Gyroscope 2of2

7/23/2019 Gyroscope 2of2

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M.KHURRAM JAVED

FAHAD BIN WALEED

WAQAS AHMED

GUL HASSAN NIAZI

GROUP MEMBERS



GYROSCOPE

AN OVERVIEW

Presenter:

MUHAMMAD KHURRAM JAVED

2!"EP"#$



Gyroscope

WHA% IS A G&ROS'OPE(

DEFINI%ION: A gyroscope )s * +e,)-e /r 0e*s1r)n

/r 0*)nt*)n)n /r)ent*t)/n3 4*se+ /n t5e6r)n-)67es / -/nser,*t)/n / *n17*r0/0ent10.



A 0e-5*n)-*7 8r/s-/6e )s essent)*778 *s6)nn)n 95ee7 /r +)s 95/se *;7e )s ree

t/ t*e *n8 /r)ent*t)/n. %5)s /r)ent*t)/n-5*nes 01-5 7ess )n res6/nse t/ * ),ene;tern*7 t/r<1e t5*n )t 9/17+ 9)t5/1t t5e

7*re *n17*r 0/0ent10 *ss/-)*te+ 9)t5t5e 8r/s-/6e=s 5)5 r*te / s6)n.





EXAMPLES

G8r/s-/6)- e>e-ts *re *7s/ -entr*7 t/t5)ns 7)e 8/"8/s *n+ Fr)s4ees.

G8r/s-/6es -*n 4e ,er8 6er67e;)n/4?e-ts 4e-*1se t5e8 0/,e )n 6e-17)*r9*8s *n+ e,en see0 t/ defy gravity.

%5ese s6e-)*7 6r/6ert)es 0*e8r/s-/6es e;tre0e78 )06/rt*nt )ne,er8t5)n r/0 8/1r 4)-8-7e t/ t5e*+,*n-e+ n*,)*t)/n s8ste0 /n t5e

s6*-e s51tt7e.



%5e essen-e / t5)s +e,)-e )s * s6)nn)n

95ee7 /n *n *;7e. %5e +e,)-e /n-es6)nn)n3 ten+s t/ res)st -5*nes t/ )ts/r)ent*t)/n +1e t/ t5e *n17*r0/0ent10 / t5e 95ee7.

@B*7*n-)n t5e s6)nn)n 4)-8-7e 95ee7



PROPERTIES OFGYROSCOPES

G8r/s-/6es 5*,e t9/ 4*s)- 6r/6ert)es:

R))+)t8 *n+ Pre-ess)/n

%5ese 6r/6ert)es *re +ene+ *s /77/9s:

#. RIGIDI%&: %5e *;)s / r/t*t)/n Cs6)n *;)s/ t5e 8r/ 95ee7 ten+s t/ re0*)n )n *;e+ +)re-t)/n )n s6*-e ) n/ /r-e )s

*667)e+ t/ )t.2. PRE'ESSION: %5e *;)s / r/t*t)/n 5*s *

ten+en-8 t/ t1rn *t * r)5t *n7e t/ t5e+)re-t)/n / *n *667)e+ /r-e.



PRECESSION

Te f!"da#e"ta$ e%!atio" descri&i"g te &eavior of tegyroscope is'

95ere t5e ,e-t/rs *n+ L *re3 res6e-t),e783 t5e t/r<1e /n t5e8r/s-/6e *n+ )ts *n17*r 0/0ent103 t5e s-*7*r I )s )ts 0/0ent/ )nert)*3 t5e ,e-t/r )s )ts *n17*r ,e7/-)t83 *n+ t5e ,e-t/r )s)ts *n17*r *--e7er*t)/n.

It /77/9s r/0 t5)s t5*t * t/r<1e *667)e+ 6er6en+)-17*r t/ t5e

*;)s / r/t*t)/n3 *n+ t5ere/re 6er6en+)-17*r t/ L3 res17ts )n *r/t*t)/n *4/1t *n *;)s 6er6en+)-17*r t/ 4/t5 *n+ L. %5)s 0/t)/n)s -*77e+ precessio". %5e *n17*r ,e7/-)t8 / 6re-ess)/n 9P )s),en 48 t5e -r/ss 6r/+1-t:

% 96 7



%51s ) t5e 8r/s-/6e=s s6)n s7/9s +/9nC/r e;*067e3 +1e t/ r)-t)/n3 )ts *n17*r

0/0ent10 +e-re*ses *n+ s/ t5e r*te /6re-ess)/n )n-re*ses. %5)s -/nt)n1es 1nt)7t5e +e,)-e )s 1n*47e t/ r/t*te *st en/15t/ s166/rt )ts /9n 9e)5t3 95en )t st/6s

6re-ess)n *n+ *77s /> )ts s166/rt30/st78 4e-*1se r)-t)/n **)nst6re-ess)/n -*1se *n/t5er 6re-ess)/n t5*t/es t/ -*1se t5e *77.



B8 -/n,ent)/n3 t5ese t5ree ,e-t/rs3 t/r<1e3s6)n3 *n+ 6re-ess)/n3 *re *77 /r)ente+ 9)t5

res6e-t t/ e*-5 /t5er *--/r+)n t/ t5er)5t"5*n+ r17e.



Te Ca!se of Precessio"

Let=s 7// *t t9/ s0*77 se-t)/ns / t5e8r/s-/6e *s )t )s r/t*t)n "" t5e t/6 *n+t5e 4/tt/03 7)e t5)s:



W5en t5e /r-e )s *667)e+ t/ t5e *;7e3 t5ese-t)/n *t t5e t/6 / t5e 8r/s-/6e 9)77

tr8 t/ 0/,e t/ t5e 7et3 *n+ t5e se-t)/n *tt5e 4/tt/0 / t5e 8r/s-/6e 9)77 tr8 t/0/,e t/ t5e r)5t. B8 Ne9t/n=s rst 7*9/ 0/t)/n3 t5e t/6 6/)nt /n t5e 8r/s-/6e)s *-te+ /n 48 t5e /r-e *667)e+ t/ t5e*;7e *n+ 4e)ns t/ 0/,e t/9*r+ t5e 7et.It -/nt)n1es tr8)n t/ 0/,e 7et9*r+

4e-*1se / Ne9t/n=s rst 7*9 / 0/t)/n341t t5e 8r/=s s6)nn)n r/t*tes )t3 7)et5)s:





Tis e(ect is te ca!se of precessio".

%5e +)>erent se-t)/ns / t5e 8r/s-/6ere-e),e /r-es *t /ne 6/)nt 41t t5en r/t*tet/ ne9 6/s)t)/ns W5en t5e se-t)/n *t t5et/6 / t5e 8r/ r/t*tes +erees t/ t5e

s)+e3 )t -/nt)n1es )n )ts +es)re t/ 0/,e t/t5e 7et. %5ese /r-es r/t*te t5e 95ee7 )nt5e 6re-ess)/n +)re-t)/n. As t5e )+ent)e+6/)nts -/nt)n1e t/ r/t*te 0/re

+erees3 t5e)r /r))n*7 0/t)/ns *re-*n-e77e+. S/ t5e 8r/s-/6e=s *;7e 5*ns)n t5e *)r *n+ 6re-esses.



E(ect of Gyroscopic Co!p$e o"Aerop$a"es

W5en t5e 6r/6e77er r/t*tes )n *nt)"-7/-9)se+)re-t)/n :

#. %5e *er/67*ne t*es * r)5t t1rn3 t5e

8r/s-/6e 9)77 r*)se t5e n/se *n+ +)6 t5et*)7.

2. %5e *er/67*ne t*es * 7et t1rn3 t5e

8r/s-/6e 9)77 +)6 t5e n/se *n+ r*)se t5e



E(ect of Gyroscopic Co!p$e o"Nava$ Sip

S%EERING:

Steer)n )s t5e t1rn)n / t5e -/067ete s5)6 )n *-1r,e t/9*r+s 7et /r r)5t3 95)7e )t 0/,es/r9*r+.

PI%'HING:

P)t-5)n )s t5e 0/,e0ent / t5e

-/067ete s5)6 16 +/9n )n *

,ert)-*7 67*ne.ROLLING:

In r/77)n3 t5e *;)s / 6re-)s)/n )s *79*8s 6*r*77e7 t/t5e *;)s / s6)n /r *77 6/s)t)/ns.



STA)ILITY OF A FO*R+,EEL -RI.E MO.ING IN AC*R.E- PAT,

PRESEN%ER:

WAQAS AHMED2!"EP"#



Sta&i$ity of a Fo!r +ee$ -rive Movi"g i" a C!rved Pat

'/ns)+er t5e /1r 95ee7s A, B, C and D ofan

*1t/0/4)7e 7/-/0/t),e t*)n * t1rn

t/9*r+s 7et)n F). %5e 95ee7s A and C are inner wheels,

whereas

B and D are outer wheels. The centre ofgravity (C.G.) of

t5e ,e5)-7e 7)es ,ert)-*778 *4/,e t5e r/*+s1r*-e.



Let m = ass of the vehicle in !g, " = "eight of the vehicle in newtons = m.g, r " = #adius of the wheels in metres, # = #adius of curvature in metres C# $ r " ),

h = Distance of centre of gravity, vertically *4/,e t5e r/*+ s1r*-e )n 0etres3 % = "idth of trac! in metres, &" = ass moment of inertia of one of the 95ee7s )n "023 W An17*r ,e7/-)t8 / t5e 95ee7s /r ,e7/-)t8 / s6)n )n r*+s3



&' = ass moment of inertia of therotating

6*rts / t5e en)ne )n "023 E An17*r ,e7/-)t8 / t5e r/t*t)n

6*rts /

t5e en)ne )n r*+s3 G = Gear ratio = ' ", v = *inear velocity of the vehicle in ms =

".r"



A 7)tt7e -/ns)+er*t)/n 9)77 s5/93

t5*t t5e 9e)5t / t5e ,e5)-7e C") will +e

e<1*778 +)str)41te+ /,er t5e /1r 95ee7s

95)-5 9)77 *-t +/9n9*r+s. %5e re*-t)/n

4et9een e*-5 95ee7 *n+ t5e r/*+ s1r*-e

/ t5e s*0e 0*n)t1+e 9)77 *-t 169*r+s. %5ere/re

R/*+ re*-t)/n /,er e*-5 95ee7

" = m.g newtons

Let 1s n/9 -/ns)+er t5e e>e-t /

t5e 8r/s-/6)- -/167e *n+ -entr)1*7 -/167e /nt5e ,e5)-7e



EFFECT OF THE GYROSCOPIC

COUPLES)n-e t5e ,e5)-7e t*es * t1rn t/9*r+s 7et+1e t/ t5e 6re-ess)/n *n+ /t5er r/t*t)n6*rts3

t5ere/re * 8r/s-/6)- -/167e 9)77 *-t.

Net 8r/s-/6)- -/167e3

C = C" - C' = &" ." . - &'.G." .

W.P C &" - G.&e )



%5e positive sign is used when thewheels and rotating parts o theengine rotate in the sa!e

+)re-t)/n. I t5e r/t*t)n 6*rts / t5e en)nere,/7,es )n /66/s)te +)re-t)/n3 t5en

negative sign is used"W5en C' $ C" , then C will +e /ve. Thus the

reaction will +e vertically downwards onthe outer wheels

*n+ ,ert)-*778 169*r+s /n t5e )nner 95ee7s



E#e$t o the $entriugal $ouple

S)n-e t5e ,e5)-7e 0/,es *7/n * -1r,e+6*t53 t5ere/re -entr)1*7 /r-e 9)77 *-t/1t9*r+78 *t

t5e -entre / r*,)t8 / t5e ,e5)-7e. %5ee>e-t / t5)s -entr)1*7 /r-e )s *7s/ t//,ert1rn t5e ,e5)-7e.

We n/9 t5*t -entr)1*7 /r-e3

F- C0 ; ,2 R



%/t*7 ,ert)-*7 re*-t)/n *t e*-5 / t5e /1ter 95e

An+ t/t*7 ,ert)-*7 re*-t)/n *t e*-5 / t5e)nner 95ee7



STA)ILITY OF A T+O+,EEL .E,ICLE

TA/ING A T*RNPresenter:

MUHAMMAD FAHAD BIN WALEED2!"EP"#!



T+O +,EEL -RI.E



Let m = ass of the vehicle and its

r)+er )n 3 " = "eight of the vehicle and )ts r)+er )n ne9t/ns m.g, h = 0eight of the centre of r*,)t8 / t5e ,e5)-7e *n+ r)+er3

r " = #adius of the wheels,

# = #adius of trac! or -1r,*t1re3 &" = ass moment of inertia of each wheel, &' = ass moment of inertia of the rotating 1arts of the

engine, W An17*r ,e7/-)t8 / t5e 95ee7s3 E An17*r ,e7/-)t8 / t5e en)ne3

G = Gear ratio = ' " , v = *inear velocity of the vehicle = " 2 r " , An7e / 5ee7. It )s )n-7)n*t)/n / t5e ,e5)-7e t/ t5e

,ert)-*7 /r e<1)7)4r)10.

% E# t i



%"E#e$t o g&ros$opi$$ouple

We n/9 t5*t

An+



%/t*7

*n+ ,e7/-)t8 /6re-ess)/n3

W5en t5e 95ee7s 0/,e /,er t5e -1r,e+ 6*t53 t5e

,e5)-7e )s *79*8s )n-7)ne+ *t *n *n7e 9)t5 t5e,ert)-*7 67*ne *s s5/9n )n F). This angle is !nown *s

angle o heel"



Notes '0a' (hen the engine is rotating in the sa!e dire$tion as

that o wheels) then the positive sign is used in t5e *4/,ee;6ress)/n *n+ ) t5e en)ne r/t*tes )n /66/s)te +)re-t)/n3 t5ennegative sign is used"

0*' The g&ros$opi$ $ouple will a$t over the vehi$le

outwards i"e" in the anti$lo$+wise dire$tion 95en seenr/0 t5e r/nt / t5e ,e5)-7e. %5e ten+en-8 / t5)s -/167e )s t//,ert1rn t5e ,e5)-7e )n /1t9*r+

+)re-t)/n.

G8r/s-/6)- -/167e



," E#e$t o $entriugal $ouple

'entr)1*7 /r-e3

'entr)1*7 '/167e 3

% 7 ) 7



%/t*7 /,ert1rn)n -/167e3

C3 = Gyrosco1ic cou1le 4Centrifugal cou1le

We n/9 t5*t 4*7*n-)n -/167e m.g.h sin 5

As t5e st*4)7)t83 t5e /,ert1rn)n -/167e 01st 4e e<1*7t/ t5e 4*7*n-)n -/167e3 ).e

Fr/0 t5)s e;6ress)/n3 t5e ,*71e / t5e *n7e / 5ee7 C

0*8 4e +eter0)ne+.



E1a#p$e

Fi"d te a"g$e of i"c$i"atio" 2itrespect to te vertica$ of a t2o 2ee$er"egotiati"g a t!r"3

Give" ' co#&i"ed #ass of te veic$e2it its rider 456 7g 8 #o#e"t of i"ertiaof te e"gi"e 9y2ee$ 63: 7g;#4 8 #o#e"t of i"ertia of eac road 2ee$ <

7g;#4 8 speed of e"gi"e 9y2ee$ 5ti#es tat of road 2ee$s a"d i" tesa#e directio" 8 eigt of ce"tre ofgravity of rider 2it veic$e 63= # 8 t2o

2ee$er speed >6 7#? 8 2ee$ radi!s



APPLICATIONS OFGYROSCOPE

Presente+ 48 G17 H*ss*n K5*n2!"EPK"#



Gravity -e@a"ce



Spi""ig Tops a"d YOYO

G8r/s-/6)- e>e-ts *re *7s/ -entr*7 t/t5)ns 7)e 8/"8/s *n+ Fr)s4ees.



GyroCo#pass a"d -irectio"Fi"di"g

A 8r/-/06*ss )s s)0)7*r t/ * 8r/s-/6e. It )s *-/06*ss t5*t n+s tr1e n/rt5 48 1s)n *nCe7e-tr)-*778 6/9ere+ *st"s6)nn)n 95ee7 *n+r)-t)/n /r-es )n /r+er t/ e;67/)t t5e r/t*t)/n /

t5e E*rt5. G8r/-/06*sses *re 9)+e78 1se+ /ns5)6s. %5e8 5*,e t9/ 0*)n *+,*nt*es /,er0*net)- -/06*sses:

#. %5e8 n+ tr1e n/rt53 ).e.3 t5e +)re-t)/n / E*rt5=s

r/t*t)/n*7 *;)s3 *s /66/se+ t/ 0*net)- n/rt5.2. %5e8 *re *r 7ess s1s-e6t)47e t/ e;tern*7

0*net)- e7+s3 e.. t5/se -re*te+ 48 err/1s0et*7 )n * s5)6=s 5177.



Sip Sta&$iers a"d a"ti ro$$devices

A667)-*t)/ns / 8r/s-/6es )n-71+e n*,)*t)/n CINS95en 0*net)- -/06*sses +/ n/t 9/r3 /r t5est*4)7)*t)/n / 8)n ,e5)-7es 7)e R*+)/"-/ntr/77e+5e7)-/6ters /r UAVs.

In *n INS3 sens/rs /n t5e )04*7s *;7es +ete-t 95ent5e 67*t/r0 r/t*tes. %5e INS 1ses t5/se s)n*7s t/1n+erst*n+ t5e ,e5)-7e=s r/t*t)/ns re7*t),e t/ t5e67*t/r0. I 8/1 *++ t/ t5e 67*t/r0 * set / t5reesens)t),e *--e7er/0eters3 8/1 -*n te77 e;*-t78 95ere

t5e ,e5)-7e )s 5e*+)n *n+ 5/9 )ts 0/t)/n )s-5*n)n )n *77 t5ree +)re-t)/ns. W)t5 t5)s)n/r0*t)/n3 *n *)r67*ne=s *1t/6)7/t -*n ee6 t5e67*ne /n -/1rse3 *n+ * r/-et=s 1)+*n-e s8ste0 -*n)nsert t5e r/-et )nt/ * +es)re+ /r4)t.



A!toPi$ot

A t86)-*7 *)r67*ne 1ses 8r/s-/6es )ne,er8t5)n r/0 )ts -/06*ss t/ )ts*1t/6)7/t.

%5e R1ss)*n M)r s6*-e st*t)/n 1se+ ##8r/s-/6es t/ ee6 )ts /r)ent*t)/n t/ t5es1n3 *n+ t5e H1447e S6*-e %e7es-/6e 5*s* 4*t-5 / n*,)*t)/n*7 8r/s *s 9e77.



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Gyroscope 2of2