chapter 1_introduction to tom

8/20/2019 Chapter 1_Introduction to TOM

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INTRODUCTIONProf. Bharath V GAssistant Professor

School of Mechanical EngineeringREVA UNIVERSITY

Prof. Bharath V GSchool of ME, REVA Universit


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Beginning of T!M

• Theory of machines (TOM) has t"o #arts$ Kinematics of Machines (TOM 1) and Dynamics of Machines (TOM 2)

• In the starting of Theor of Machines "e nee% to &n%erstan% theconce#ts of ‘Kinematics’ an% ‘Dynamics’.

• Kinematics of 'echanis's is concerne% "ith the 'otion of the #arts "itho&t consi%ering ho" the infl&encing factors (force an%'ass) affect the 'otion. Therefore, *ine'atics %eals "ith thef&n%a'ental conce#ts.

• Kinetics %eals "ith action of forces on +o%ies.• Dynamics is the co'+ination of kinematics an%kinetics .• Dynamics of 'echanis's concerns the forces that act on the #arts $$

+oth +alance% an% &n+alance% forces, ta*ing into acco&nt the 'assesan% accelerations of the #arts as "ell as the e ternal forces.



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-efinition of Mechanis's

• The +asic of !M is incl&%e / Mechanisms 0 an% /Machines 0.• The "or% Mechanism has 'an 'eanings.

– In kinematics , a 'echanis' is a 'eans of transmitting,contro ing, or constraining re ati!e mo!ement .

• Move'ents "hich are electricall , 'agneticall , #ne&'aticallo#erate% are e cl&%e% fro' the conce#t of 'echanis'.

• The central theme for 'echanis's is rigi% +o%ies connecte%together + "oints .

•

A mechanism is a fundamental unit an% one has to start "ith itsst&% .

• The st&% of a 'echanis' involves its ana ysis as "ell as synthesis .



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-efinition of Machine

• A machine is a co'+ination ofrigi% or resistant +o%ies, for'e%an% connecte% %o that the'ove "ith %efinite relative

'otions an% trans'it force fro'the so&rce of #o"er to theresistance to +e overco'e.

• A 'achine has t"o f&nctions1trans'itting %efinite relative'otion an% trans'itting force .These f&nctions re2&ire

strength an% rigi%it to trans'itthe forces.



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ine'atics v3s - na'ics

Kinematics• It %eals "ith the relative

motions of %ifferent #arts of a

'echanis' "itho&t ta*ing intoconsideration the forces #ro%&cing the 'otions.

• Th&s, it is the st&% , fro' ageo'etric #oint of vie", to

*no" the displacement,velocity and acceleration of a

#art of a 'echanis'.

Dynamics• It involves the calc&lations of

forces i'#resse% on %ifferent #arts of a 'echanis'.

• The forces can +e either static ordynamic . - na'ics is f&rthers&+%ivi%e% into #inetics an$statics .

•

Kinetics is the st&% of forces"hen the %o$y is in motion"hereas statics %eals "ith forces"hen the %o$y is stationary.



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ine'atic 4in* or Ele'ent• Each #art of a 'achine, "hich 'oves relative to so'e other #art, is

*no"n as a Kinematic Link (or simply link) or element .• A lin* 'a consist of several #arts, "hich are rigi%l fastene%

together, so that the %o not 'ove relative to one another.• &or e'am e , in a reci#rocating stea' engine, as sho"n in fig&re,

#iston, #iston ro% an% crosshea% constit&te one lin* 5connecting ro%"ith +ig an% s'all en% +earings constit&te a secon$ lin* 5 cran*,cran* shaft an% fl "heel a thir$ lin* an% the c lin%er, engine fra'ean% 'ain +earings a fo rth lin*.



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T #es of 4in*

Ri id link ! ri id link is one "hich does not #nder o any deformation "hiletransmittin 'otion. Strictl s#ea*ing, rigi% lin*s %o not e ist . 6o"ever,as the %efor'ation of a connecting ro%, cran* etc. of a reci#rocating

stea' engine is not a##recia+le, the can +e consi%ere% as rigi% lin*s. $le%i&le link

! fle%i&le link is one "hich is partly deformed in a manner not to affectthe trans'ission of 'otion. 7or e a'#le, +elts, ro#es, chains an% "iresare fle i+le lin*s an% trans'it tensile forces onl .

$l#id link ! fl#id link is one "hich is formed &y havin a fl#id in a receptacle andthe 'otion is trans'itte% thro&gh the fl&i% + #ress&re or co'#ressiononl , as in the case of h %ra&lic #resses, 8ac*s an% +ra*es.



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4in* or ele'ent• Link' t is the name iven to any &ody "hich has motion relative to

another All 'aterials have so'e elasticit . A rigi% lin* is one,"hose %efor'ations are so s'all that the can +e neglecte% in%eter'ining the 'otion #ara'eters of the lin*.

• *inary in#+ 4in* "hich is connecte% to other lin*s at t"o #oints.

(7ig.a)• Ternary in#+ 4in* "hich is connecte% to other lin*s at three #oints.

(7ig.+)• aternary in#+ 4in* "hich is connecte% to other lin*s at fo&r

#oints. (7ig. c)



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Str&ct&re•

t is an assem&la e of a n#m&er ofresistant &odies (*no"n as 'e'+ers)havin no relative motion &et"een them

and meant for carryin loads havinstrainin action

• A rail"a +ri%ge, a roof tr&ss, 'achinefra'es etc., are the e a'#les of astr&ct&re.



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-ifferences +et"een a 'achine an% a str&ct&re

The follo"ing %ifferences +et"een a 'achine an% astr&ct&re are i'#ortant fro' the s&+8ect #oint of vie"1 – The #arts of a machine 'ove relative to one another,

"hereas the 'e'+ers of a str ct re %o not 'ove relative toone another. – A machine transfor's the availa+le energ into so'e &sef&l

"or*, "hereas in a str ct re no energ is transfor'e% into&sef&l "or*.

– The lin*s of a machine 'a trans'it +oth #o"er an% 'otion,"hile the 'e'+ers of a str ct re trans'it forces onl .



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9o'#arison of Mechanis', Machine an%Str&ct&re

- No. Mechanism Machine -tr ct reThere is relative'otion +et"een the

#arts of a 'echanis'

Relative 'otione ists +et"een #artsof a 'achine.

There is no relative 'otion +et"een the 'e'+ers of astr&ct&re. It is rigi% as a"hole.

/

A 'echanis' 'o%ifiesan% trans'its 'otion.

A 'achine consistsof one or 'ore'echanis's an%hence transfor's'otion

A str&ct&re %oes nottransfor' 'otion.

0

A 'echanis' %oes not

trans'it forces an%%oes not %o "or*

A 'achine

'o%ifies energ or%o so'e "or*

A str&ct&re %oes not %o

"or*. It onl trans'itsforces.

1Mechanis's are %ealt"ith in *ine'atics.

Machines are %ealt"ith in *inetics.

Str&ct&res are %ealt "ith instatics.



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ine'atic Pair

• The t"o lin*s or ele'ents of a 'achine, whenin contact with each other, are said to form a

pair.• If the relative 'otion +et"een the' is

com ete y or s ccessf y constraine$(i.e. in a definite direction ), the #air is *no"nas kinematic pair



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T #es of 9onstraine% Motions

• 7ollo"ing are the three t #es of constraine%'otions 1

– 9o'#letel constraine% 'otion – Inco'#letel constraine% 'otion – S&ccessf&ll constraine% 'otion



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9o'#letel constraine% 'otion

• :hen the 'otion +et"een a #air is li'ite% to a %efinite %irectionirres#ective of the %irection of force a##lie%, then the 'otion is sai%to +e a completely constrained motion .

– 7or e a'#le, the #iston an% c lin%er (in a stea' engine) for' a

#air an% the 'otion of the #iston is li'ite% to a %efinite %irection(i.e. it "ill onl reci#rocate) relative to the c lin%er irres#ectiveof the %irection of 'otion of the cran*.

– The motion of a square bar in a square hole an% the motion of a shaft with collars at each end in a circular hole are alsoe a'#les of co'#letel constraine% 'otion.



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Inco'#letel constraine% 'otion

• :hen the 'otion +et"een a #air can ta*e #lace in more than one$irection , then the 'otion is calle% an incompletely constrainedmotion.

• The change in the %irection of i'#resse% force 'a alter the

%irection of relative 'otion +et"een the #air.• A circular bar or shaft in a circular hole is an e a'#le of an

inco'#letel constraine% 'otion as it 'a either rotate or sli%e in ahole. These +oth 'otions have no relationshi# "ith the other.



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S&ccessf&ll constraine% 'otion• 2hen the motion %et3een the e ements, forming

a air, is s ch that the constraine$ motion is notcom ete$ %y itse f , +&t + so'e other 'eans, thenthe 'otion is sai% to +e s&ccessf&ll constraine%'otion.

• 9onsi%er a shaft in a foot4ste %earing . The shaft'a rotate in a +earing or it 'a 'ove "ar%s.This is a case of inco'#letel constraine% 'otion.

But if the load is placed on the shaft to prevent axialupward movement of the shaft, then the motion ofthe pair is said to be successfully constrained

motion.• The motion of an * en ine valve and the piston

reciprocatin inside an en ine cylinder are also thee a'#les of s&ccessf&ll constraine% 'otion.



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9lassification of ine'atic Pairs. 5ccor$ing to the ty e of re ati!e motion %et3een the e ements

a) - i$ing air%) T rning airc) - herica air$) Ro ing aire) -cre3 air

/. 5ccor$ing to the ty e of contact %et3een the e ementsa) 6o3er air%) 7igher air

0. 5ccor$ing to the ty e of c os rea) -e f4c ose$ air%) &orce$4c ose$ air



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Sli%ing #air

When the two elements of a pair are connected in such a waythat one can onl slide relative to the other, the pair is *no"nas a slidin pairThe #iston an% c lin%er, cross$hea% an% g&i%es of a

reci#rocating stea' engine, ra' an% its g&i%es in sha#er, tailstoc* on the lathe +e% etc. are the e a'#les of a sli%ing #air. Alittle consi%eration "ill sho", that a sli%ing #air has aco'#letel constraine% 'otion.



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T&rning #air +hen the t"o elements of a pair areconnected in s#ch a "ay that one canonly t#rn or revolve a&o#t a fi%ed a%isof another link , the #air is *no"n ast rning air.

S#herical #air When the two elements of a pair are connected in

such a way that one element ("ith s#herical sha#e)

t&rns or s"ivels a+o&t the other fi e% ele'ent, the #air for'e% is calle% a s herica air. The +all an% soc*et 8oint, attach'ent of a car 'irror,

#en stan% etc., are the e a'#les of a s#herical #air.



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Rolling #air +hen the t"o elements of a pair are

connected in s#ch a "ay that one rollsover another fi%ed link, the pair iskno"n as rollin pair all and roller&earin s are e%amples of rollin pair

Scre" #air +hen the t"o elements of a pair areconnected in s#ch a "ay that oneelement can t#rn a&o#t the other &yscre" threads, the pair is kno"n as scre"

pair The lead scre" of a lathe "ith n#t,and &olt "ith a n#t are e%amples of ascre" pair



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4o"er #air •

When the two elements of a pair have a surfacecontact when relative motion ta*es #lace an% thes&rface of one ele'ent sli%es over the s&rface of theother, the #air for'e% is *no"n as o3er air.

• It "ill +e seen that sli%ing #airs, t&rning #airs an%scre" #airs for' lo"er #airs.



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6igher #air •

When the two elements of a pair have a line or pointcontact when relative 'otion ta*es #lace an% the'otion +et"een the t"o ele'ents is #artl t&rningan% #artl sli%ing, then the #air is *no"n as higher

air .A #air of friction %iscs, toothe% gearing, +elt an% ro#e%rives, +all an% roller +earings an% ca' an% follo"erare the e a'#les of higher #airs.



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Self close% #air When the two elements of a pair are connected

together mechanically in such a way that onlyrequired kind of relative motion occurs , it is then*no"n as se f c ose$ air . The lo"er #airs are selfclose% #air.

7orce% close% #air When the two elements of a pair are not connectedmechanically but are kept in contact by the action ofexternal forces , the #air is sai% to +e a force4c ose$ air .The ca' an% follo"er is an e a'#le of force close% #air,as it is *e#t in contact + the forces e erte% + s#ring an%gravit .



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ine'atic 9hain• :hen the *ine'atic #airs are cole% in s&ch a "a that the

last lin* is 8oine% to the first lin* to trans'it %efinite 'otion(i.e. completely or s&ccessf&ll constraine% 'otion), it iscalle% a kinematic chain

• In other "or%s, a #inematic chain 'a +e %efine% as acombination of kinematic pairs, oined in such a way that eachlink forms a part of two pairs and the relative motion betweenthe links or elements is completely or successfully constrained .



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• The 'ost i'#ortant *ine'atic chains are those"hich consist of four lower pairs , each #air +eing asli%ing #air or a t&rning #air.

• The follo"ing three t #es of *ine'atic chains "ithfo&r lo"er #airs are i'#ortant fro' the s&+8ect

#oint of vie" 1. &o r %ar chain or 8 a$ric cyc ic chain,

/. -ing e s i$er cran# chain, an$0. Do % e s i$er cran# chain.

T #es of ine'atic 9hains



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7o&r Bar 9hain or ;&a%ric 9 cle 9hain• :e have alrea% %isc&sse% that the *ine'atic chain is a co'+ination

of fo&r or 'ore *ine'atic #airs, s&ch that the relative 'otion +et"een the lin*s or ele'ents is co'#letel constraine%.

• The si'#lest an% the &asic kinematic chain is a fo&r +ar chain or2&a%ric c cle chain, as sho"n in 7ig.

• It consists of fo&r lin*s, each of the' for's a t&rning #air at A, B, !and ". #he four links may be of %ifferent lengths.

• 5 !ery im ortant consi$eration in $esigning a mechanism is toens re that the in t cran# ma#es a com ete re!o tion re ati!eto the other in#s. The mechanism in 3hich no in# ma#es a

com ete re!o tion 3i not %e sef .• In a fo&r +ar chain, one of the lin*s, in #artic&lar the shortest lin*,

"ill 'a*e a co'#lete revol&tion relative to the other three lin*s.S&ch a lin* is *no"n as crank or driver



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• In 7ig. A- (lin* < ) is a cran# . The lin* B9 (lin* =) "hich'a*es a #artial rotation or oscillates is *no"n as e!er orroc#er or fo o3er an% the lin* 9- (lin* >) "hich connectsthe cran* an% lever is calle% connecting ro$ or co er . Thefi e% lin* AB (lin* ?) is *no"n as frame of the mechanism .

• :hen the cran* (lin*


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Grashof @s la" for a fo&r +ar 'echanis'

•

The Grashof@s con%ition for a fo&r$+ar lin*agestates that / If the sum of the shortest and longestlink of a planar four bar linkage is less than orequal to the sum of the remaining two links, thenthe shortest link can rotate fully with respect to aneighbouring link$

• 9on%ition

- 9 L : . 9 / "here % is the shortest lin*, & is the longest, an% ' an%( are the other lin*s.



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Grashof @s la" for a fo&r +ar 'echanis'

Im ortant for;5T


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• A 'echanis' is one in "hich one of the lin*s of a kinematic chainis fixed .

• -ifferent 'echanis's can +e o+taine% + fi ing %ifferent lin*s ofthe sa'e *ine'atic chain.

• These are calle% as in!ersions of the mechanism .• B changing the fi e% lin*, the n&'+er of 'echanis's "hich can

+e o+taine% is e2&al to the n&'+er of lin*s.• 0%cept the ori inal mechanism, all other mechanisms "ill +e

*no"n as inversions of ori inal mechanism .• The in!ersion of a mechanism $oes not change the motion of its

in#s re ati!e to each other.

Inversions of 'echanis'



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Inversions of fo&r +ar Mechanis'



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In this 'echanis', either lin* ? or lin* > is fi e%. 4in* =

(cran*) rotates co'#letel an% lin* < (roc*er) oscillates.

?. 9ran*$roc*er 'echanis'



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?. 9ran*$roc*er 'echanis'$*eam


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This is one t #e of %rag lin* 'echanis', "here, lin*s? > are e2&al an% #arallel an% lin*s = < are e2&alan% #arallel.

=. -o&+le cran* 'echanis'



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=. -o&+le cran* 'echanis'$ Co ing ro$ of a ocomoti!e

• #he mechanism of a co#plin ro% of aloco'otive (also *no"n as %o&+lecran* 'echanis') "hich consists offo&r lin*s, is sho"n in 7ig.

• In this 'echanis', the lin*s A" and B!)having equal length* act as cranks andare connected to the res#ective "heels.

• The lin* !" acts as a co#plin rod andthe link ! is fi%ed in order to'aintain a constant centre to centre%istance +et"een the'.

• This 'echanis' is 'eant fortrans'itting rotar 'otion fro' one"heel to the other "heel.



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In this 'echanis', lin* < is fi e%. 4in* ='a*es co'#lete rotation, "hereas lin*s > < oscillate.

>. -o&+le roc*er 'echanis'


> &+l * ' h i '$


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>. -o&+le roc*er 'echanis'$2att’s in$icator mechanism

• A Watt+s indicator mechanism (also *no"n as

2att>s straight ine mechanism or $o % e e!ermechanism ) "hich consists of fo&r lin*s, issho"n in 7ig.

• The fo&r lin*s are 1 fi e% lin* at A, lin* A9, lin*9E an% lin* B7-. It 'a +e note% that B7 an%7- for' one lin* +eca&se these t"o #arts have no

relative 'otion +et"een the'. The lin*s 9E an%B7- act as levers .

• The %is#lace'ent of the lin* B7- is %irectl #ro#ortional to the #ress&re of gas or stea' "hichacts on the indicator plunger.

• !n an s'all %is#lace'ent of the 'echanis', thetracing #oint E at the en% of the lin* 9E traces o&ta##ro i'atel a straight line.

• The initial #osition of the 'echanis' is sho"n in7ig. + f&ll lines "hereas the %otte% lines sho"the #osition of the 'echanis' "hen the gas orstea' #ress&re acts on the in%icator #l&nger.



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Single Sli%er 9ran* 9hain• A single slider crank chain is a 'o%ification of the +asic fo&r +ar chain.•

It consist of one sliding pair an% three turning pairs . It is, &s&all , fo&n% inreciprocatin steam en ine mechanism .• This t #e of 'echanis' converts rotar 'otion into reci#rocating 'otion an% vice

versa.• In a single sli%er cran* chain, as sho"n in 7ig., the lin*s ? an% =, lin*s = an% >, an%

lin*s > an% < for' three t&rning #airs "hile the lin*s < an% ? for' a sli%ing #air.• The lin* ? corres#on%s to the frame of the engine , "hich is fi'e$ . The lin* =

corres#on%s to the crank 5 lin* > corres#on%s to the connecting rod an% lin* <corres#on%s to cross head .

• As the cran* rotates, the cross$hea% reci#rocates in the g&i%es an% th&s the #istonreci#rocates in the c lin%er.


Inversions of Single Sli%er 9ran*


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Inversions of Single Sli%er 9ran*9hain

7o&r inversions of a single sli%er cran* chain are #ossi+le.

These inversions are fo&n% in the follo"ing 'echanis's.1 Reciprocatin en ine ($irst nversion)2 Oscillatin cylinder en ine (-econd nversion)

Rotary internal comstion en ine (Third nversion).end#l#m p#mp or #ll en ine ($o#rth nversion)

3 *rank and slotted lever 4#ick ret#rn motion mechanism (-econd nversion)5 +hit"orth 4#ick ret#rn motion mechanism (Third nversion)6 7and .#mps ($o#rth nversion)

(a) cran* fi e% (+) connecting ro% fi e%(c) sli%er fi e%


I i f Si l Sli% 9 *


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• &irst in!ersion+ This inversion is o+taine% "hen lin* ? (gro&n% +o% ) isfi e%.

– 5 ication4 Reci rocating engine, Reci rocating com ressoretc...

• -econ$ in!ersion+ This inversion is o+taine% "hen lin* = (cran*) isfi e%.

–

5 ication4 2hit3orth 8 ic# ret rn mechanism, Rotary engine,etc...

• Thir$ in!ersion+ This inversion is o+taine% "hen lin* > (connecting ro%)is fi e%.

– 5 ication4 - otte$ cran# mechanism, Osci atory engine etc..,• &o rth in!ersion+ This inversion is o+taine% "hen lin* < (sli%er) is

fi e%. – 5 ication4 7an$ m , en$ m m or * engine, etc...

Inversions of Single Sli%er 9ran*9hain


? R i# i i ' h i '


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?. Reci#rocating engine 'echanis'• In the first inversion, the lin* ? i.e., the c lin%er an% the

fra'e is *e#t fi e%. The fig +elo" sho"s a reci#rocatingengine.• Slotte% lin* ? is fi e%. :hen the cran* = rotates a+o&t !,

the sli%ing #iston < reci#rocates in the slotte% lin* ? .•

This 'echanis' is &se% in steam en ine, p#mps,compressors, * en ines, etc


! ill i li % i


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=. !scillating c lin%er engine• #he arrangement of oscillating c lin%er engine 'echanis', as

sho"n in 7ig., is &se% to convert reciprocating motion into rotarymotion.

• In this 'echanis', the link - forming the turning pair is fixed . Thelin* > corres#on%s to the connecting rod of a reciprocating steam

engine mechanism.• :hen the crank )link * rotates , the #iston attache% to piston rod

)link /* reciprocates an% the cylinder )link 0* oscillates a+o&t a #in #ivote% to the fi e% lin* at A.


> Rotar internal co'+&stion engine


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>. Rotar internal co +&stion engine(Gno'e engine)

• %ometimes back, rotary internal com% stion engines "ere &se% inaviation. B&t no"$a$%a s as t#r&ines are &se% in its #lace.

• It consists of seven c lin%ers in one #lane an% all revolves a+o&t fi e%centre ", as shown in 7ig., "hile the crank (link 2) is fi%ed .

• In this 'echanis', "hen the connectin rod (link ) rotates , the #iston(lin* >) reciprocates inside the cylinders formin link 1 .


< P %&l&' #&'# B&ll gi


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)

oscillates a+o&t a #in #ivote% to the fi e% lin* < at A and the pistonattached to the piston rod )link /* reciprocates .

• The %le #&'# "hich is &se% to s#l fee% "ater to +oilers havet"o #istons attache% to lin* ?, as sho"n in 7ig.


9ran* an% slotte% lever 2&ic* ret&rn 'otion


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•

It is an a##lication of secon$ in!ersion . The cran*an% slotte% lever 'echanis' is sho"n in fig&re +elo".

• This 'echanis' is &se% in shapin machines,

slottin machines and in rotary en ines .

. 9ran an% slotte% lever 2&ic ret&rn otion'echanis'


. 9ran* an% slotte% lever 2&ic* ret&rn 'otion


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• In this 'echanis' in# 0 is fi'e$ . The

s i$er ( in# ) reci rocates in osci atings otte$ e!er ( in# 1) an% cran# ( in# /)rotates .

• 4in* connects lin* < to the ra' (lin* C).The ra' "ith the c&tting tool reci#rocates

#er#en%ic&lar to the fi e% lin* >. The ra'"ith the tool reverses its %irection of'otion "hen lin* = is #er#en%ic&lar tolin*


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C. :hit"orth 2&ic* ret&rn 'otion 'echanis'• Thir$ in!ersion is o+taine% + fi ing the cran* i.e. lin* =.•

+hit"orth 4#ick ret#rn mechanism is an a##lication of thir% inversion.• This 'echanis' is sho"n in the fig&re +elo". The cran* !9 is fi e% an%

!; rotates a+o&t !. The sli%er sli%es in the slotte% lin* an% generates acircle of ra%i&s 9P. 4in* connects the e tension !; #rovi%e% on theo##osite si%e of the lin* ? to the ra' (lin* C). The rotar 'otion of P is

ta*en to the ra' R "hich reci#rocates. The 8 ic# ret rn motionmechanism is se$ in sha ers an$ s otting machines. The angle covere%%&ring c&tting stro*e fro' P? to P= in co&nter cloc*"ise %irection is D or0@A 4/ . -&ring the ret&rn stro*e, the angle covere% is / or ?.


Ra$ia engine 1 Is it sa'e as rotary en ine


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Ra$ia engine 1 Is it sa e as rotary en ine


F 6 % #&'#


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+ater hand p#mps are 'an&all o#erate% #&'#s

The are &se% for +ringing "ater fro' earth &n%ergro&n% to earths&rface an% is &se% in ever co&ntr for a variet of in%&strial,'arine, irrigation an% ho&sehol% #&r#oses.

F. 6an% #&'#s

I'age sho"n +elo" is the t #ical%esign of 6an% P&'#.


o&+le$Sli%er cran* chain


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• It consists of fo#r pairs o&t of "hich two are turning pairs an% twoothers are sli%ing #airs.

• Also the t"o #airs of the sa'e *in% are a%8acent.• Do#&le8slider crank chain is sho"n in 7ig• 6in# an$ in# / is s i$ing air , in# / an$ in# 0 is t rning air ,

in# 0 an$ in# 1 is secon% t rning air , in# 1 an$ in# issecon% s i$ing air .

• 6ence there are t3o t rning airs an%t3o s i$ing airs .• Also the #airs of the sa'e *in% are a%8acent.

-o&+le$Sli%er cran* chain


Inversions of %o&+le sli%er cran*


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Inversions of %o&+le sli%er cran'echanis'

• Elli#tical tra''els• Scotch o*e 'echanis'• !l%ha'@s coling


? Elli#ti l t '' l


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• It is an instr#ment #sed for dra"in ellipses . #his inversion is obtained +fi ing the slotte% #late (lin*


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The lin* ? an% lin* >, are *no"n as sli%ers an% for' sli%ing #airs "ith lin* sli%e along their res#ective grooves, an #oint on the lin* =s&ch as ' traces out an ellipse on the surface of link 0, as shown in 1ig. ! littleconsideration "ill sho3 that !. and . are the semi8ma9or a%is and semi8minora%is of the ellipse respectively

?. Elli#tical tra''els


Scotch o*e 'echanis'


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• The -cotch yo#e is a 'echanis' for

converting the inear motion of a s i$erinto rotationa motion or !ice4!ersa .The #iston or other reci#rocating #art is%irectl cole% to a sli%ing o*e "ith aslot that engages a #in on the rotating

#art. • This mechanism is #sed for convertin

rotary motion into a reci rocatingmotion . The inversion is o+taine% +fi ing either the lin* ? or lin* >. In 7ig.lin* ? is fi e%.

• In this 'echanis', "hen the lin* =("hich corres#on%s to cran*) rotatesa+o&t B as centre, the link 1 ("hichcorres#on%s to a fra'e) reci#rocates.

• The fi'e$ in# g i$es the frame .

=. Scotch o*e 'echanis'


> !l%ha'@s coling


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!n oldham:s co#plin is &se% for connecting t"o #arallel shafts"hose a es are at a s'all %istance a#art. The shafts are cole% ins&ch a "a that if one shaft rotates, the other shaft also rotates atthe sa'e s#ee%.

– This inversion is o+taine% + fi ing the lin* =, as sho"n in 7ig (a) . – #he shafts to be connected have two flanges (lin* ? an% lin* >)

rigi%l fastene% at their en%s + forging. – The lin* ? an% lin* > for' t&rning #airs "ith lin* =.

>. !l%ha'@s coling


> !l%ha'@s coling


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>. !l%ha'@s colingThese flanges have %ia'etrical slots c&t in their inner faces, as sho"n in 7ig.

(b*.The intermediate piece (link ) which is a circ#lar disc , have t"o tong&es ( i.e.diametrical pro ections* # ? an% # = on each face at right angles to each other, assho"n in 7ig.The ton #es on the link closely fit into the slots in the t"o flan es (link 1and in# 0) . The link can slide or reciprocate in the slots in the flanges.


-egrees of free%o'3'o+ilit of a


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• It is the n m%er of in ts (n m%er of in$e en$entcoor$inates) re2&ire% to %escri+e the config ration or

osition of a the in#s of the mechanism , "ith res#ect tothe fi'e$ in# at an given instant.

• ;r % er’s e8 ation or K tE%ach Criterion &or F anarMechanism + N&'+er of %egrees of free%o' of a 'echanis'is given +

:here n total %egrees of free%o' in the 'echanis'l n&'+er of lin*s (incl&%ing the fra'e)

N&'+er o e2&ivalent +inar 8oints h n&'+er of higher #airs (t"o %egrees offree%o')

-egrees of free%o 3 o+ilit of a'echanis'




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BASE- !N T6E P!SSIB4E M!TI!NS(7e" I'#ortant T #es onl )

egrees of free%o 3 o+ilit of a'echanis'

- No. Name of Fair 6etter -ym%o D.O.&

? Re!o te = T rning Fair R

= Frismatic = - i$ing Fair P

> 7e ica = -cre3 Fair 6

< Cy in$rica Fair 9 /

- herica = ; o% ar Fair S (or G) 0

C & at = F anar Fair E 0

F Cy in$ric F ane Fair 9# 1

H - heric F ane Fair S# G




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egrees of free%o 3 o+ilit of a'echanis'


egrees of free%o'


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?. The 'echanis', as sho"n in 7ig. )a*, has three lin*san% three +inar 8oints, i.e. l2 > an% 8 >.

n H 0 (04 )4/'0HAThis is -tr ct re

=. The 'echanis', as sho"n in 7ig. )b*, has fo&r lin*san% fo&r +inar 8oints, i.e. l2 < an% 8


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N&'+er of lin*s, l F

N&'+er of E2&ivalent +inar 8oints, + H N&'+er of 6igher #airs, h J$of H 0( l 4 ) B / % Bh >(F$?) K = H K J ?H K ?C

H /

N&'+er of lin*s, l L N&'+er of E2&ivalent +inar 8oints, + ?J

N&'+er of 6igher #airs, h J$of H 0( l 4 ) B / % Bh >(L$?) K = ?J K J =< K =J H 1

-egrees of free%o


egrees of free%o'


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N&'+er of lin*s, l < N&'+er of E2&ivalent +inar 8oints, + <

N&'+er of 6igher #airs, h ?$of H 0( l 4 ) B / % Bh >(


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N&'+er of lin*s, l ?? N&'+er of E2&ivalent +inar 8oints, + ? N&'+er of 6igher #airs, h J$of H 0( l 4 ) B / % Bh >(??$?) K = ? K J >J K >J K J H A

N&'+er of lin*s, l < N&'+er of E2&ivalent +inar 8oints, + > N&'+er of 6igher #airs, h ?$of H 0( l 4 ) B / % Bh >( K ? L K C K ? H /

-egrees of free%o


egrees of free%o'


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(a)

N&'+er of lin*s, l N&'+er of E2&ivalent +inar 8oints, + N&'+er of 6igher #airs, h $of H 4

(+)

N&'+er of lin*s, l N&'+er of E2&ivalent +inar 8oints, + N&'+er of 6igher #airs, h $of H

(c) N&'+er of lin*s, l N&'+er of E2&ivalent +inar 8oints, + N&'+er of 6igher #airs, h $of H A

Solve this

-egrees of free%o


egrees of free%o'


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-egrees of free%o


-egrees of free%o'


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-egrees of free%o


-egrees of free%o'


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-egrees of free%o


-egrees of free%o'


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n C

P ? F

P = J7 > (C K ?) K = F K ? J

? K ?< K J

H

This is a Constraine$ Mechanism.

-egrees of free%o


G & +l @ 9 it i


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Gr&e+ler@s 9riterion

This criterion is &se% to fin% o&t "hether anasse'+l of lin*s "ith ? %.o.f. lo"er #airs is aconstraine% 'echanis' or not.

0n B / B 1 H A n K no. of lin*s l K no. of lo"er #airs "ith

one %.o.f


egrees of free%o' (7 or n)


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-egrees of free%o (7 or n)

7 J Pre$loa%e% str&ct&re Ser str&ct&re

7 J Str&ct&re

7 ? 9onstraine% Mechanis'

7 ? Unconstraine% Mechanis'


-egrees of free%o' (7 or n)


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9onstraine% Mechanis' (7 ?)

Unconstraine% Mechanis' (7 ?)

-egrees of free%o (7 or n)


E a'#le


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E a #le



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Than# Jo

chapter 1_introduction to tom

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