 0 L3 0 R
Vit cc ma trn H1, H2, H3
H1 = ; H2 = ; H3 =
D3 =
[
]
Vit phng trnh th hin v tr im chp hnh cui
rE = Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
vE= l l
aE=
[
l
l
l l
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
99/114
BI TP LN: RBT CNG NGHIP
Trang:99LP : CTK8LC1
GVHD: Trn Xun Tin
A1 =
; A2 =
; A3 =
= ; = ; =
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
=
;
=
;
=
;
= ; =
; =
=
;
=
;
=
Xy dng v tnh ton cc phn t trong ma trn Jacobi
JT = JR =
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
100/114
BI TP LN: RBT CNG NGHIP
Trang:100LP : CTK8LC1
GVHD: Trn Xun Tin
Jb =
[
]
H19
di ai i Khp1 1 0 0 0 R2
L1 L2 0 P
3 3 0 L3 0 R
Bng D-H:
[ q1, 0, 0, 0]DH= [ 0, l1, l2, 0]
[ q3, 0, l3, 0]
Vit cc ma trn H1, H2, H3
[ c1, -s1, 0, 0]H1= [ s1, c1, 0, 0]
[ 0, 0, 1, 0][ 0, 0, 0, 1]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
101/114
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
102/114
BI TP LN: RBT CNG NGHIP
Trang:102LP : CTK8LC1
GVHD: Trn Xun Tin
0
A1 =
[ C1, -S1, 0][ S1, C1, 0][ 0, 0, 1]
A2 =
[ 1, 0, 0][ 0, 1, 0][ 0, 0, 1]
A3 =
[ C3, -S3, 0][ S3, C3, 0][ 0, 0, 1]
W10 =
[ 0, -dq1, 0][ dq1, 0, 0][ 0, 0, 0]
W21 =
[ 0, 0, 0][ 0, 0, 0]
[ 0, 0, 0]
W32 =
[ 0, -dq3, 0][ dq3, 0, 0]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
103/114
BI TP LN: RBT CNG NGHIP
Trang:103LP : CTK8LC1
GVHD: Trn Xun Tin
[ 0, 0, 0]
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
w10 =
00
dq1
w21 =
0
00
w32 =
00
dq3
w1 =
00
dq1
w2 =
00
dq1
w3 =
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
104/114
BI TP LN: RBT CNG NGHIP
Trang:104LP : CTK8LC1
GVHD: Trn Xun Tin
00
dq1 + dq3
a1 =
00
ddq1
a2 =
00
ddq1
a3 =
00
ddq1 + ddq3
Xy dng v tnh ton cc phn t trong ma trn Jacobi
JT =
[ - l3.sin(q1 + q3) - l2.S1, C1, -l3.sin(q1 + q3)][ l3.cos(q1 + q3) + l2.C1, S1, l3.cos(q1 + q3)][ 0, 0, 0]
JR =
[ 0, 0, 0][ 0, 0, 0][ 1, 0, 1]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
105/114
BI TP LN: RBT CNG NGHIP
Trang:105LP : CTK8LC1
GVHD: Trn Xun Tin
Jb =
[ - l3.sin(q1 + q3) - l2.S1, C1, -l3.sin(q1 + q3)][ l3.cos(q1 + q3) + l2.C1, S1, l3.cos(q1 + q3)][ 0, 0, 0][ 0, 0, 0][ 0, 0, 0][ 1, 0, 1]
H20
Bng D-H:
di ai i Khp
1 L0 L1 -90 P2 2 0 L2 -90 R3 3 0 L3 0 RVit cc ma trn H1, H2, H3
L0
L1
L2
L3
2 3
z 0
x 0
z1
x1z 2
x 2
z 3
x 3
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
106/114
BI TP LN: RBT CNG NGHIP
Trang:106LP : CTK8LC1
GVHD: Trn Xun Tin
Vit phng trnh th hin vtr im chp hnh cui
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
( )
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
107/114
BI TP LN: RBT CNG NGHIP
Trang:107LP : CTK8LC1
GVHD: Trn Xun Tin
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
108/114
BI TP LN: RBT CNG NGHIP
Trang:108LP : CTK8LC1
GVHD: Trn Xun Tin
;
;
;
; ;
Xy dng v tnh ton cc phn t trong ma trn Jacobi
;
[
]
-
7/31/2019 De Cuong Thi Robot Cong Nghiep
109/114
BI TP LN: RBT CNG NGHIP
Trang:109LP : CTK8LC1
GVHD: Trn Xun Tin
H1
di ai i Khp1 1 0 l1 0 R2 2 0 l2 -90 R3 3 0 l3 0 R
Bng D-H:
DH =
[ q1, 0, l1, 0][ q2, 0, l2, -/2][ q3, 0, l3, 0]
Vit cc ma trn H1, H2, H3
H1 =
[ C1, -S1, 0, l1.C1][ S1, C1, 0, l1.S1][ 0, 0, 1, 0][ 0, 0, 0,
H2 =[ C2, 0, -S2, l2.C2][ S2, 0, C2, l2.S2][ 0, -1, 0, 0][ 0, 0, 0, 1]
H3 =
[ C3, -S3, 0, l3.C3][ S3, C3, 0, l3.S3][ 0, 0, 1, 0][ 0, 0, 0, 1]
D3 =
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[ C3.(C1.C2 - S1.S2), -S3.(C1.C2 - S1.S2), - C1.S2 - C2.S1, l1.C1 + l3.C3.(C1.C2 -S1.S2) + l2.C1.C2 - l2.S1.S2][ C3.(C1.S2 + C2.S1), -S3.(C1.S2 + C2.S1), C1.C2 - S1.S2, l1.S1 + l3.C3.(C1.S2 +C2.S1) + l2.C1.S2 + l2.C2.S1][ -S3, -C3, 0,-l3.S3][ 0, 0, 0,1]
Vit phng trnh th hin v tr im chp hnh cui
rE =
l1.C1 + l3.C3.(C1.C2 - S1.S2) + l2.C1.C2 - l2.S1.S2l1.S1 + l3.C3.(C1.S2 + C2.S1) + l2.C1.S2 + l2.C2.S1-l3.S3
Vit biu thc vn tc, gia tc tuyt i ca im chp hnh cui
vE =2
1
- 1 .(l2.S12 + l1.S1 + l3.S12.C3) -
2 .(l2.S12 + l3.S12.C3) -
3 .l3.C12.S3
1 .(l2.C12 + l1.C1 + l3.C12.C3) + 2 .(l2.C12 + l3.C12.C3) -
3 .l3.S12.S3.
3
- .l3.C3
aE =
( 3
.l3.s(q1 + q2 - q3))/2 - (2
2
.l3.c(q1 + q2 - q3))/2 - (
2
3
.l3.c(q1 + q2 - q3))/2 -
1 .l1.S1 -
2
1
.l2.C12 -
2
2
.l2.C12 - ( 1 .l3.S123)/2 - (
2 .l3.S123)/2 - (
3
.l3.S123)/2 -2
1
.l1.C1 - (
2
1
.l3.C123)/2 - (
2
2
.l3.C123)/2 - (
2
3
.l3.C123)/2 - (
1 .l3.sin(q1 + q2 - q3))/2 - (
2 .l3.sin(q1 + q2 - q3))/2 - (
2
1
.l3.cos(q1 + q2 -
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q3))/2 - 1 .l2.S12 -
2 .l2.S12 -
1 .
2 .l3.cos(q1 + q2 - q3) +
1 .
3
.l3.cos(q1 + q2 - q3) + 3 .
2 .l3.cos(q1 + q2 - q3) - 2.
1
. 2 .l2.C12 -
1
. 2 .l3.C123 -
1 .
3 .l3.C123 -
3 .
2 .l3.C123
1
.l1.C1 - (2
1
.l3.sin(q1 + q2 - q3))/2 - (
2
2
.l3.sin(q1 + q2 - q3))/2 - (
2
3
.l3.sin(q1 + q2 - q3))/2 -2
1
.l2.S12 -
2
2
.l2.S12 + ( 1 .l3.C123)/2 + (
2
.l3.C123)/2 + ( 3
.l3.C123)/2 -2
1
.l1.S1 + ( 1 .l3.cos(q1 + q2 - q3))/2 + (
2 .l3.cos(q1 + q2 - q3))/2 - (
3 .l3.cos(q1 + q2 - q3))/2 - (
2
1
.l3.S123)/2 - (
2
2
.l3.S123)/2 - (
2
3
.l3.S123)/2 + 1 .l2.C12 +
2 .l2.C12 -
1
. 2
.l3.sin(q1 + q2 - q3) + 1 .
3 .l3.sin(q1 + q2 - q3) +
3 .
2 .l3.sin(q1 + q2 -
q3) - 2. 1 .
2 .l2.S12 -
1 .
2 .l3.S123 -
1 .
3 .l3.S123 -
3 .
2 .l3.S123
l3.( 23
.S3 - 3 .C3)
A1 =
[ C1, -S1, 0][ S1, C1, 0][ 0, 0, 1]
A2 =
[ C2, 0, -S2][ S2, 0, C2][ 0, -1, 0]
A3 =
[ C3, -S3, 0][ S3, C3, 0][ 0, 0, 1]
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W10 =
[ 0, - 1 , 0]
[ 1 , 0, 0]
[ 0, 0, 0]
W21 =
[ 0, - 2 , 0]
[ 2 , 0, 0][ 0, 0, 0]
W32 =
[ 0, - 3 , 0]
[ 3 , 0, 0]
[ 0, 0, 0]
Vit biu thc vn tc gc, gia tc gc a phng v tuyt i ca tng khu
w10 =
00
1
w21 =
00
2
w32 =
0
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GVHD: Trn Xun Tin
0
3
w1 =
00
1
w2 =
00
1 +
2
w3 =
- 3 .(C1.S2 + C2.S1)
3 .(C1.C2 - S1.S2)
1 + 2
a1 =
00
1
a2 =
00
-
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1 +
2
a3 =
-
3 .S12 -
1 +
3
.C12 - 2 +
3 .C12
3 .C12 -
1 +
3
.S12 - 2 +
3 .S12
1 +
2
Xy dng v tnh ton cc phn t trong ma trn Jacobi
JT =
[ - l2.S12 - l1.S1 - l3.S12.C3, -S12.(l2 + l3.C3), -l3.C12.S3][ l2.C12 + l1.C1 + l3.C12.C3, C12.(l2 + l3.C3), -l3.S12.S3][ 0, 0, -l3.C3]
JR =
[ 0, 0, -S12][ 0, 0, C12][ 1 1 0]