kom Unit-I

8/16/2019 kom Unit-I

1/18

Unit I: Basics of Mechanisms KOMUnit I: Basics of Mechanisms

Classification of mechanism-Basic kinematic concepts and definitions-degree of freedom, Mobility-Kutzbach criterion, ruebler!s criterion- rashof!s "a#-Kinematic in$ersions of four bar chain and slider crank chains-"imit positions-Mechanical ad$antage-%ransmission angle-&escription of some commonmechanisms-'uick return mechanisms, (traight line generators, Uni$ersal

)oint-*ocker mechanisms

Mechanism:Mechanism is combinations of number of bodies (usually rigid bodies) are

assembled in such a way that the motion of one causes constrained and predictablemotion to the others. A mechanism transmits and modifies a motion.

Machine:A Machine is a mechanism or combination of mechanisms imparting

definite motions to the parts. Also, it transmits and modifies the available mechanicalenergy into desired (or useful) work.

*igid and *esistance bodies:

Rigid body: A rigid body does not suffer any distortion (or the distance between anytwo points on it remains constant) under the action of force.

Resistance body or semi-rigid body: A Resistant body or semi-rigid body arenormally fle ible under the action of force.

!ut resistance bodies, under certain loading conditions, act as rigid bodies for thelimited purpose.

(".g.) !elt, #luids and $pring etc A !elt is rigid when sub%ected to tensile forces. &herefore, the belt-drive acts as aresistant body.

$imilarly, fluids can also act as resistant bodies when compressed as in case of ahydraulic press.

#or some purposes, springs are also resistant bodies.

"ink:• A resistant body or a group of resistant bodies with rigid connections

preventing their relative movement is known as a link.

• A link may also be defined as a member or a combination of members of amechanism, connecting other members and having motion relative to them.&hus, a link may consist of one or more resistant bodies.

• A link is also known as kinematic link or element.

• 'inks can be classified into binary, ternary, quaternary, etc. ependingupon their ends on which revolute or turning pairs can be placed.

!inary link &ernary link uaternary link

KI+ M %IC . I* A kinematic pair or simply a pair is a %oint of two links having relative motion

between them.

*n a slider-crank mechanism link + rotates relative to link and constitutes arevolute or turning pair. $imilarly, links +, and , constitute turning pairs. 'ink (slider) reciprocates relative to link and is a sliding pair.

%ypes of Kinematic .airs/inematic pairs can be classified according to01 2ature of contact31 2ature of mechanical constraint31 2ature of relative motion.

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2/18

Unit I: Basics of Mechanisms KOMKinematic .airs ccording to +ature of Contact/a0 "o#er .air A pair of links having surface or area contact between the members is known asa lower pair. &he contact surfaces of the two links are similar. " amples0 2ut turning on a screw, shaft rotating in a bearing, all pairs of aslider-crank mechanism, universal %oint, etc./b0 1igher .air 4hen a pair has a point or line contact between the links, it is known as a higher

pair. &he contact surfaces of the two links are dissimilar. " amples0 4heel rolling on a surface, cam and follower pair, tooth gears, balland roller bearings, etc.

Kinematic .airs ccording to +ature of Mechanical Constraint/a0 Closed .air

/b0Unclosed pair

Kinematic .airs ccording to +ature of *elati$e Motion

/a0 Sliding Pair

/b0 Turning .air

(c) Rolling .air

(d) Screw .air (Helical .air0

/e0(pherical pair


4hen the elements of a pair are heldtogether mechanically, it is known as a closed pair.&he two elements are geometrically identical3 oneis solid and full and the other is hollow or open.&he latter not only envelops the former but alsoencloses it. &he contact between the two can be

broken only by destruction of at least one of themembers. All the lower pairs and some of thehigher pairs are closed pairs. A cam and follower

pair (higher pair) shown in #igure and a screw pair (lower pair) belong to the closed pair category.

4hen two links of a pair are in contact either due toforce of gravity or some spring action they constitutean unclosed pair. *n this, the links are not heldtogether mechanically, e.g. carn and follower pair

shown in figure.

*f two links have a sliding motion relative to each other,they form a sliding pair. A rectangular rod in a rectangular hole in a prism is asliding pair.

4hen one link has a turning or revolving motion relative tothe other, they constitute a turning or revolving pair. *n a slider-crank mechanism, all pairs e cept the slider andguide pair are turning pairs. A circular shaft revolving inside a

bearing is a turning pair.

4hen the links of a pair have a rolling motion relative toeach other, they form a rolling pair, e.g. a rolling wheel on aflat surface, ball and roller bearings, etc. *n a ball bearing, the ball and the shaft constitute onerolling pair, whereas the ball and the bearing is the secondrolling pair.



*f two mating links have a turning as well as slidingmotion between them, they form a screw pair. &his isachieved by cutting matching threads on the two links. &he lead screw and the nut of a lathe is a screw pair.

4hen one link in the form of a sphere turns inside afi ed link, it is a spherical pair. &he ball and socket %oint is a spherical pair.


3/18

Unit I: Basics of Mechanisms KOM& * ( 23 3* &2MAn unconstrained rigid body moving in spacecan describe the following independentmotions

. &ranslational motions along any threemutually perpendicular a es x, y and 5,

+. Rotational motions about these a es.&hus, a rigid body possesses si degreesof freedom. &he connection of a link withanother imposes certain constraints on their relative motion.

Degrees of freedom of a pair is defined as the number of independent relati$emotions, both translational and rotational, a pair can ha$e4

egrees of freedom 6 7 - 2umber of restraints

*n general egree of freedom is defined as the number of independent coordinatesre8uired to specify the position of point in a space uni8uely.

C" ((I3IC %I2+ 23 KI+ M %IC . I*( epending upon the number of restraints imposed on the relative motion of thetwo links connected together, a pair can be classified as given in &able which givesthe possible form of each class.

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4/18

Unit I: Basics of Mechanisms KOMKinematic Chain: A kinematic chain is an assembly of links in which the relative motions of thelinks is possible and the motion of each relative to the other is definite.

+on-Kinematic chain: &he motion of a link results in indefinite motions of other links, then it is a nonkinematic chain.

*edundant chain: A redundant chain does not allow any motion of a link relative to the other link.

"inkage: A linkage is obtained if one of the links of a kinematic chain is fi ed to the ground.

(tructure*f one of the links of a redundant chain is fi ed, it is known as a structure

(uperstructure:&he degree of freedom of a structure with negative degree of freedom is known as a

superstructure.

M2BI"I%5 23 M C1 +I(M(:

Mobility is also known as egrees of freedom of a Mechanism.

A mechanism may consist of a number of pairs belonging to different classes havingdifferent number of restraints. *t is also possible that some of the restraints imposedon the individual links are common or general to all the links of the mechanism.

According to the number of these general restraints a mechanism may be classifiedinto different order.A zero order mechanism will have no such general restrain. 9f course, some of the

pairs may have individual restraints.A first order mechanism has one general restraint3A second order mechanism has two general restraints and so on up to fifth ordermechanismA si th order mechanism cannot e ist since all the links become stationary and nomovement is possible.

egrees of freedom of a mechanism in space can be determined as follows0 2 6 total number of links in a mechanism3# 6 degrees of freedom3: 6 number of pairs having one degree of freedom3: + 6 number of pair having two degrees of freedom and so on.

*n a mechanism, one link is fi ed.&herefore,

2umber of movable links 6 2 - 3 2umber of degrees of freedom of (2 - ) movable links 6 7(2 - ) "ach pair having one degree of freedom imposes ; restraints on themechanism reducing its degrees of freedom by ;: . "ach pair having two degrees of freedom will impose restraints reducing thedegrees of freedom of the mechanism by : +.

$imilarly, other pairs having , and ; degrees of freedom reduce the degreesof freedom of the mechanism.&hus, 3 6 7 /+ - 80 - 9. l - . ; - s criterion: &wo-dimensional mechanism such as a four-link or a slider-crank mechanism inwhich displacement is possible along two a es (one restraint) and rotation about onlyone a is (two restraints). &hus, there are three general restraints.

&herefore, for plane mechanisms, the following relation may be used to find thedegrees of freedom, 3 6 < /+ - 80 - ;. l = 8. ; &his is known as


5/18

Unit I: Basics of Mechanisms KOMmpirical *elations:

&he following empirical relations give the degree of freedom of a linkage when thenumber of links and number loops in a kinematic chain is known. &hese relations are valid for linkages with turning pairs, # 6 2 - (+' ? ) : 6 2 ? (' - )4here ' 6 2umber of loops in a linkage.+ote:

&he above empirical relations can give incorrect results. &his is due to the reasonthat the lengths of the links or other dimensional properties are not considered inthese empirical relations. $o, e ceptions are bound to come with e8ual lengths or

parallel links.

.roblems:84 3or the kinematic linkages sho#n in 3igure, calculate the follo#ing: thenumber of binary links /+b0? the number of ternary links /+ t0? the number of other /@uaternary etc40 links /+ o0? the number of total links /+0? the number of loops /"0? the number of )oints or pairs /. 80? +umber of degrees of f reedom /30

(olution:

(a) 2 b 6 3 2 t 6 3 2 o 6 >3 2 6 @3 ' 6 3 : 6 by counting (or): 6 (2 ? ' - ) 6

Kutzbach criterion mpirical *elation

# 6 (2 - ) +: or # 6 2 - (+' ? )

6 (@ - ) (+ B ) or 6 @ - (+ B ? ) 6 - or 6 -&he linkage has negative degree of freedom and thus it is a superstructure4

(b) 2 b 6 3 2 t 6 3 2o 6 >3 2 6 @3 ' 6 : 6 > (by counting) or : 6 (2 ? ' - ) 6 >

Kutzbach criterion: mpirical relation: # 6 (2 - ) -+: # 6 2 - (+' ? ) 6 (@ - ) (+B >) 6 @ ((+ B ) ? )

6 6 ( i.e.) &he linkage has one degree of freedom. &hus it is completely constrainedmotion when one of the seven moving links is driven by an e ternal source.

(c) 2 b 6 C3 2 t 6 +3 2 o 6 +3 2 6 3 ' 6 ;3 : 6 ;

Kutzbach criterion: mpirical relation: # 6 (2 - ) -+: # 6 2 - (+' ? ) 6 ( - ) (+B ;) 6 ((+ B ;) ? )

6 > 6 >&herefore, the linkage is a $tructure.

;4 &etermine the degrees of freedom of the follo#ing:

(a) (b)

(olution:(a) 2o.of links 2 6

2o.of pairs with 9# : 6 + 2o.of pairs with + 9# : +6

ruebler!s criterion:&egrees of freedom 3 6


6/18

Unit I: Basics of Mechanisms KOM32U*-B * C1 I+:

3ig /80• A four-bar chain is the most fundamental of the plane kinematic chains.• !asically, it consists of four rigid links which are connected by four pin-%oints.• A link that acts as frame is called fiAed link4• A link that makes complete revolution is called the crank4• &he link opposite to the fi ed link, the coupler and• &he fourth link, a le$er or rocker if oscillates (another crank, if rotates)

rashof!s la#:


7/18

Unit I: Basics of Mechanisms KOM Elass ** Mechanisms not generate different nature of mechanism.M C1 +IC " &D +% &he Mechanical Advantage (M.A.) of a mechanism is the ratio of the output forceor tor8ue to the input force or tor8ue at any instant.

#or the linkage of #ig (;) below, if friction and inertia forces are ignored and theinput tor8ue & + is applied to link + to drive the output link with a resisting tor8ue &then

3ig4 /90:ower input 6 :ower output &+ K+ 6 & K

Mechanical Advantage+

+

.ω

ω ==T

T A M

&hus, Mechanical Advantage (M.A) is the reciprocal of the velocity ratio.*n crank-rocker mechanisms, the velocity (K ) of the output link E (rocker)

becomes 5ero at the e treme positions. 4hen the input link AB is in line with the coupler BC and angle L between themis either 5ero or @> which makes the mechanical advantage to be infinite at such

positions. 9nly a small input tor8ue can overcome a large output tor8ue load.&he e treme positions of the linkage are known as toggle positions.

%* +(MI((I2+ + " : &he angle ( μ) between the output link and the coupler is known as transmissionangle.

3ig4 /70

*n Fig.( ) , if link AB is the input link, the force applied to the output link E istransmitted through the coupler BC.

#or a particular value of force in the coupler rod, the tor8ue transmitted to theoutput link (about point ) is ma imum, when the transmission angle μ is N> .

*f links BC and E become coincident, the transmission angle is 5ero and themechanism would lock or %am.

*f μ deviates significantly from N> , the tor8ue on the output link decreases.$ometimes it may not be sufficient to overcome the friction in the system and themechanism may be .locked or Oammed. Pence μ is usually kept more than ; .

&herefore, the best mechanisms have a transmission angle that does not deviatemuch from N> >. Applying cosine law to triangles AB! and BC! (#ig. 7),

+++ cos+ k a" " a =−+ θ +++ cos+ k bccb =−+ µ

#rom (i) and (ii), µ θ cos+ cos+ ++++ bccba" " a −+=−+>cos+cos+++++ =+−−−+ µ θ bca" cb" a

&he ma imum or minimum values of the transmission angle can be found by putting"μ#"$ e8ual to 5ero.

ifferentiating the above e8uation with respect to $ ,

>dQdR

sin bcsinQad =− µ

µ θ

sin bcsinad

dQdR

=

&hus, if d SdQis to be 5ero, the term a" sin$ %as to be 5ero which means Q iseither > or @> . *t can be seen that μ is ma imum when $ is @> and minimumwhen $ is > .

Powever, this would be applicable to the mechanisms in which the link a is ableto assume these angles, i.e. in double-crank or crank rocker mechanisms.

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8/18

Unit I: Basics of Mechanisms KOM

3ig4E 3ig4F

#ig.C and #ig.@ show a crank-rocker mechanism indicating the positions of thema imum and the minimum transmission angles.

3ig4G 3ig48H#ig.N and #ig. > show the ma imum and the minimumT transmission angles for adouble-rocker mechanism.

.roblems:


9/18


10/18

Unit I: Basics of Mechanisms KOMMa imum transmission angle is when Q is @>> as shown in figure below&hus (a ? ") & 6 b& ? c + '&bc E9$ μ (C? @)+ 6 7 + ? > + (+ B 7 B >cos μ) ++;6 7 ? >> - +> cos

C +.>,+>@N

cos −=−= µ 6 C.N>

Minimum transmission angle is when the angle at ! is @> > shown in figure below&hus ( ") & 6 (a? b)& ? c + '&(a b)c E9$ μ (@)+ 6 (C?7) + ? > + H+ (C?7) B >cos μ 7 6 7N ? >> - +7> cos

C@@.>+7>+>;

cos == µ 6 @>

/c0 In this mechanism, 'ength of the longest link 6 C3

'ength of the shortest link 6 3

'ength of other links 6 7 and C.

$ince C ? F 7 ? 7, it belongs to class-*mechanism.

*n this case as the shortest link is fi ed, it is adouble-crank

or drag-link mechanism.

Ma imum transmission angle is when Q is @>> as shown in figure below&hus, (a ? ") & 6 b& ? c + - &bc cos μ(7 ? ) + 6 7 + ? C + H+ B 7 B C cos μ@ 6 7 ? N - @ cos μ

@cos = µ cos μ * >. C7

μ 6 @C.+C>

Minimum transmission angle is when Q is >> as shown in figure below&hus, (a - ") & 6 b& ? c + - &bc cos μ

(7 - ) + 6 7 + ? C + H+ B 7 B C cos μ N 6 7 ? N - @ cos μ

@C7

cos = µ cos μ * >.N> @ μ 6 +;.+ >

In$ersion of 3our bar chain:(i) !eam "ngine Mechanism(ii ) Eoupling rod of locomotive(iii) 4att *ndicatorDs Mechanism

/i0 Beam ngine Mechanism:

• A part of the mechanism of a beam engine which consist of four links, isshown is figure.

• Ad%acent link to the shortest link is fi ed. &herefore, the mechanism alsoknown as Erank-'ever Mechanism.

•

*n this mechanism, when the crank rotates about the fi ed centre A, thelever oscillates about a fi ed centre .• &he end " of the lever E " is connected to a piston rod which reciprocates

due to the rotation of the crank.• *n other words, the purpose of this mechanism is to convert rotary motion

into reciprocating motion.

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11/18

Unit I: Basics of Mechanisms KOMCoupling rod of a locomoti$e:

• &he mechanism of a coupling rod of a locomotive which consist of four link as shown in figure.

• &he mechanism also known as double crank mechanism.• *n this mechanism, the links A and !E having e8ual length.• A and !E are act as crank and connected to the respective wheels.• &he link E acts as a coupling rod and the link A! is fi ed in order to

maintain a constant centre to centre distance between them.• &his mechanism is mean for transmitting rotary motion from one wheel to

the other wheel.att!s indicator mechanism:

• A 4attDs indicator mechanism also known as wattDs straight line mechanismor double lever mechanism.

• *t consists of four links is shown in figure.• &he four links are 0

#i ed link A 'ink AE 'ink E" 'ink !# .

• *t may be noted that !# and # form on link because these two parts haveno relative motion between them.

• &he links E" and !# act as levers. &he displacement of the link !# isdirectly proportional to the pressure of gas or stream which acts on theindicator plunger.

• 9n any small displacement of the mechanism, the tracing point " at the endof the link E" trances out appro imately a straight line.

• &he initial position of the mechanism is shown in figure by full lines

whereas the dotted lines show the position of the mechanism when the gasor stream pressure acts on the indicator plunger.

("I& *-C* +K C1 I+: A single slider crank chain is a modification of the basic four bar chain. *t consistof one sliding pair and three turning pairs. *t is, usually, found in reciprocating steamengine mechanism. &his type of mechanism converts rotary motion into reciprocating motion andvice versa. *n a single slider crank chain, as shown in #igure , the links and +,links + and , and links and form three turning pairs while the links and forma sliding pair.

3ig488

&he link corresponds to the frame of the engine, which is fi ed. &he link +corresponds to the crank3 link corresponds to the connecting rod and link corresponds to cross-head. As the crank rotates, the cross-head reciprocates in theguides and thus the piston reciprocates in the cylinder.

In$ersions of (ingle (lider Crank Chain!y fi ing different links in a kinematic chain, an inversion is obtained and can obtainas many mechanisms as the links in a kinematic chain. *t is thus obvious, that four



12/18

Unit I: Basics of Mechanisms KOMinversions of a single slider crank chain are possible. &hese inversions are found inthe following mechanisms.

84 .endulum pump or Bull engine 0*n this mechanism, the inversion is obtained by fi ing the cylinder or link (i.e.

sliding pair), as shown in #ig. +. *n this case, when the crank (link +) rotates, theconnecting rod (link ) oscillates about a pin pivoted to the fi ed link at A and the

piston attached to the piston rod (link ) reciprocates. &he duple pump which is

used to supply feed water to boilers have two pistons attached to link , as shown in#ig. +.

3ig48; 3ig48<

;4 2scillating cylinder engine .&he arrangement of oscillating cylinder engine mechanism, as shown in

#ig. , is used to convert reciprocating motion into rotary motion. *n thismechanism, the link forming the turning pair is fi ed. &he link corresponds to theconnecting rod of a reciprocating steam engine mechanism. 4hen the crank (link +)rotates, the piston attached to piston rod (link ) reciprocates and the cylinder (link )oscillates about a pin pivoted to the fi ed link at A.


13/18

Unit I: Basics of Mechanisms KOMdirection. &he return stroke occurs when the crank rotates from the position CB+ toCB (or through angle V) in the clockwise direction. $ince the crank has uniformangular speed, therefore,

α

α β

β α β −

−==

-7>)(

-7>strokereturnof &imestrokecuttingof &ime

or

$ince the tool travels a distance of + during cutting and return stroke, thereforetravel of the tool or length of stroke 6 + 6 + + + 6 + + - 6 + A+ sin WX + A-

+cos+

+N>sin+ ,

α α A+ A+ =

−= (A: 6A:)

AC

CB A+ ,

,+ ×= = AC CB

,

+cos

α

AC

CB A+ ×= + (E B 6E!)

+ote: #rom #ig. ;, we see that the angle U made by the forward or cutting stroke isgreater than the angle VX Xdescribed by the return stroke. $ince the crank rotates withuniform angular speed, therefore the return stroke X completed within shorter time.&hus it is called 8uick return motion mechanism.

94 hit#orth @uick return motion mechanism: &his mechanism is mostly used in shaping and slotting machines. *n thismechanism, the link E (link +) forming the turning pair is fi ed, as shown in#ig. 7. &he link + corresponds to a crank in a reciprocating steam engine. &hedriving crank EA (link ) rotates at a uniform angular speed. &he slider (link )attached to the crank pin at A slides along the slotted bar :A (link ) which oscillatesat a pivoted point . &he connecting rod :R carries the ram at R to which a cuttingtool is fi ed. &he motion of the tool is constrained along the line R produced, i.e.along a line passing through and perpendicular to E .

3ig487

4hen the driving crank CA moves from the position CA to CA+ (or the link !+ from the position !+ to !+ +) through an angle V (in the clockwise direction,the tool moves from the left hand end of its stroke to the right hand end through adistance + +! .

2ow when the driving crank moves from the position CA+ to CA (or the link !+ from !+ + to !+ ) through an angle U in the clockwise direction, the tool moves back from right hand end of its stroke to the left hand end. A little consideration will show that the time taken during the left to rightmovement of the ram ( i.e. during forward or cutting stroke) will be e8ual to the timetaken by the driving crank to move from CA to CA+. $imilarly, the time takenduring the right to left movement of the ram (or during the idle or return stroke) will

be e8ual to the time taken by the driving crank to move from CA+ to CA . $ince the crank link CA rotates at uniform angular velocity therefore time taken

during the cutting stroke (or forward stroke) is more than the time taken during thereturn stroke. *n other words, the mean speed of the ram during cutting stroke is lessthan the mean speed during the return stroke. &he ratio between the time takenduring the cutting and return strokes is given by

β β

α α

β α −

−==

-7>)(

-7>strokereturnof &imestrokecuttingof &ime

or

+ote4 *n order to find the length of effective stroke +, mark + 6 + + + 6 + .&he length of effective stroke is also e8ual to + +!

&ouble (lider Crank ChainA kinematic chain which consists of two turning pairs and two sliding pairs is knownas double slider crank c ain , as shown in #ig. C. &he link + and link form oneturning pair and link + and link form the second turning pair. &he link and link form one sliding pair and link and link form the second sliding pair.

In$ersions of &ouble (lider Crank Chain



14/18

Unit I: Basics of Mechanisms KOM&he following three inversions of a double slider crank chain are important from thesub%ect point of view084 !lli"tical trammels . *t is an instrument used for drawing ellipses. &his inversion isobtained by fi ing the slotted plate (link ), as shown in #ig. C. &he fi ed plate orlink has two straight grooves cut in it, at right angles to each other. &he link andlink , are known as sliders and form sliding pairs with link . &he link AB (link +) isa bar which forms turning pair with links and . 4hen the links and slide alongtheir respective grooves, any point on the link + such as + traces out an ellipse on the

surface of link , as shown in #ig. C. A little consideration will show that A+ and B+ are the semi-ma%or a is and semi-minor a is of the ellipse respectively. &his can be proved as follows

3ig48E 3ig48F 'et us take / and 0 as hori5ontal and vertical a es and let the link BA isinclined at an angle with the hori5ontal, as shown in #ig. @. 2ow the co-ordinates ofthe point + on the link BA will be x * +- * A+ cos Q3 and y * + * B+ sin Q

or sinQ!:y

and cosQA:

==

s8uaring on both sides

,Qsincos!:y

A:

++

+

+

+

+

=+=+ θ

&his is the e8uation of an ellipse. Pence the path traced by point + is an ellipsewhose semi ma%or a is is A+ and semi-minor a is is B+ .

+ote : *f + is the mid-point of link BA, then A+ 6 B+ . &he above e8uation can bewritten as

,A:y

A: +

+

+

+

=+ or +++ A:y =+&his is the e8uation of a circle whose radius is A+ . Pence if + is the mid-point of link

BA, it will trace a circle.

;4 Scotc yoke mec anism 0

3ig48G &his mechanism is used for converting rotary motion into a reciprocating motion.&he inversion is obtained by fi ing either the link or link .

*n #ig. N, link is fi ed. *n this mechanism, when the link + (which corresponds tocrank) rotates about B as centre, the link (which corresponds to a frame)reciprocates. &he fi ed link guides the frame.


15/18


3ig4;H /a0 3ig4;H/b0 3ig4;H/c0

An 9ldhamDs coupling is used for connecting two parallel shafts whose a esare at a small distance apart. &he shafts are coupled in such a way that if one shaftrotates, the other shaft also rotates at the same speed. &his inversion is obtained byfi ing the link +, as shown in #ig.+> (a). &he shafts to be connected have two flanges(link and link ) rigidly fastened at their ends by forging. &he link and link form turning pairs with link +. &hese flanges havediametrical slots cut in their inner faces, as shown in #ig. +> ( b). &he intermediate

piece (link ) which is a circular disc, have two tongues ( i.e. diametrical pro%ections)& and &+ on each face at right angles to each other, as shown in #ig.+>( c).&he tongues on the link closely fit into the slots in the two flanges (link and link

). &he link can slide or reciprocate in the slots in the flanges.

4hen the driving shaft A is rotated, the flange C (link ) causes the intermediate piece (link ) to rotate at the same angle through which the flange has rotated, and itfurther rotates the flange ! (link ) at the same angle and thus the shaft B rotates.Pence links , and have the same angular velocity at every instant. A littleconsideration will show that there is a sliding motion between the link and each ofthe other links and .

*f the distance between the a es of the shafts is constant, the centre of intermediate piece will describe a circle of radius e8ual to the distance between the a es of thetwo shafts. &herefore, the ma imum sliding speed of each tongue along its slot ise8ual to the peripheral velocity of the centre of the disc along its circular path.

'et K6 Angular velocity of each shaft in radSs, andr 6 istance between the a es of the shafts in metres.

Ma imum sliding speed of each tongue (in mSs), 1 6 K r

.art-

. $tate the difference between mechanism and structure.(MaySOune +> , R+>>@S+> >)

+. ifferentiate the machine and structure (MaySOune +> , R+>>@S+> >). Elassify the constraint motion (MaySOune +> , R+>>@S+> >). 4hat is meant by /inematic :airY (MaySOune +> , R+>>@S+> >)

;. ifferentiate rotation and translation. (2ovS ec +> , R+>>@S+> >)7. efine sliding connectors. (2ovS ec +> , R+>>@S+> >)C. efine the term egree of freedom. (MaySOune +> , R+>> S+>>C)@. #ind the degree of freedom of a Eam mechanism with knife-edge follower.(2ovS ec +> , R+>> S+>>C)N. etermine the degree of freedom for the linkage shown in #igure.

Department of Mechanical, AAMEC Page 1"


16/18

Unit I: Basics of Mechanisms KOM (2ovS ec +> , R+>> S+>>C)

>. 4rite +, R+>>@). efine0 Mechanical advantage. (2ovS ec +> , R+>> S+>>C)

+. efine the term Z&ransmission angle[ of a mechanism. (2ovS ec +> ,R+>> S+>>C)

. $ketch and define transmission angle of a four bar mechanism. 4hat are theworst values of transmission angleY (MaySOune +> +, R+>>@)

. 4hat are the three conditions to obtain a four bar drag-link mechanismY

(MaySOune +> , R+>> S+>>C);. 4hat are condition for correct steering of an automobile (MaySOune +> +,R+>>@)

.art-B

84 &etermine the degree of freedom for follo#ing linkages4 (7) (2ovS ec +> ,R+>>@S+> >)

;4 Aplain kutzbach criterion for the mobility of a mechanism #ith suitableeAample ( ) (MaySOune +> +, R+>>@)

, R+>> S+>>C)

4 Identify the type of mechanisms sho#n in 3ig /a0 to 3ig /d0, #hether it iscrank-rocker or double-crank or double-rocker and )ustify the ans#er4 %hedimensions are pro$ided in standard units of length4 /F0

(2ovS ec +> , R+>> S+>>C)

3ig4/a0 3ig4/b0 3ig4/c0 3ig 4/d0

94 M8, M;, M< and M are four-bar linkages as sho#n in figure4 %he numberson the figure indicate the respecti$e link lengths in cm4

imensions are in cm

Identify the nature of the mechanism, i4e4 #hether double crank, crank rockeror double rocker4 i$e reason in brief4 ( +) (MaySOune +> +, R+>>@)

Department of Mechanical, AAMEC Page 1#


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Department of Mechanical, AAMEC Page 1%

kom Unit-I

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