Robotics File

7/26/2019 Robotics File

1/120

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


2/120

RollNo%+.K//0EC0/12

Bach+ECE 3D.4


3/120

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.:

/


5/120

8>21>

.2/651

2/>26>.

2/659

2/>

26>.2

/66:

2/

>26>.

2/677


6/120

Attendance(Out of 10classes)

Internal Assessment

Marks


7/120

?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


8/120

?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%


9/120

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


10/120

?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

;


11/120

?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/


12/120

/ 2 2 52 / 2 22 2 / /

2 2 2 /


13/120

?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


14/120

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


15/120

?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%


16/120

?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


17/120

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


18/120

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 .


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


19/120

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


20/120


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


21/120

2>B.F Lin*2 2 5 2PF

3>B5F Lin*2 2

. 2PF B


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


22/120

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


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@


23/120

>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%


24/120


25/120

2>i

$672%i*ine7sT@ l'F

i


26/120

?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


27/120

HH$672%$loiF


28/120

?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


29/120

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


30/120

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


31/120

?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


32/120

s'ccess'll! s'(ies or (ierenro;os in var!ing cong'raions%


33/120

)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


34/120

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%


35/120

)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


36/120


37/120

)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


38/120

2 2/%222

2 /%/227

2 2 2 /%2222

Ro;oanal!sero'$'+


39/120

)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


40/120

>>

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'$'+


41/120

)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


45/120

)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

[email protected]

14> h.5$i>h./h.1$i>h..

15> r.(/920$i

HHh//(h//r.(


46/120

)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%


47/120

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


48/120

>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


49/120

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


50/120

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


51/120


52/120

2 2 2 /%2222

HH J r.acTF

ge ne= aco;ian #ari< =%r%% ne=ra#e


53/120

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


54/120

/%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


55/120

(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


56/120

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%


57/120

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


58/120

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


59/120

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


60/120

=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


61/120

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%


62/120

8earnin9 Outcome+ In his e


63/120

)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


64/120

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%


65/120

)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;%


66/120

)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


67/120

)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)

olor

00The l'#inosi! 'ncion is $rovi(e( ;! heTool;o


68/120


69/120


70/120


71/120

)a! /@ .2/6 SAUA!" #U$%A (&'11E1*0)

HHcolorna#e;s@


72/120


73/120


74/120

HHca#%$lo-Fh

/85%22..


75/120

)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


76/120

)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


77/120

.8/.%2/

92>2%/215

2%2:962%71

:1/%2222

00

lDecomp

osin9t

eameraal

i-rationat

rixes

invca#ca


78/120

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


85/120


86/120

)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

Documents

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