robotics file
TRANSCRIPT
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ROBOTICS & OBJECTTRACKING
LABORATORY
Delhi Technological Universi!
"III Se#eser
De$% o Elecronics &Co##'nicaion Engg%
Un(er he G'i(ance o K'#ar
)a!an*
Na#e+ SAURAB,GU-TA
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RollNo%+.K//0EC0/12
Bach+ECE 3D.4
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INDEX
S.No.
/%
.%
5%
1
%
6%
7%
8%
9%
:%
/2%
NameofExperiment
To
s'(!vario's
s$aial(escri$
ionsan(
ransor#a
ions'sing-eer
Cor*eool
;o.2/65
/5>2.>.2/6:
/:>2.>.2/6/6
.2
>25>.
2/6.2
.8>25>.2/6.6
/8>21>.2/6.:
/
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8>21>
.2/651
2/>26>.
2/659
2/>
26>.2
/66:
2/
>26>.
2/677
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Attendance(Out of 10classes)
Internal Assessment
Marks
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?e;r'ar! 7@ .2/6 SAUA!" #U$%A (&'11E1*0)
E-ERI)ENT /
Aim(a)(i) +To s'(! vario's s$aial(escri$ionsan( ransor#aions'sing -eer Cor*e ool;o< in
)ala;%
T/ se./@ .@ 52$i0/92F se.+
Creae $lanar ranslaionan(
roaion ransor#aionHHT/
2%9772 >2%6222 /%2222
2%6222 2%9772 .%2222
0 2 /%2222
2>T. se..@ /@ 2F
T.
/ 2 .
2 / /
2 2 /
H
H
T
5
T
/
T
.
T
5
2%9772 >2%6222 .%.5./
2%6222 2%9772 5%9772
0 2 /%2222
2>T1 T.T/
T1
2%9772 >2%6222 5%2222
2%6222 2%9772 5%2222
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?e;r'ar! 7@ .2/6 SAUA!" #U$%A (&'11E1*0)
2 2 /%2222
As =e can see@ T5 an( T1#arices
are no e'al% ,ence =e can sa!
ha ho#ogeno's ransor#s are
no co##'aive%
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Aim(a)(ii)+ Using aY @
convenion@=rie
)ala; $rogra# he roaion
#ari< ARB=hen he 'ser enersE'ler
% /2@ .2@
% Also (e#onsrae heinverse
$ro$er! o roaional#ari
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?e;r'ar! 7@ .2/6 SAUA!" #U$%A (&'11E1*0)
mult =
0-.1 0-1!1 0-!!8
0-!!. 0-..1! 0-030-232 0-1.10 0-3!3.
"rp =
0-.1 0-1!1 0-!!8
0-!!. 0-..1! 0-030-232 0-1.10 0-3!3.
0 0 0
Aim(a)(iii)+ Mrie a )ala; $rogra# o calc'lae@ he
E'ler anglesroaion #ari< i%e%ARB
ang = tr2eul("rp) % alulates rotation angles rom transormation matr
ang/dr % onvert angles ba4 to degree
10-0000 20-0000 !0-0000
Aim(a)(i,)+ ?or a si#$le roaion o angle .2@ an(
beta1 = input('enter beta in degree'
5b = input('enter 5b olumn 6ise'" = rot(beta1*dr); % get rotation matri or rotation along & ais
5a = "*(5b) % get oordinates 6-r-t- 7 rame
ener ;ea in (egrees .2
ener -;col'#n =ise /2/P
-a
/%5./2
2
>2%621:
Aim(-)(i)+ Mrie o calc'lae he
ho#ogeno's ransor#aion ATB@=hen he 'ser eners
Y E'lar angles he $osiion vecorA$B% E%g% /2@ .2@ 52@
A$B/ .
5P
dr = pi/180;
ang =input('enteralpha, betaand gamma indegrees');alpha =ang(1)*dr;
b
e
t
a
=
a
n
g
(
2
)
*
d
r
;
ga
m
m
a
=
a
n
g
(
!
)
*
d
r
;
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?e;r'ar! 7@ .2/6 SAUA!" #U$%A (&'11E1*0)
"rp1 = rp2tr(gamma,beta,alpha);
%get transormation matri or
&$ rotation
"trn = transl(1,2,!); % transl 9reate
" = transl(,
transorm ()representing
"ba = "trn*"rp1; % inal transormation matriand translational omponents
nter alpha beta and gamma in
degrees +10 20 !0
Trn
/ 2 2 /2 / 2 .2 2 / 5
2 2 2 /
Tr$!/
2%:.61
>2%/75. 2%51.2 2
2%5/992%9.5. >2%17:9 2
>2%.21: 2%6159 2%9/59 2
2 2 2 /%2222
T;a 2%:.61 >2%/75. 2%51.2 /%2222
2%5/992%9.5.
>2%17:9 .%2222
>2%.21:2%61592%9/59 5%2222
2 2 2 /%
Aim(-)(ii)+ ?or.2@
A$B 5 2 /PT an(
5b = input('enter 5b olumn 6ise'
Trn/ ransl5@2@/FT;a/ [email protected](r@2F
ge ransor#aion #ari< or he given
T;a. Trn/T;a/ge ranslaional #ari< having ranslaional
5a = "ba*+5b;1;
Ener -; col'#n =ise /2/PTrn/
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/ 2 2 52 / 2 22 2 / /
2 2 2 /
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?e;r'ar! 7@ .2/6 SAUA!" #U$%A (&'11E1*0)
T;a.
2%:5:8 2
2%51.
2
5%222
22 /%2222 2 2
>2%51.2 22%:5:8/%222
22 2 2 /%2222
-a
1%.9/82
/%6:88/%2222
Aim(-)(iii)+ Mrie a)ala;$rogra# o calc'lae heinverse ho#ogeneo'sransor#aion #ari< i%e%
ATBF>/ BTA% Also sho= ha
ATB%
ATBF>/ I1
T;aQinv invDT;a.FO inv calc'laes )ari< inversee!e1F >
T;aQinvT;a. e!eDNF is he N>;!>N i(eni!#ari/6E2%///2 2 2 2
2 2 2 22%2666 2 2 2
2 2 2 2e!e1F >
T;a.T;aQinvans
/%2e>/6
E2%///2 2 >2%2666 2
2 2 2 2
2 2 2>
2%///2
2 2 2 2
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Aim(-)(i,)+ Mriea)ala; o calc'lae
ATCan(CTA@ given
ha ATBan(BTCare
o;aine(
$ar% BTC
.2@
Dene ATBo ;e he res'l
ro#
/2 .2 52P@ A$B / . BTCas
.2 2P@ B$C52 /P
aTc T;aT;a.
ATCATB
BTC
aTc
2%86.7>
2%/75. 2%758:1%//95
2%1725 2%9.5.>2%55.6.%1976
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?e;r'ar! 7@ .2/6 SAUA!" #U$%A (&'11E1*0)
>2%182: 2%61592%7:17 5%/::.
2 2 2 /%2222
aTcQinv invaTcFaTcQinv
2%86.72%1725
>2%182:>.%8588
>2%/75. 2%9.5.2%6159>5%//18
2%758:>
2%55.62%7:17>1%2..8
2 2 2 /%2222
esult+ ,ence he ;asic relae( o
ho#ogeno's ransor#aion #ari< or;oh E'lerian an( Car(anian!$e
roaion =ere s'ccess'll! s'(ie(
along =ih is $ro$eries%
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?e;r'ar! /5@ .2/6 SAUA!" #U$%A (&'11E1*0)
Eeecorgiven he val'es or he oin varia;les o he ro;o%
HHL Lin*2@ 2%/@ 2%.@ $i0.@ 2PF A Lin* o;ec hol(s all inor#aion relae( o aro;o lin*
L hea@
(
2%/@
a
2%.@
al$ha
/%68/
R@s(D,FHHL%A2%6F
o;ain ransor#aion #ari< or hea 2%6ra(
ans 2%9887 >2%2222 2%18:1
2%/866
2%18:12%2222
>2%988
7 2%2:6:
2/%222
22%2222 2%/222
2 2 2 /%2222
HHL%R-
ges !$e ooin HH L%a ges lin* lengh
ans ans
R 2%.222HH L%ose 2%6 s$eci! hea in a(vance i%e% 2%6 ra(HHL%A2F ge ransor#aion #ari< no=
ans $ro('ces sa#e #ari< as a;ove as lin* oSse =ass$ecie( iniiail!2%9887 >2%2222 2%18:1
2%/866
2%18:12%2222
>2%988
7 2%2:6:
2/%222
22%2222 2%/222
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2 2 2/%222
2
LD/F Lin*D2 2/ 2PF
creae L/F Lin*o;ec
L hea@( 2@ a
/@al$ha 2 R@s(D,F
HH L.F Lin*2 2/ 2PF creae L.FLin*o;ec
?e;r'ar! /[email protected]/6
SAUA!" #U$%A(&'11E1*0)
L hea/@( 2@ a
/@al$ha 2 R@s(D,F
hea.@( 2@ a
/@al$ha 2 R@s(D,F
HH =oQlin* SerialLin*L@ na#e@ =o lin*F Serial>lin* ro;o class
re$resens a serial>lin* ar#>!$e ro;o%
=oQlin*
=o lin* . a>>V >>>>>>>>>>>V >>>>>>>>>>>V >>>>>>>>>>>V>>>>>>>>>>>V
W W hea W ( W a Wal$ha WV>>> V>>>>>>>>>>> V>>>>>>>>>>> V>>>>>>>>>>> V>>>>>>>>>>> VW /W /W 2W /W 2WW .W .W 2W /W 2WV>>> V>>>>>>>>>>> V>>>>>>>>>>> V>>>>>>>>>>> V>>>>>>>>>>> V
grav2 ;ase / 2 2 2 ool / 2 2
2 grav s$ecies ha gravi! =ill ;e a$$lie( inX (irecion
2 2 / 2 2 2 / 2 2 ;ase s$ecies he iniial $osiion o ro;o:%9/ 2 2 / 2 2 2 / 2 ool s$ecies he en( eecor (irecion
2 2 2 / 2 2 2 /
HH #(lQ=olin* scri$ o (irecl! $ro('ce a =o lin* ro;o
=olin*
=o lin* . a
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W
V>>>V>>>>>>>>>>>
V>>>>>>>>>>> V>>>>>>>>>>> V>>>>>>>>>>> V
W /W /W 2W /W2W
W .W .W 2W /W2W
V>>>V>>>>>>>>>>>
V>>>>>>>>>>> V>>>>>>>>>>> V>>>>>>>>>>> V
grav 2 ;ase / 2 2 2 ool / 2
2 22 2 / 2 2 2 /22
:%9/ 2 2 / 2 2 2 / 2
222
/ 2 2 2 /HH=olin*%*ine22PF
&*ine gives he $ose D1eSecoras a
ho#ogeneo'sransor#aion
ans
/ 2 2 .
?e;r'ar! /[email protected]/6
SAUA!" #U$%A(&'11E1*0)
2 / 2 22 2 / 2
2 2 2 /HH =olin*%*ine$i01>$i01PFans
/%2222 2 2
/%828
/
2 /%2222 22%828
/2 2 /%2222 2
0 2 2 /%2222
2% $lo (is$la!s he ro;o orienaion in 5D
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HH=olin*%$lo2 2PF HH =olin*%$lo$i01 $i01PF
ro;o =ih one revol'e an( one $ris#aic oin
L/F Lin*2 2 / 2 2PF
L.F Lin*2 2 / 2 /PF
Lin*ing SerialLin*L@3na#e4@ 3#!ro;o4F
Lin*ing%$lo2 /PF
HH#(lQ$'#a672
HH$672%$loXF HH $672%$lorF
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?e;r'ar! /[email protected]/6
SAUA!" #U$%A(&'11E1*0)
HH $672%$losF HH$672%$lonF
ode+
Mrie (o=n a )ala; $rogra# or he $lanar 5 DO? RRR ro;o =ih he ollo=ing
$ara#eers
L/ 1#@ L.5#@L5 .#
To (erive heor=ar( *ine#aics i%e% 2T5@ =ih he ollo=ing in$' cases+
(1) 2 2 2PT
(2) /2 .2 52PT
(3) :2 :2 :2PT
1>B/F Lin*2 2 1 2PF
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2>B.F Lin*2 2 5 2PF
3>B5F Lin*2 2
. 2PF B
?e;r'ar! /[email protected]/6
SAUA!" #U$%A(&'11E1*0)
hea/@( 2@ a
1@al$ha 2 R@s(D,F
hea.@( 2@ a
5@al$ha 2 R@s(D,F
hea5@( 2@ a
.@al$ha 2 R@s(D,F
HH sa'ra;h SerialLin*B@ na#e@ #!BoF
sa'ra;h
#!Bo5 a>>V>>>>>>>>>>> V>>>>>>>>>>>V
>>>>>>>>>>> V>>>>>>>>>>> VW Whea W ( W a W al$ha W
V>>> V>>>>>>>>>>>
V>>>>>>
>>>>>
V>>>>>>>>>>> V>>>>>>>>>>> V
W /W /W 2W 1W 2WW .W .W 2W 5W 2WW 5W 5W 2W .W 2W
V>>> V>>>>>>>>>>>
V>>>
>>>>>>>>
V>>>>>>>>>>> V>>>>>>>>>>> V
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grav 2 ;ase / 2 2 2 ool / 22 2
2 2 / 2 2 2 /22:%9
/ 2 2 / 2 2 2 / 2222
/ 2 2 2 /
1>(r $i0/92
2>/ 2 2 2P(r
3>. /2 .2 52P(r
4>5 :2 :2:2P(r
T52Q/ sa'ra;h%*ine/F
T52Q/
/ 2 2 :2 / 2 22 2 / 2
2 2 2 /
HH T52Q. sa'ra;h%*ine.F
T52Q.
2%6222 >2%9772 2
8%658
5
2%9772 2%6222 25%:.77
2 2 /%2222 20 2 2 /%2222
2>T52Q5 sa'ra;h%*ine5F
?e;r'ar! /[email protected]/6
SAUA!" #U$%A(&'11E1*0)
T52Q5
>2%2222 /%2222 2
>
5%2222
>/%2222>2%2222 2
.%2222
2 2 /%2222 2
2 2 2 /%2222HHsa'ra;h%$lo2 2 2P@ =or*s$ace@ >6 6 HHsa'ra;h%$lo/2(r@ .2(r@ 52(rP@
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>6 6 >6 6 >6 6PF =or*s$ace@ >6 6 >6 6PF
HHsa'ra;h%$lo:2(r@ :2(r@ :2(rP@ =or*s$ace@ >6 6 >6 6 >6 6PF
esult+ ,ence he ro;o si#'laion in )ala; =as s'ccess'll! $eror#e( or
(ieren !$es o ro;os in(ieren cong'raions%
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2>i
$672%i*ine7sT@ l'F
i
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?e;r'ar! .2@ .2/6 SAUA!" #U$%A (&'11E1*0)
>2%2222 2%8961 5%/1/7 5%/1/7 >2%8961 >5%/1/7
$672%$loiF
HH i $672%i*ine7sT@ r'F
i
.%7197 >.%529/ 5%/1/7 >.%1785 >2%9721 >2%1926
1>$672%$loiF
2>$672%i*ine7s ransl5@
2@ 2F F ans
NaN NaN NaN NaN NaN NaN sho=s ha he $oin is 'nreacha;le
HH i $672%i*ineTF i*ine gives he oin coor(inaes corres$on(ing o hero;o en(>eecor =ih
$ose T
i
>2%2222 >2%9556 2%2:12 >2%2222 >2%95/. >2%2222
HH $672%*ineiF
ans
2%2222 2%2222 /%22222%6:75 >2%2222 /%2222>2%2222 >2%/62/ >/%2222>2%2222 2%2222 >2%2/11
0 2 2 /%2222
2>$672%$loiF
i $672%i*ineT@ 2 2 5 2 2 2P here 2 2 5 2 2 2P gives he iniial esi#ae oro;o
i
>2%2222 2%8961 5%/1/7 2%2222 2%8961 >2%2222
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HH$672%$loiF
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?e;r'ar! .2@ .2/6 SAUA!" #U$%A (&'11E1*0)
ode+
Mrie (o=n a )ala; $rogra# o solve $lanar RRR ro;o inverse *ine#aics
$ro;le# having he lengh $ara#eers L/1#@ L.5#@ L5.#%
?or he ollo=ing relaive $ose
aF 2T, / 2 2 : 2 / 2 2 2 2 / 2 2 2 2 /P
;F 2T, 2%6 >2%977 2 8%6585 2%977 2%7 2 5%:.77 2 2 / 2 2 2 2 /P
cF 2T, 2 / 2 >5 >/ 2 2 . 2 2 / 2 2 2 2 /P
(F 2T, 2%977 2%6 2 >5%/.16 >2%6 2%977 2 :%/781 2 2 / 2 2 2 2 /P
aF T,2
/ 2 2 :
2 / 2 22 2 / 22 2 2 /
(r $i0/92/
sa'ra;h%i*ineT,2@ 2 2 2P@ / / 2 2 2/PF
/
2 2 2/
sa'ra;h%i*ineDT,2@ :2 >:2 :2PE(r@ // 2 2 2 /PF
/
/%2e>25
2%/:51 >2%16/. 2%.689
sa'ra;h%$lo/@ =or*s$ace@ >9 9 >9 9 >9 9PF
HHsa'ra;h%*ine/F ans
/%2222>
2%2222 2:%222
2
2%2222 /%2222 22%2222
2 2 /%2222 20 2 2 /%2222
(2)T,/ 2%6 >2%977 2 8%6585 2%977 2%7 2 5%:.77 2
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2 / 2 2 2 2 /P T,/
2%6222>
2%9772 28%658
5
2%9772 2%7222 25%:.77
2 2 /%2222 20 2 2 /%2222
2>/ sa'ra;h%i*ineT,/@ 2 2 2P@ / / 2 2 2 /PF
#ari< no orhonor#al roaion #ari2%2977 /%//22 2
0 2 /%2222
(3) T,. 2 / 2 >5 >/ 2 2 .
2 2 / 2 2 2 2 /P T,.
2 / 2 >5>/ 2 2 .2 2 / 22 2 2 /
HH . sa'ra;h%i*ineT,.@ 2 2 2P@ / /2 2 2 /PF
.
sa'ra;h%i*ineDT,.@ :2 >:2 :2PE(r@ // 2 2 2 /PF
. .
/%6829 /%6829 /%6829 .%9689 >/%6829 >.%9689
HH sa'ra;h%$lo.F HH sa'ra;h%$lo.F
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T,5
2%9772 2%6222 2
>5%/.1
6
>2%6222 2%9772 2:%/78
12 2 /%2222 2
0 2 2 /%2222
2>5 sa'ra;h%i*ineT,5@ 2 2 2P(r@/ / 2 2 2 /PF 5
/%796. /%771:.%12:6sa'ra;h%*ine5Fans
2%9772 2%6222 2 >/%76:7
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?e;r'ar! [email protected]/6
SAUA!" #U$%A(&'11E1*0)
>2%62222%9772
2.%56.:
2 2 /%2222 2
2 2 2 /%2222
5 sa'ra;h%i*ineDT,5@ :2 >:2 :2PE(r@ / /
2 2 2 /PF or (ieren iniial esi#ae
5
/%2eV21 >.%7817 7%1:5. >5%829/
HH sa'ra;h%*ine5F
ans
2%987:2%1929 2 >/%7/..
>2%19292%987: 2 .%588.
2 2/%222
2 2
2 2 2 /%2222
5 sa'ra;h%i*ineR@ 2 2 2P@ . 2 2 2 2/PF
&or (iSeren#as*
5
>.%2766>
2%:286 .%11:1
HH sa'ra;h%*ine5F
ans
2%9772 2%6222 2
>5%/.16
>2%6222 2%9772 2
>6%2.59
2 2 /%2222 20 2 2 /%2222
2>sa'ra;h%$lo5F
The (ieren res'l or he sa#e $os 2T,is ('e o (ieren 'sage o Iniialesi#ae 2F an( #as* )F%
esult+ ,ence he vario's conce$s relae( o inverse *ine#aics =ere
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s'ccess'll! s'(ies or (ierenro;os in var!ing cong'raions%
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)arch .2@ .2/6 SAUA!" #U$%A (&'11E1*0)
Experiment 2 *
Aim+ To $eror# or=ar( *ine#aic o 5 DO? -lanar ro;o@ Sanor( #ani$'laor@-U)A ro;o or hegiven D, $ara#eers 'sing Ro;oanal!ser an( calc'lae he en(>
eecor $osiion or a given se o oin val'es 'sing )ala;an( veri! he res'ls
=ih Ro;oanal!ser%
%eor/+
?or=ar( Kine#aics+ To (eer#ine he $osiion an( orienaion o he en(>eecorgiven he val'es or he oin varia;les o he ro;o%
Using Ro;oanal!ser+ Ro;oAnal!Xer is a 5D )o(el Base( Ro;oics Learning S!se#(evelo$e( 'sing O$enTK an( "is'al CZ%
The a;ove g'res have ;een s'ia;l! la;ele( or $ro$er (escri$ion% The UI #a! ;ee
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raecor! $loe( aer hiing he $la!;'on%5. This screen is o;aine( ;! hiing he [Gra$h\ a; on o$ o he screen% ,ere
one can see he variaion in $osiion or each lin* se$arael! =ih i#e an(he oin $ara#eers s'ch as oin val'e@ veloci!@ acceleraion ec%
6. This ;loc* sho=s hegra$h or selece( $ara#eer in ;loc* 6%
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)arch .2@ .2/6 SAUA!" #U$%A (&'11E1*0)
ode+
(a) DO3 $lanar ro-ot
1>L/F Lin*2@2@2%5@2PF
2>L.F Lin*2@2@2%.6@2PF
3>L5F Lin*2@2@2%/@2PF
4>sa'ra;h SerialLin*L@ na#e@
#!BoF sa'ra;h
#!Bo 5 a>>
V>>>>>>>>>>>
V>>>>>>>>>>> V
> >> > > >> > >>>
V>>>>>>>>>>> V
W W hea W ( W aW
al$ha W
V>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>> V
W /W /W 2W2%5W
2WW .W .W 2W
2%.6W
2WW 5W 5W 2W
2%/W
2W
V>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>> V
grav
2 ;ase /2
2 2 ool / 2 22
2 2 / 2 2 2 / 2 2:%9/ 2 2 / 2 2 2/2
22 2
/ 2 2 2 /
1>(r $i0/92 (r 2%2/86
2>T52Q/ sa'ra;h%*ine2 2 2PF
T52Q/
/%2222 2 22%762
22 /%2222 2 22 2 /%2222 2
2 2 2 /%2222
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)arch .2@ .2/6 SAUA!" #U$%A (&'11E1*0)
(-) $uma o-ot
HHB/F Lin*2 2%881./ 2 >$i0.PF
1>B.F Lin*2 2%/2/6:. 2%6277.9 $iPF2>B5F Lin*2 >2%259/ 2%2. >$i0.PF3>B1F Lin*2 2%.78:7: 2 $i0.PF4>B6F Lin*2 2 2 >$i0.PF5>B7F Lin*2 2%2691. 2 2PF
6>sa'ra;hQ$'#a SerialLin*B@
na#e@ #!BoF sa'ra;hQ$'#a
#!Bo 7 a>>V>>>>>>>>>>>V >>>>>>>>>>>V>>>>>>>>>>> V>>>>>>>>>>> V
W W hea W ( W a W al$ha WV>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>> V
W /W /W 2%881
.W 2W >/%68/W
W .W .W 2%/2/
7W
2%6277W5%/1.W
W 5W 5W >
2%259/W 2%2.W >/%68/W
W 1W 1W
2%.79
W 2W /%68/WW 6W 6W 2W 2W >/%68/W
W 7W 7W 2%2691
.W 2W 2WV>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>> V
grav
2 ;ase / 2 2 2 ool / 22 2
2 2 / 2 2 2 / 2 2:%9/ 2 2 / 2 2 2 / 2
2 2 2 / 2 2 2 /
HH T52Q/ sa'ra;hQ$'#a%*ine2 2 2 2 2 2PF
T52Q/
/%2222 2 22%6.7
72 /%2222 2 2%/5:8
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2 2/%222
2 /%/227
2 2 2 /%2222
Ro;oanal!sero'$'+
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)arch .2@ .2/6 SAUA!" #U$%A (&'11E1*0)
(c) Stanford o-ot
1>S/F Lin*2 2%87. 2 >$i0.PF2>S.F Lin*2 2%5:51/. 2 >$i0.PF3>S5F Lin*>$i0. 2 2 2 /PF4>S1F Lin*2 2%..79 2 >$i0.PF5>S6F Lin*2 2 2 >$i0.PF6>S7F Lin*2 2%15/9 2 2PF
7>sa'ra;hQsanor( SerialLin*S@
na#e@ #!BoF sa'ra;hQsanor(
#!Bo 7 a>> V>>>>>>>>>>>
V>>>>>>>>>>>V
>>>>>>>>>>> V
>>>>>>>>>>>V
W W
hea
W
(W a W al$ha W
V>>> V>>>>>>>>>>>
V>>>>>
>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>> V
W /W/W
2%87.W 2W
> /%68/W
W .W .W 2%5:51W 2W> /%68/W
W 5W
>/%6
8/W
5
W 2W 2WW 1W 1W 2%..79W 2W> /%68/W
W 6W6W
2W 2W >/%68/W
W 7W 7W 2%15/9W 2W 2WV>>> V>>>>>>>>>>>
V>>>>>>>>>
V>>>>>>>>
>>>
V>>>>>>>>>>>
V
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>>
grav
2 ;ase / 2 22
ool / 2 22
2 2 / 2 2 2 / 2 2:%9/ 2 2 / 2 2 2/2
2
2 2
/
222
/
HH T52Q/ sa'ra;hQsanor(%*ine2 >$i0. 2%756 2 $i $iPF
T52Q/2%2222
2%2222 /%2222
/%.:57
/%2222 2 >2%2222 2%5:51
>2%2222
/%2222>2%2222
2%87.2
2 2 2/%222
2
Ro;oanal!sero'$'+
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)arch .2@ .2/6 SAUA!" #U$%A (&'11E1*0)
esult+ ,ence he vario's ro;os =ere s'ccess'll! si#'lae( in he Ro;oAnal!ser
environ#en =ih (ieren cong'raions% ?'rher he ransor#aion #ariXero consan D, $ara#eers
$hi$i05 $< .%6 V sr5F $! / V sr5F0. In$'
=< $< > a5cos$hiF
=! $!>a5sin$hiF (el=a/a/>a.a.F0.a/a.F Calc'laion or hea.
s. sr/>c.c.F
h./[email protected] h..aan.>[email protected]
Calc'laion or hea/
s// a/Va.cosh./FF=!>a.sinh./F=h/.>h.. calc'laion or hea5
r.(/920$i Angle in (egrees
h//( h//r.( h/.(h/.r.( h./ h./r.(
h..(h..r.( h5/(h5/r.( h5.( h5.r.(
o-oAnal/5er Output
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)arch .8@ .2/6 SAUA!" #U$%A (&'11E1*0)
(2) Articulated
2>a./ a5/
3>$(el
5>h//aan.$!@$h/.$iVaan.$!@$c5(el>a.a.>a5a5F0.a.a5F s5sr/>c5c5F
8>h5/aan.s5@c5F h5.aan.>s5@c5F
9>s./>a.Va5cosh5/FF$X>a5s5(el
10> c./
a.Va5cosh5/FF(el
11> s..>a.Va5cosh5/FF$XVa5s5(el
12> c..a.Va5cosh5/FF(ela5s5$XF0(el
13> h./aan.s./@c./F
14> h.5$i>h./h.1$i>h..
15> r.(/920$i
HHh//(h//r.(
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)arch .8@ .2/6 SAUA!" #U$%A (&'11E1*0)
1>h/.(h/.r.(
2>h./(h./r.(
3>h..(h..r.(
4>h.5(h.5r.(
5>h.1(h.1r.(
6>h5/(h5/r.(
7>h5.(h5.r.(
8>h//(h//r.(
o-oAnal/5er Output
esult+ ,ence he Inverse Kine#aic Anal!sis or vario's ro;os is s'ccess'll!(one 'sing Ro;oAnal!Xer%
The res'ls are hen verie( 'sing )ala; oo%
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A$ril /8@ .2/6 SAUA!" #U$%A (&'11E1*0)
Experiment 6
Aim+To s'(! veloci! *ine#aics 'sing -eer Cor*e ool ;o2%2222
2%2222 /%2222 2%6:75
>2%2222
/%2222
>2%2222>2%/62/
>/%2222
>2%2222
>2%2222 >2%2/11
2 2 2/%2222
HH ( /e>7 give sligh (is'r;ance
HH T$ $672%*inen V ( 2 2 22 2PF
o;ain ne= ransor#aion#ari2%2222
>2%2222/%2222 2%6:75
>2%2222 /%22222%2222
>2%/622
>/%222
2
>
2%2222
>
2%2222 >2%2/112 2 2/%2222
HH (T(/ T$ >T2F 0 ( o;ain he (ierenial(T(/
2>/%2222 >2%2222 2%/622
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>2%2222
>2%2222/%2222 2%6:75
2 2 2 2
2 2 2 2
HH (R(/ (T(//+5@/+5F
ge he 5/%2222 >2%2222
>2%2222
>2%2222/%2222
2 2 2
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A$ril /8@ .2/6 SAUA!" #U$%A (&'11E1*0)
HH R T2/+5@ /+5F o;ain roaional #ari< ro# T2
18
>
2
%
2
2
2
2
2
%
2
2
2
2
/
%
2
2
2
2
>
2
%
2
2
2
2
/
%
2
2
2
2
>
2
%
2
2
2
2
>
/
%
2
2
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2
2
>
2
%
2
2
2
2
>
2
%
2
2
2
2
HH S (R(/ R o;ain hes*e= s!##eric #ari2%2222 >/%2222 2%2222
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2 2 2 /%2222
HH J r.acTF
ge ne= aco;ian #ari< =%r%% ne=ra#e
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A$ril /8@ .2/6 SAUA!" #U$%A (&'11E1*0)
J
2%2222 2>/%2222 2 /%2222 22 /%2222 2 2 2/%2222
/%2222 2
2%222
2 2>2%2222 2
2 2 2 2%2222 2>
/%22222 2 2 2 /%2222 2
2 2 2 /%2222 22%2222
1>vB J/ 2 2 2 2 2P
2>vB
ans
2%2222 2 /%2222 2 2 2HH$672%aco;nnF
ge aco;ian #ari< =%r%% en(>eSecor
ans >2%2222 >2%6:75
>2%.:/2 2 2 2
2%6:75 2%22222%2222 2 2 2
2%/622 2%2/11
2%5/:
8 2 2 2>/%2222 2 2 2%828/ 2 2>2%2222 >/%2222
>/%2222
>2%2222
>/%2222 2
>2%2222 2%2222
2%2222 2%828/
2%2222 /%2222
HH $672%aco;2n@e'lF
ge aco;ian #ari< or E'larval'es
ans
2%/62/ 2%2/112%5/:8 2 2 2
2%6:75 2%22222%2222 2 2 2
2 2%6:75 2%.:/2 2 2 2/%2222 2%2222 2%2222 >2%828/ 2%2222 2%22222%2222 >/%2222 > > > 2
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/%2222 2%2222
/%2222
>2%2222 2%2222
2%2222 2%828/
2%2222 /%2222
To s'(! inverse *ine#aics an( (evelo$ a )ATLAB $rogra# 'sing $eer coor*eool;o< o calc'lae a aco;ian#ari< or $lanar 5R ro;o@ given he ro;os lengh
l/1#@ l.5#@ l5.# an( iniial oin angles ]]/@].@]5F/2o
@ .2o
@52o
P%
1>L/F Lin*2 2 1 2 PF
2>L.F Lin*2 2 5 2 PF
3>L5F Lin*2 2 . 2 PF
A$ril /[email protected]/6
SAUA!" #U$%A(&'11E1*0)
L hea/@( 2@ a
1@al$ha 2 R@s(D,F
hea.@( 2@ a
5@al$ha 2 R@s(D,F
hea5@( 2@ a
.@al$ha 2 R@s(D,F
HH =oQlin*Qaco; SerialLin*L@ na#e@ =oQlin*Qaco;F
=oQlin*Qaco; =oQlin*Qaco; 5 a>>V
>>>>>>>>>>>
V
>>>>>>>>>>>
V
>>>>>>>>>>>
V >>>>>>>>>>>V
W W hea W ( Wa Wal$haW
V>>>V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>> V
W /W /W 2W 1W 2WW .W .W 2W 5W 2WW 5W 5W 2W .W 2W
V>>>V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>>
V>>>>>>>>>>> V
grav 2 ;ase / 2 2 2 ool / 2
2 22 2 / 2 2 2 / 2 2
:%9/ 2 2 / 2 2 2 / 2
2 2 2 / 2 2 2 /
1>(r
$i0/92
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(r
2%2/86
2>2 /2 .2 52P(r
2
2%/816 2%51:/ 2%6.57
3>aco;ian
aco;2=oQlin*Qaco;@ 2F
aco;ian
>5%:.77 >5%.5./ >/%85./
8%65855%6:9/
/%2222
2 2 22 2 2
2 2 2
/%2222/%2222
/%2222
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A$ril /8@ .2/6 SAUA!" #U$%A (&'11E1*0)
esult+ "ario's conce$s relae( o veloci! *ine#aics =ere s'(ie( an( aco;ian
#ari< =ere o;aine(s'ccess'll! or he 5DO? $lanar ro;o%
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A$ril /8@ .2/6 SAUA!" #U$%A (&'11E1*0)
Experiment 7
Aim+ To s'(! or=ar( (!na#ics o a 5DO? o 5R ro;o%
%eor/+
D!na#ics+Ro;o(!na#icsis concerne( =ih he relaionshi$ ;e=een he orces
acing on a ro;o #echanis# an( he acceleraions he! $ro('ce% ?or=ar(
(!na#ics =or*s o' he acceleraions given he orces%
HH#(lQ$'#a672
$672%rnen@ X@ XF oin or'e re'ire( or he ro;o R o achieve hes$ecie( oin
$osiion @ veloci! D an( acceleraion DD%
>2%2222 5/%75:: 7%256/ 2%2222 2%2.95 2
$672%rnen@ X@ X@ 2 2 :%9/PF 2 2 :%9/P gives he graviaional vecor
>2%22225/%75:
: 7%256/2%2222 2%2.95 2@ /@ .P raX@
r@ /2F
Co#$'e a oin s$ace raecor! ;e=een
=o $oins
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A$ril /8@ .2/6 SAUA!" #U$%A (&'11E1*0)
$672%lin*s/F%(!n
$672%gravi! Dea'l gravi! ass'#e( ;! $'#a ro;o
ans
2 2 :%9/22
HH $672%gravloa(nF Tor'e re'ire( o #ainain he ro;o in
$osiion
ans >2%2222 5/%75:: 7%256/ 2%2222
2%2.95$672%gravi!$672%gravi!07
HH $672%gravloa(nF
ans 2%2222
6%.855 /%226:
2%2222 2%2218 2
$672%;ase ro6%.855 >/%226:>2%2222 >2%2218 2
HH $672%gravloa(sF Ro;o in 3s4 $osiion >2%2222
17%227:9%88..
2%22222%2.95 2
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HH $672%gravloa(rF
2 >2%886. 2%.19: 2 2 2
A$ril /[email protected]/6
SAUA!" #U$%A(&'11E1*0)
To s'(! or=ar( (!na#ics o 5 DO? 5R ro;oan( a $rogra# $eer coor*eool;o< o calc'lae he or=ar( (!na#ics or$lanar ro;os as L/1#@
L.5#@ L5.# an( #/.2Kg@ #./6Kg@
#5/2Kg an( .@ .@ .%Ignore gravi! ;! ass'#ing ha he gravi!acs in a nor#al $lane % Using -eer
Coor*e ool;o< an( )ala; co##an(s solve he or=ar( (!na#ics $ro;le# i%e%=ih he availa;le
(rivingoinor'es an
oinanglesan(iniialoinraesF
-eror#
si#'laionor 1sec%
^ @ _
L/F Lin*2 2 1 22.2 . 2
2 22
%
_ @
.
2%6 2 2 2 2 /222PF
Lin*/ =ih a1#@ #.2*g@I2%6*g#
L.F Lin*2 2 5 22 /6
/%6
2 22
2 2%. 2 2 2 2/ 22 2PF
Lin*. =ih a5#@ #/6*g@
I2%.*g#.
L5F Lin*2 2 . 22 /2
/ 2 2 22
2%/ 2 2 2 2 /2 22PF
Lin*5 =ih a.#@ #/2*g@
I2%/*g#.
L/F%#(h/ Use #o(ie( D, $ara#eers
L.F%#(h/
L5F%#(h/
=oQlin*Qsa' SerialLin*L@ na#e@ =o lin*Qsa'F
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=oQlin*Qsa'
=o lin*Qsa' 5 a>>V>>>>>>>>>>> V>>>>>>>>>>>V >>>>>>>>>>> V>>>>>>>>>>> V
W Whea W ( W a W al$ha W
V>>> V>>>>>>>>>>>
V>>>>>>>>>>
>
V>>>>>
>>>>>> V>>>>>>>>>>> VW /W /W 2W 1W 2WW .W .W 2W 5W 2WW 5W 5W 2W .W 2W
V>>> V>>>>>>>>>>>
V>>>>>>>
>>>>
V>>>>>>>>>>> V>>>>>>>>>>> V
grav 2 ;ase / 2 2 2 ool / 2
2 22 2 / 2 2 2 /22
:%9/ 2 2 / 2 2 2 / 2
222
/ 2 2 2 /
22 1 N12 (>2F0N
HH (
(
2%/222
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A$ril /8@ .2/6 SAUA!" #U$%A (&'11E1*0)
2+(+P
(r $i0/92
Y2
>72
:252PE(r
Y2 S$eci! iniial ro;o $osiion
>/%218. /%6829 2%6.57
(P =oQlin*Qsa'%(!n/@ .26/P@ 2@ 2%6 2 2PF Do or=ar( (!na#ics or/s & .26/P or'e
onclusion+ ,ence or=ar( (!na#ics o 5DO? $lanar ro;o is s'(ie(
s'ccess'll! =ih he given lin*cong'raions%
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8earnin9 Outcome+ In his e
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)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)
Experiment :
Aim+To s'(! -eer Cor*e Co#$'er "ision ool;o:00in his case ro# 522 o / 222 n#@ an( hen co#$'e he;lac*;o(! s$ecra00 HHor T/222+/222+7222HH$lo la#;(a/e:@ ;lac*;o(!la#;(a@
TFF hol( all HHen(
as sho=n in ?ig% 9%/a%
00The la#en o 'ngsen la#$ has a e#$era're o . 722 K an( glo=s=hieho% The S'n has a s'race e#$era're o 7 622 K% The s$ecra o heseso'rcesare co#$are( in ?ig% 9%/;%00
HHla#$ ;lac*;o(!la#;(a@ .722FHHs'n ;lac*;o(!la#;(a@7622FHH$lola#;(a/e:@ la#$0#a
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00The S'n4s s$ecr'# a gro'n( level on he Earh has ;een #eas're( an(a;'lae(00
HHs'nQgro'n( loa(s$ecr'#la#;(a@solar%(aF HH$lola#;(a/e:@s'nQgro'n(Fan( is sho=n in ?ig% 9%5a%
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)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)
AI+ A-sorption
1>A@ la#;(aP
loa(s$ecr'#122+/2+822P/e>:@
=aer%(aF 00Ais he a;sor$ion
coe`cien00
2>( 6(is he $ah lengh00
3>T /2%>A(F00 Trans#issionTis heinverse o a;sor$ion00
HH$lola#;(a/e:@ TF
=hich is $loe( in ?ig% 9%5;%
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)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)
e;ection
00he rebecivi! o a re( ho'se;ric*00
HH R@ la#;(aP loa(s$ecr'#/22+/2+/2222P/e>:@re(;ric*%(aF HH$lola#;(a/e7@ RF=hich is $loe( in ?ig% 9%1% Me see ha i rebecs re( colors #ore han ;l'e%
00The ill'#inance o he S'n in he visi;leregion00 HHla#;(a 122+/2+822P/e>: visi;le s$ecr'# HH E
loa(s$ecr'#la#;(a@ solar%(aF00a gro'n( level% The rebecivi! o he ;ric* is001>R loa(s$ecr'#la#;(a@re(;ric*%(aF 00an( he lighrebece( ro# he ;ric* is00
2>L E % RHH$lola#;(a/e:@ LF00=hich is sho=n in ?ig% 9%6% I is his s$ecr'# ha is iner$ree( ;! o'r e!es as hecolor re(%00
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)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)
olor
00The l'#inosi! 'ncion is $rovi(e( ;! heTool;o
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)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)
HHcolorna#e;s@
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HHca#%$lo-Fh
/85%22..
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)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)
HH Tca# ransl>/@2@2%6Fro!2%:F 00 o;li'e vie= o
he $lane 001>ca#%$lo-@ Tca#@ Tca#F
2>ca#%$roec/ 2 2 2P@Tca#@ Tca#Fans
/%2eV25
/%95252%6/.2
HH $ ca#%$lo-@ Tca#@ Tca#F
HH$+@/+1F
00 o;li'e vie=ing case he i#age $lane
ans 998%875
9998%875
9998%875
9:66%.16
/571%555
26/.%222
276:%778
2581%:26
2
HH c';e #*c';e2%.@ T@ ransl2@2@ /PF F 00 $roecion o c';e 001>ca#%$loc';eF
2>@Y@P #*c';e2%.@ T@ransl2@ 2@ /%2PF@ e(geF
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)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)
HH ca#%#esh@ Y@ FHHca#%Tra
nsl>/@2@2%6Fro!2%9F 00o;li'evie= 00
HHca#%#esh@
Y@@Tca#@
Tca
#F
ll amera ali-ration
1/ l"omo9eneous%ransformation Approac
2>- #*c';e2%.F3>TQ'n*no=n ransl2%/@ 2%.@ /%6F
r$!.r2%/@ 2%.@ 2%5F4>ca# CenralCa#eraocal@ 2%2/6@
%%%$i7@ resol'ion@ /.92/2.1P@ cenre@ 6/. 6/.P@
%%%noise@ 2%26F5>$ ca#%$roec-@ To;@
TQ'n*no=nF
6>C ca#cal(-@ $F#a
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.8/.%2/
92>2%/215
2%2:962%71
:1/%2222
00
lDecomp
osin9t
eameraal
i-rationat
rixes
invca#ca
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lCFes na#
e+invca#cal
cenral>$e
rs$eciveP
ocalleng
h+/621
$iUo@"oP #eshgri(2+M>/@ 2+M>/F 00 The (o#ain ohe o'$'i#age 00
HH r srUo>'2F%. V "o>v2F%.F 00 $olar coor(inaes 001>$hi aan."o>v2F@ Uo>'2FF2>-hiQo $hi 00 s$herical
coor(inaes 001>TheaQo $i >
acos lV#Fsrr%./>l.F VlV#F.F >lr%.F %0 r%. V
lV#F.F F2>i(is$$ers$eciveF3>s$herical
s$hereQroaes$herical@ro!/%.FroX>/%6FF
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)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)
The ool;o< consis o irea('ncion o rea( an i#age
HHsree irea(sree%$ngF Mhich re'rns a #ari