143913277 Kinematics of Machinery Lecturer Notes All 5 Units

8/13/2019 143913277 Kinematics of Machinery Lecturer Notes All 5 Units

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P.A. COLLEGE OF ENGINEERING AND TECHNOLOGYPALLADAM ROAD, POLLACHI - 642 002

DEPARTMENT OF MECHANICAL ENGINEERING

ACADEMIC YEAR 2012 - 2013

ME 2202 - KINEMATICS OF MACHINERY

LECTURE NOTES - ALL 5 UNITS

Pr!"r# $%

MR. &. P. S'r() K'*"r M.E., MISTE

Mr. M. M+)" Pr"("# M.E., M$A.


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Unit I BASICS OF MECHANISMS

Introduction:

Definitions : Link or Element, Pairing of Elements with degrees of freedom,

Grublers criterion (without derivation), inematic chain, !echanism, !obilit"

of !echanism, #nversions, !achine$

Kinematic Chains and Inversions :

inematic chain with three lower %airs, &our bar chain, 'ingle slider crank chain

and Double slider crank chain and

their inversions$

Mechanisms:

i) uick return motion mechanisms Drag link mechanism, *hitworth

mechanism and +rank and slotted lever mechanism

ii) 'traight line motion mechanisms Peaceliers mechanism and obertsmechanism$

iii) #ntermittent motion mechanisms Geneva mechanism and atchet - Pawl

mechanism$

iv) .oggle mechanism, Pantogra%h, /ookes 0oint and 1ckerman 'teering gear

mechanism$

1. ermino!o"# and $e%initions&$e"ree o% Freedom' Mo(i!it#

Kinematics: .he stud" of motion (%osition, velocit", acceleration)$ 1 ma0or

goal of understanding kinematics is to develo% the abilit" to design a s"stem

that will satisf" s%ecified motion re2uirements$ .his will be the em%hasis ofthis class$

Kinetics: .he effect of forces on moving bodies$ Good kinematic design

should %roduce good kinetics$

Mechanism: 1 s"stem design to transmit motion$ (low forces)

Machine: 1 s"stem designed to transmit motion and energ"$ (forces

involved)

Basic Mechanisms: #ncludes geared s"stems, cam3follower s"stems and

linkages (rigid links connected b" sliding or rotating 0oints)$ 1 mechanism

has multi%le moving %arts (for e4am%le, a sim%le hinged door does not

2ualif" as a mechanism)$ E)am*!es o% mechanisms: .in sni%s, vise gri%s, car sus%ension, backhoe,

%iston engine, folding chair, windshield wi%er drive s"stem, etc$

Ke# conce*ts:

$e"rees o% %reedom: .he number of in%uts re2uired to com%letel" control a

s"stem$ E)am*!es: 1 sim%le rotating link$ 1 two link s"stem$ 1 four3bar

linkage$ 1 five3bar linkage$

#*es o% motion: !echanisms ma" %roduce motions that are %ure rotation,

%ure translation, or a combination of the two$ *e reduce the degrees of

freedom of a mechanism b" restraining the abilit" of the mechanism to move

in translation (43" directions for a 5D mechanism) or in rotation (about the 63

a4is for a 53D mechanism)$


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+in,: 1 rigid bod" with two or more nodes (0oints) that are used to connect

to other rigid bodies$ (*! e4am%les: binar" link, ternar" link (7 0oints),

2uaternar" link (8 0oints))

-oint: 1 connection between two links that allows motion between the links$

.he motion allowed ma" be rotational (revolute 0oint), translational (sliding

or %rismatic 0oint), or a combination of the two (roll3slide 0oint)$

Kinematic chain: 1n assembl" of links and 0oints used to coordinate an

out%ut motion with an in%ut motion$

+in, or e!ement:

1 mechanism is made of a number of resistant bodies out of which some ma" have

motions relative to the others$ 1 resistant bod" or a grou% of resistant bodies with

rigid connections %reventing their relative movement is known as a link$


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1 link ma" also be defined as a member or a combination of members of a

mechanism, connecting other members and having motion relative to them, thus a

link ma" consist of one or more resistant bodies$ 1 link is also known as inematic

link or an element$

Links can be classified into 9) inar", 5) .ernar", 7) uarternar", etc$

Kinematic air:

1 inematic Pair or sim%l" a %air is a 0oint of two links having relative motion

between them$

E)am*!e:

#n the above given 'lider crank mechanism, link 5 rotates relative to link 9 and

constitutes a revolute or turning %air$ 'imilarl", links 5, 7 and 7, 8 constitute turning

%airs$ Link 8 ('lider) reci%rocates relative to link 9 and its a sliding %air$

#*es o% Kinematic airs:

inematic %airs can be classified according to

i) ;ature of contact$

ii) ;ature of mechanical constraint$

iii) ;ature of relative motion$

i/ Kinematic *airs accordin" to nature o% contact :

a) Lower Pair: 1 %air of links having surface or area contact between the members is

known as a lower %air$ .he contact surfaces of the two links are similar$

E4am%les: ;ut turning on a screw, shaft rotating in a bearing, all %airs of a slider3crank mechanism, universal 0oint$

b) /igher Pair: *hen a %air has a %oint or line contact between the links, it is known

as a higher %air$ .he contact surfaces of the two links are dissimilar$

E4am%les: *heel rolling on a surface cam and follower %air, tooth gears, ball and

roller bearings, etc$

ii/ Kinematic *airs accordin" to nature o% mechanica! constraint.

a) +losed %air: *hen the elements of a %air are held together mechanicall", it is

known as a closed %air$ .he contact between the two can onl" be broken onl" b" thedestruction of at least one of the members$ 1ll the lower %airs and some of the higher

%airs are closed %airs$


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b)


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#n case, the motion of a link results in indefinite motions of other links, it is a non3

kinematic chain$ /owever, some authors %refer to call all chains having relative

motions of the links as kinematic chains$

+in,a"e' Mechanism and structure:

1 linkage is obtained if one of the links of kinematic chain is fi4ed to the ground$ #f

motion of each link results in definite motion of the others, the linkage is known asmechanism$ #f one of the links of a redundant chain is fi4ed, it is known as a

structure$

.o obtain constrained or definite motions of some of the links of a linkage, it is

necessar" to know how man" in%uts are needed$ #n some mechanisms, onl" one in%ut

is necessar" that determines the motion of other links and are said to have one degree

of freedom$ #n other mechanisms, two in%uts ma" be necessar" to get a constrained

motion of the other links and are said to have two degrees of freedom and so on$

.he degree of freedom of a structure is 6ero or less$ 1 structure with negative

degrees of freedom is known as a Su*erstructure.

Motion and its t#*es:


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The three main types of constrained motion in kinematic pair are,

9$Com*!ete!# constrained motion : #f the motion between a %air of links is limited

to a definite direction, then it is com%letel" constrained motion$ E$g$: !otion of a

shaft or rod with collars at each end in a hole as shown in fig$

7. Incom*!ete!# Constrained motion : #f the motion between a %air of links is not

confined to a definite direction, then it is incom%letel" constrained motion$ E$g$: 1

s%herical ball or circular shaft in a circular hole ma" either rotate or slide in the hole

as shown in fig$

+om%letel"

+onstrained!otion

Partiall"

+onstrained!otion

#ncom%letel"

+onstrained!otion


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4. Success%u!!# constrained motion or artia!!# constrained motion: #f the motion

in a definite direction is not brought about b" itself but b" some other means, then it

is known as successfull" constrained motion$ E$g$: &oot ste% earing$

Machine:

#t is a combination of resistant bodies with successfull" constrained motion which isused to transmit or transform motion to do some useful work$ E$g$: Lathe, 'ha%er,

'team Engine, etc$

Kinematic chain with three lower pairs

#t is im%ossible to have a kinematic chain consisting of three turning %airs onl"$ ut

it is %ossible to have a chain which consists of three sliding %airs or which consists of

a turning, sliding and a screw %air$

.he figure shows a kinematic chain with three sliding %airs$ #t consists of a frame ,

wedge + and a sliding rod 1$ 'o the three sliding %airs are, one between the wedge +

and the frame , second between wedge + and sliding rod 1 and the frame $

This figure shows the mechanism of a fly press..he element forms a sliding with

1 and turning %air with screw rod + which in turn forms a screw %air with 1$ *hen

link 1 is fi4ed, the re2uired fl" %ress mechanism is obtained$


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7. Kut9(ach criterion' 0rasho%%s !a;

Kut9(ach criterion:

Fundamenta! E2uation %or 7&$ Mechanisms: ! = 7(L 9) 5?9 ?5

Can ;e intuitive!# derive Kut9(achs modi%ication o% 0ru(!ers

e2uationA degrees of rotation in a Grashoff

linkages$ .his gives us 8 %ossible linkages: crank3rocker (in%ut rotates 7>A),

rocker3crank3rocker (cou%ler rotates 7>A), rocker3crank (follower)F double

crank (all links rotate 7>A)$ ;ote that these mechanisms are sim%l" the

%ossible inversions (section 5$99, &igure 539>) of a Grashoff mechanism$

Non 0rasho%% = (ar: ;o link can rotate 7>A if: ' L @ P

+ets e)amine ;h# the 0rasho%% condition ;or,s:

+onsider a linkage with the shortest and longest sides 0oined together$

E4amine the linkage when the shortest side is %arallel to the longest side (5

%ositions %ossible, folded over on the long side and e4tended awa" from the

long side)$ /ow long do P and have to be to allow the linkage to achievethese %ositions

+onsider a linkage where the long and short sides are not 0oined$ +an "ou

figure out the re2uired lengths for P and in this t"%e of mechanism

4. Kinematic Inversions o% =&(ar chain and s!ider cran, chains:

Types of Kinematic Chain: 9) &our bar chain 5) 'ingle slider chain 7) Double

'lider chain

Four (ar Chain:

.he chain has four links and it looks like a c"cle frame and hence it is also calledquadric cycle chain$ #t is shown in the figure$ #n this t"%e of chain all four %airs will

be turning %airs$


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Inversions:

" fi4ing each link at a time we get as man" mechanisms as the number of links,

then each mechanism is called B#nversion of the original inematic +hain$

Inversions o% %our (ar chain mechanism:

.here are three inversions: 9) eam Engine or +rank and lever mechanism$ 5)+ou%ling rod of locomotive or double crank mechanism$ 7) *atts straight line

mechanism or double lever mechanism$

Beam En"ine:

*hen the crank 1 rotates about 1, the link +E %ivoted at D makes vertical

reci%rocating motion at end E$ .his is used to convert rotar" motion to reci%rocating

motion and vice versa$ #t is also known as +rank and lever mechanism$ .his

mechanism is shown in the figure below$

7. Cou*!in" rod o% !ocomotive: #n this mechanism the length of link 1D =

length of link +$ 1lso length of link 1 = length of link +D$ *hen 1 rotates about

1, the crank D+ rotates about D$ this mechanism is used for cou%ling locomotivewheels$ 'ince links 1 and +D work as cranks, this mechanism is also known as

double crank mechanism$ .his is shown in the figure below$


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7$ >atts strai"ht !ine mechanism or $ou(!e !ever mechanism: #n this

mechanism, the links 1 - DE act as levers at the ends 1 - E of these levers are

fi4ed$ .he 1 - DE are %arallel in the mean %osition of the mechanism and cou%ling

rod D is %er%endicular to the levers 1 - DE$ n an" small dis%lacement of the

mechanism the tracing %oint B+ traces the sha%e of number BH, a %ortion of which

will be a%%ro4imatel" straight$ /ence this is also an e4am%le for the a%%ro4imatestraight line mechanism$ .his mechanism is shown below$

7. S!ider cran, Chain:

#t is a four bar chain having one sliding %air and three turning %airs$ #t is shown in the

figure below the %ur%ose of this mechanism is to convert rotar" motion to

reci%rocating motion and vice versa$

#nversions of a 'lider crank chain:

here are %our inversions in a sin"!e s!ider chain mechanism. he# are:

9) eci%rocating engine mechanism (9st inversion)

5) scillating c"linder engine mechanism (5nd inversion)

7) +rank and slotted lever mechanism (5nd inversion)8) *hitworth 2uick return motion mechanism (7rd inversion)

I) otar" engine mechanism (7rd inversion)

>) ull engine mechanism (8th inversion)

J) /and Pum% (8th inversion)

1. ?eci*rocatin" en"ine mechanism :

#n the first inversion, the link 9 i$e$, the c"linder and the frame is ke%t fi4ed$ .he fig

below shows a reci%rocating engine$


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1 slotted link 9 is fi4ed$ *hen the crank 5 rotates about , the sliding %iston 8

reci%rocates in the slotted link 9$ .his mechanism is used in steam engine, %um%s,

com%ressors, #$+$ engines, etc$

7. Cran, and s!otted !ever mechanism:

#t is an a%%lication of second inversion$ .he crank and slotted lever mechanism isshown in figure below$

#n this mechanism link 7 is fi4ed$ .he slider (link 9) reci%rocates in oscillating slotted

lever (link 8) and crank (link 5) rotates$ Link I connects link 8 to the ram (link >)$

.he ram with the cutting tool reci%rocates %er%endicular to the fi4ed link 7$ .he ram

with the tool reverses its direction of motion when link 5 is %er%endicular to link 8$

.hus the cutting stroke is e4ecuted during the rotation of the crank through angle K

and the return stroke is e4ecuted when the crank rotates through angle or 7>A K$

.herefore, when the crank rotates uniforml", we get,

.ime to cutting = K = K

.ime of return 7>A K.his mechanism is used in sha%ing machines, slotting machines and in rotar"

engines$

4. >hit;orth 2uic, return motion mechanism:

Third inversion is obtained by fixing the crank i.e. link 2. Whitworth quick return

mechanism is an application of third inversion. This mechanism is shown in the

figure below. The crank OC is fixed and OQ rotates about O. The slider slides in the

slotted link and generates a circle of radius CP. Link 5 connects the extension OQ

provided on the opposite side of the link 1 to the ram (link 6). The rotary motion of P

is taken to the ram R which reciprocates. The quick return motion mechanism is usedin shapers and slotting machines. The angle covered during cutting stroke from P1 to

P2 in counter clockwise direction is K or 7>A 35M$ During the return stroke, the angle


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covered is 5M or $


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.herefore, .ime to cutting = 7>A 35M = 9HA M

.ime of return 5MM = K = K $ 7>A K

=. ?otar# en"ine mechanism or 0nome En"ine:

otar" engine mechanism or gnome engine is another a%%lication of third inversion$

#t is a rotar" c"linder N t"%e internal combustion engine used as an aero engine$ut now Gnome engine has been re%laced b" Gas turbines$ .he Gnome engine has

generall" seven c"linders in one %lane$ .he crank 1 is fi4ed and all the connecting

rods from the %istons are connected to 1$ #n this mechanism when the %istons

reci%rocate in the c"linders, the whole assembl" of c"linders, %istons and connecting

rods rotate about the a4is , where the entire mechanical %ower develo%ed, is

obtained in the form of rotation of the crank shaft$ .his mechanism is shown in the

figure below$

$ou(!e S!ider Cran, Chain:

1 four bar chain having two turning and two sliding %airs such that two %airs of the

same kind are ad0acent is known as double slider crank chain$

Inversions o% $ou(!e s!ider Cran, chain:

#t consists of two sliding %airs and two turning %airs$ .he" are three im%ortant

inversions of double slider crank chain$ 9) Elli%tical trammel$ 5) 'cotch "oke

mechanism$ 7) ldhams +ou%ling$

1. E!!i*tica! ramme!:

.his is an instrument for drawing elli%ses$ /ere the slotted link is fi4ed$ .he sliding

block P and in vertical and hori6ontal slots res%ectivel"$ .he end generates an

elli%se with the dis%lacement of sliders P and $

.he co3ordinates of the %oint are 4 and "$ &rom the fig$ cos M = 4$ P

and 'in M = "$ Squaring and adding (i) and (ii) we get x2 + y2 = cos2 + sinM 2M

(PR)2 (QR)2


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x2 + y2 = 1

(PR)2 (QR)2

The equation is that of an ellipse, Hence the instrument traces an ellipse. Path traced

by mid-point of PQ is a circle. In this case, PR = PQ and so x2+y2 =1 (PR)2 (QR)2

It is an equation of circle with PR = QR = radius of a circle.

7. Scotch #o,e mechanism:.his mechanism, the slider P is fi4ed$ *hen P

rotates above P, the slider reci%rocates in the vertical slot$ .he mechanism is used

to convert rotar" to reci%rocating mechanism$

4. O!dhams cou*!in": .he third inversion of obtained b" fi4ing the link

connecting the 5 blocks P - $ #f one block is turning through an angle, the frame

and the other block will also turn through the same angle$ #t is shown in the figure

below$

1n a%%lication of the third inversion of the double slider crank mechanism is

ldhams cou%ling shown in the figure$ .his cou%ling is used for connecting two

%arallel shafts when the distance between the shafts is small$ .he two shafts to be

connected have flanges at their ends, secured b" forging$ 'lots are cut in the flanges$

.hese flanges form 9 and 7$ 1n intermediate disc having tongues at right angles and

o%%osite sides is fitted in between the flanges$ .he intermediate %iece forms the link8 which slides or reci%rocates in flanges 9 - 7$ .he link two is fi4ed as shown$ *hen

flange 9 turns, the intermediate disc 8 must turn through the same angle and whatever

angle 8 turns, the flange 7 must turn through the same angle$ /ence 9, 8 - 7 must

have the same angular velocit" at ever" instant$ #f the distance between the a4is of

the shaft is 4, it will be the diameter if the circle traced b" the centre of the

intermediate %iece$ .he ma4imum sliding s%eed of each tongue along its slot is given

b"

v=x where, = angular velocity of each shaft in rad/sec v = linear velocity in m/secO O

=. Mechanica! Advanta"e' ransmission an"!e:

.he mechanical advantage (!1) is defined as the ratio of out%ut tor2ue to the

in%ut tor2ue$ (or) ratio of load to out%ut$


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.ransmission angle$

.he e4treme values of the transmission angle occur when the crank lies along

the line of frame$

@. $escri*tion o% common mechanisms&Sin"!e' $ou(!e and o%%set s!ider

mechanisms & uic, return mechanisms:

uic, ?eturn Motion Mechanisms:

!an" a times mechanisms are designed to %erform re%etitive o%erations$ During

these o%erations for a certain %eriod the mechanisms will be under load known as

working stroke and the remaining %eriod is known as the return stroke, the

mechanism returns to re%eat the o%eration without load$ .he ratio of time of working

stroke to that of the return stroke is known a time ratio$ uick return mechanisms are

used in machine tools to give a slow cutting stroke and a 2uick return stroke$ .he

various 2uick return mechanisms commonl" used are i) *hitworth ii) Drag link$ iii)

+rank and slotted lever mechanism

1. >hit;orth 2uic, return mechanism:*hitworth 2uick return mechanism is an a%%lication of third inversion of the single

slider crank chain$ .his mechanism is shown in the figure below$ .he crank + is

fi4ed and rotates about $ .he slider slides in the slotted link and generates a

circle of radius +P$ Link I connects the e4tension %rovided on the o%%osite side

of the link 9 to the ram (link >)$ .he rotar" motion of P is taken to the ram which

reci%rocates$ .he 2uick return motion mechanism is used in sha%ers and slotting

machines$

.he angle covered during cutting stroke from P9 to P5 in counter clockwise direction

is K or 7>A 35M$ During the return stroke, the angle covered is 5M or $

7. $ra" !in, mechanism :

.his is four bar mechanism with double crank in which the shortest link is fi4ed$ #fthe crank 1 rotates at a uniform s%eed, the crank +D rotate at a non3uniform s%eed$

.his rotation of link +D is transformed to 2uick return reci%rocator" motion of the


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7. 0eneva mechanism: Geneva mechanism is an intermittent motion

mechanism$ #t consists of a driving wheel D carr"ing a %in P which engages in a slot

of follower & as shown in figure$ During one 2uarter revolution of the driving %late,

the Pin and follower remain in contact and hence the follower is turned b" one2uarter of a turn$ During the remaining time of one revolution of the driver, the

follower remains in rest locked in %osition b" the circular arc$

4. anto"ra*h:Pantogra%h is used to co%" the curves in reduced or enlarged

scales$ /ence this mechanism finds its use in co%"ing devices such as engraving or

%rofiling machines$

.his is a sim%le figure of a Pantogra%h$ .he links are %in 0ointed at 1, , + and D$

1 is %arallel to D+ and 1D is %arallel to +$ Link 1 is e4tended to fi4ed %in $

is a %oint on the link 1D$ #f the motion of is to be enlarged then the link + is

e4tended to P such that , and P are in a straight line$ .hen it can be shown that

the %oints P and alwa"s move %arallel and similar to each other over an" %ath

straight or curved$ .heir motions will be %ro%ortional to their distance from the fi4ed%oint$ Let 1+D be the initial %osition$ 'u%%ose if %oint moves to 9 , then all the

links and the 0oints will move to the new %ositions (such as 1 moves to 19 , moves


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to 9, + moves to 9 , D moves to D9 and P to P9 ) and the new configuration of the

mechanism is shown b" dotted lines$ .he movement of ( 9) will be enlarged to

PP9 in a definite ratio$

=. o""!e Mechanism:


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#n slider crank mechanism as the crank a%%roaches one of its dead centre %osition,

the slider a%%roaches 6ero$ .he ratio of the crank movement to the slider movement

a%%roaching infinit" is %ro%ortional to the mechanical advantage$ .his is the

%rinci%le used in toggle mechanism$ 1 toggle mechanism is used when large forces

act through a short distance is re2uired$ .he figure below shows a toggle mechanism$

Links +D and +E are of same length$ esolving the forces at + verticall" F Sin 3Cos 7

.herefore, & = P $ (because 'in K+os K = .an K) 5 tan K .hus for the given value of

P, as the links +D and +E a%%roaches collinear %osition (K), the force & rises

ra%idl"$

@. Hoo,es 8oint:

/ookes 0oint used to connect two %arallel intersecting shafts as shown in figure$

.his can also be used for shaft with angular misalignment where fle4ible cou%ling

does not serve the %ur%ose$ /ence /ookes 0oint is a means of connecting two

rotating shafts whose a4es lie in the same %lane and their directions making a small

angle with each other$ #t is commonl" known as


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hree correct steerin" *ositions ;i!! (e:

9) *hen moving straight$ 5) *hen moving one correct angle to the right

corres%onding to the link ratio 11 and angle K$ 7) 'imilar %osition when moving

to the left$ In a!! other *ositions *ure ro!!in" is not o(taina(!e.

Some Of The Mechanisms Which Are Used In ay To ay !ife"

BE++ C?ANK: 0ENEA SO:

BE++ C?ANK: .he bell crank was originall" used in large house to o%erate the

servants bell, hence the name$ .he bell crank is used to convert the direction of

reci%rocating movement$ " var"ing the angle of the crank %iece it can be used to

change the angle of movement from 9 degree to 9HA degrees$

0ENEA SO: .he Geneva sto% is named after the Geneva cross, a similar sha%e

to the main %art of the mechanism$ .he Geneva sto% is used to %rovide intermittentmotion, the orange wheel turns continuousl", the dark blue %in then turns the blue

cross 2uarter of a turn for each revolution of the drive wheel$ .he crescent sha%ed cut

out in dark orange section lets the %oints of the cross %ast, then locks the wheel in

%lace when it is stationar"$ .he Geneva sto% mechanism is used commonl" in film

cameras$

E++IICA+ ?AMME+ ISON A??AN0EMEN

ELLIPTICAL TRAMMEL:This fascinating mechanism converts rotary motion to

reciprocating motion in two axis. Notice that the handle traces out an ellipse rather

than a circle. A similar mechanism is used in ellipse drawing tools.

PISTON ARRANGEMENT: This mechanism is used to convert between rotary


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motion and reciprocating motion, it works either way. Notice how the speed of the

piston changes. The piston starts from one end, and increases its speed. It reaches

maximum speed in the middle of its travel then gradually slows down until it reaches

the end of its travel.

?ACK AN$ INION ?ACHE

?ACK AN$ INION:.he rack and %inion is used to convert between rotar" and

linear motion$ .he rack is the flat, toothed %art, the %inion is the gear$ ack and

%inion can convert from rotar" to linear of from linear to rotar"$ .he diameter of the

gear determines the s%eed that the rack moves as the %inion turns$ ack and %inions

are commonl" used in the steering s"stem of cars to convert the rotar" motion of the

steering wheel to the side to side motion in the wheels$ ack and %inion gears give a

%ositive motion es%eciall" com%ared to the friction drive of a wheel in tarmac$ #n the

rack and %inion railwa" a central rack between the two rails engages with a %inion on

the engine allowing the train to be %ulled u% ver" stee% slo%es$

?ACHE: .he ratchet can be used to move a toothed wheel one tooth at a time$.he %art used to move the ratchet is known as the %awl$ .he ratchet can be used as a

wa" of gearing down motion$ " its nature motion created b" a ratchet is

intermittent$ " using two %awls simultaneousl" this intermittent effect can be

almost, but not 2uite, removed$ atchets are also used to ensure that motion onl"

occurs in onl" one direction, useful for winding gear which must not be allowed to

dro%$ atchets are also used in the freewheel mechanism of a bic"cle$

>O?M 0EA? >ACH ESCAEMEN.

>O?M 0EA?: 1 worm is used to reduce s%eed$ &or each com%lete turn of the

worm shaft the gear shaft advances onl" one tooth of the gear$ #n this case, with a

twelve tooth gear, the s%eed is reduced b" a factor of twelve$ 1lso, the a4is of

rotation is turned b" RA degrees$


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%ower$ #deal for use with small electric motors$


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WATCH ESCAPEMENT: The watch escapement is the centre of the time piece. It

is the escapement which divides the time into equal segments.The balance wheel, the

gold wheel, oscillates backwards and forwards on a hairspring (not shown) as the

balance wheel moves the lever is moved allowing the escape wheel (green) to rotate

by one tooth. The power comes through the escape wheel which gives a small 'kick'

to the palettes (purple) at each tick.

0EA?S CAM FO++O>E?.

0EA?S: Gears are used to change s%eed in rotational movement$ #n the e4am%le

above the blue gear has eleven teeth and the orange gear has twent" five$ .o turn the

orange gear one full turn the blue gear must turn 5I99 or 5$5J5Jr turns$ ;otice that

as the blue gear turns clockwise the orange gear turns anti3clockwise$ #n the above

e4am%le the number of teeth on the orange gear is not divisible b" the number of

teeth on the blue gear$ .his is deliberate$ #f the orange gear had thirt" three teeth then

ever" three turns of the blue gear the same teeth would mesh together which could

cause e4cessive wear$ " using none divisible numbers the same teeth mesh onl"

ever" seventeen turns of the blue gear$

CAMS: +ams are used to convert rotar" motion into reci%rocating motion$ .he

motion created can be sim%le and regular or com%le4 and irregular$ 1s the cam turns,

driven b" the circular motion, the cam follower traces the surface of the cam

transmitting its motion to the re2uired mechanism$ +am follower design is im%ortant

in the wa" the %rofile of the cam is followed$ 1 fine %ointed follower will more

accuratel" trace the outline of the cam$ .his more accurate movement is at the

e4%ense of the strength of the cam follower$

SEAM EN0INE.

'team engines were the backbone of the industrial revolution$ #n this common designhigh %ressure steam is %um%ed alternatel" into one side of the %iston, then the other


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forcing it back and forth$ .he reci%rocating motion of the %iston is converted to

useful rotar" motion using a crank$

As the large wheel (the fly wheel) turns a small crank or cam is used to move the

small red control valve back and forth controlling where the steam flows. In this

animation the oval crank has been made transparent so that you can see how the

control valve crank is attached.

G. Strai"ht !ine "enerators' $esi"n o% Cran,&roc,er Mechanisms:

Strai"ht +ine Motion Mechanisms:

.he easiest wa" to generate a straight line motion is b" using a sliding %air but in

%recision machines sliding %airs are not %referred because of wear and tear$ /ence in

such cases different methods are used to generate straight line motion mechanisms:

1. E)act strai"ht !ine motion mechanism.

a$ Peaucellier mechanism, b$ /art mechanism, c$ 'cott ussell mechanism

7. A**ro)imate strai"ht !ine motion mechanismsa$ *att mechanism, b$ Grassho%%ers mechanism, c$ oberts mechanism,

d$ .chebicheffs mechanism

a. eauci!!ier mechanism :

The pin Q is constrained to move long the circumference of a circle by means of the

link OQ. The link OQ and the fixed link are equal in length. The pins P and Q are on

opposite corners of a four bar chain which has all four links QC, CP, PB and BQ of

equal length to the fixed pin A. i.e., link AB = link AC. The product AQ x AP remain

constant as the link OQ rotates may be proved as follows: Join BC to bisect PQ at F;

then, from the right angled triangles AFB, BFP, we have 1=1&& and

P=&&P$ 'ubtracting, 13P= 1&3&P=(1&&P)(1&&P) = 1 4 1P $

Since AB and BP are links of a constant length, the product AQ x AP is constant.

Therefore the point P traces out a straight path normal to AR.

(. ?o(erts mechanism:

This is also a four bar chain. The link PQ and RS are of e2ual length and the tracing

%int B is rigidl" attached to the link on a line which bisects at right angles$

.he best %osition for ma" be found b" making use of the instantaneous centre of

$ .he %ath of is clearl" a%%ro4imatel" hori6ontal in the oberts mechanism$

a. eauci!!ier mechanism (. Hart mechanism


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Unit II KINEMAICS

e!ocit# and Acce!eration ana!#sis o% mechanisms 50ra*hica! Methods/:

Nelocit" and acceleration anal"sis b" vector %ol"gons: elative velocit" and

accelerations of %articles in a common link, relative velocit" and accelerations ofcoincident %articles on se%arate link, +oriolis com%onent of acceleration$

Nelocit" and acceleration anal"sis b" com%le4 numbers: 1nal"sis of single slider

crank mechanism and four bar mechanism b" loo% closure e2uations and

com%le4 numbers$

. $is*!acement' ve!ocit# and acce!eration ana!#sis in sim*!e mechanisms:

Im*ortant Conce*ts in e!ocit# Ana!#sis

9$ .he absolute velocit" of an" %oint on a mechanism is the velocit" of that %oint

with reference to ground$

5$ elative velocit" describes how one %oint on a mechanism moves relative to

another %oint on the mechanism$

7$ .he velocit" of a %oint on a moving link relative to the %ivot of the link is

given b" the e2uation: N = r, where = angular velocit" of the link and r =

distance from %ivot$

Acce!eration Com*onents

#ormal Acceleration: An= 5r$ Points toward the center of rotation

Tan$ential Acceleration: At= r$ #n a direction %er%endicular to the link

Coriolis Acceleration: Ac = 5(drdt)$ #n a direction %er%endicular to the

link

Slidin$ Acceleration: As= d5rdt5$ #n the direction of sliding$

1 rotating link will %roduce normal and tangential acceleration com%onents at

an" %oint a distance, r, from the rotational %ivot of the link$ .he total

acceleration of that %oint is the vector sum of the com%onents$

1 slider attached to ground e4%eriences onl" sliding acceleration$

1 slider attached to a rotating link (such that the slider is moving in or out along

the link as the link rotates) e4%eriences all 8 com%onents of acceleration$ Perha%s

the most confusing of these is the coriolis acceleration, though the conce%t of

coriolis acceleration is fairl" sim%le$ #magine "ourself standing at the center of a

merr"3go3round as it s%ins at a constant s%eed ()$ Sou begin to walk toward the

outer edge of the merr"3go3round at a constant s%eed (drdt)$ Even though "ouare walking at a constant s%eed and the merr"3go3round is s%inning at a constant

s%eed, "our total velocit" is increasing because "ou are moving awa" from the

center of rotation (i$e$ the edge of the merr"3go3round is moving faster than the

center)$ .his is the coriolis acceleration$ #n what direction did "our s%eed

increase .his is the direction of the coriolis acceleration$

.he total acceleration of a %oint is the vector sum of all a%%licable acceleration

com%onents:

A= An At Ac As

.hese vectors and the above e2uation can be broken into 4 and " com%onents b"

a%%l"ing sines and cosines to the vector diagrams to determine the 4 and "com%onents of each vector$ #n this wa", the 4 and " com%onents of the total

acceleration can be found$


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. 0ra*hica! Method' e!ocit# and Acce!eration *o!#"ons :

0ra*hica! ve!ocit# ana!#sis:

#t is a ver" short ste% (using basic trigonometr" with sines and cosines) to convert the

gra%hical results into numerical results$ .he basic ste%s are these:9$ 'et u% a velocit" reference %lane with a %oint of 6ero velocit" designated$

5$


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1 slider attached to a rotating link (such that the slider is moving in or out along

the link as the link rotates) e4%eriences all 8 com%onents of acceleration$ Perha%s

the most confusing of these is the coriolis acceleration, though the conce%t of

coriolis acceleration is fairl" sim%le$ #magine "ourself standing at the center of a

merr"3go3round as it s%ins at a constant s%eed ()$ Sou begin to walk toward the

outer edge of the merr"3go3round at a constant s%eed (drdt)$ Even though "ouare walking at a constant s%eed and the merr"3go3round is s%inning at a constant

s%eed, "our total velocit" is increasing because "ou are moving awa" from the

center of rotation (i$e$ the edge of the merr"3go3round is moving faster than the

center)$ .his is the coriolis acceleration$ #n what direction did "our s%eed

increase .his is the direction of the coriolis acceleration$

E)am*!e:1


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Unit III KINEMAICS OF CAM

Cams:."%e of cams, ."%e of followers, Dis%lacement, Nelocit" and acceleration time

curves for cam %rofiles, Disc cam with reci%rocating follower having knife edge,

roller follower, &ollower motions including '/!,


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h#sica! com*onents: +am, follower, s%ring

#*es o% cam s#stems: scilllating (rotating), translating

#*es o% 8oint c!osure: &orce closed, form closed

#*es o% %o!!o;ers: &lat3faced, roller, mushroom

#*es o% cams: radial, a4ial, %late (a s%ecial class of radial cams)$

#*es o% motion constraints: Critical extreme position the %ositions of thefollower that are of %rimar" concern are the e4treme %ositions, with considerable

freedom as to design the cam to move the follower between these %ositions$ .his is

the motion constraint t"%e that we will focus u%on$ Critical path motion .he %ath

b" which the follower satisfies a given motion is of interest in addition to the e4treme

%ositions$ .his is a more difficult (and less common) design %roblem$

#*es o% motion: rise, fall, dwell

0eometric and Kinematic *arameters: follower dis%lacement, velocit",

acceleration, and 0erkF base circleF %rime circleF follower radiusF eccentricit"F

%ressure angleF radius of curvature$

1. ara(o!ic' Sim*!e harmonic and C#c!oida! motions:

$escri(in" the motion: 1 cam is designed b" considering the desired

motion of the follower$ .his motion is s%ecified through the use of 'N1?

diagrams (diagrams that describe the desired dis%lacement3velocit"3

acceleration and 0erk of the follower motion)

7J. +a#out o% *!ate cam *ro%i!es:

Drawing the dis%lacement diagrams for the different kinds of the motions and

the %late cam %rofiles for these different motions and different followers$ '/!,


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7@. ressure an"!e and undercuttin":

Pressure angle


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Unit I 0EA?S

Gears are used to change s%eed in rotational movement$

#n the e4am%le above the blue gear has eleven teeth and the orange gear has twent"

five$ .o turn the orange gear one full turn the blue gear must turn 5I99 or 5$5J5Jr

turns$ ;otice that as the blue gear turns clockwise the orange gear turns anti3

clockwise$ #n the above e4am%le the number of teeth on the orange gear is not

divisible b" the number of teeth on the blue gear$ .his is deliberate$ #f the orange

gear had thirt" three teeth then ever" three turns of the blue gear the same teeth

would mesh together which could cause e4cessive wear$ " using none divisible

numbers the same teeth mesh onl" ever" seventeen turns of the blue gear$

7. S*ur "ear ermino!o"# and de%initions:

S*ur 0ears:

E4ternal

#nternal Definitions

7G. Fundamenta! +a; o% toothed "earin" and Invo!ute "earin":

Law of gearing

#nvolutometr" and +haracteristics of involute action

Path of +ontact and 1rc of +ontact

+ontact atio

+om%arison of involute and c"cloidal teeth

7. Inter chan"ea(!e "ears' "ear tooth action' ermino!o"#: #nter changeable gears

Gear tooth action

.erminolog"

7. Inter%erence and undercuttin":

#nterference in involute gears

!ethods of avoiding interference

ack lash

4J. Non standard "ear teeth: He!ica!' Beve!' >orm' ?ac, and inion "ears5Basics on!#/

/elical


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evel

*orm

ack and Pinion gears

?ACK AN$ INION >O?M 0EA?

?ACK AN$ INION:.he rack and %inion is used to convert between rotar" andlinear motion$ .he rack is the flat, toothed %art, the %inion is the gear$ ack and

%inion can convert from rotar" to linear of from linear to rotar"$ .he diameter of the

gear determines the s%eed that the rack moves as the %inion turns$ ack and %inions

are commonl" used in the steering s"stem of cars to convert the rotar" motion of the

steering wheel to the side to side motion in the wheels$ ack and %inion gears give a

%ositive motion es%eciall" com%ared to the friction drive of a wheel in tarmac$ #n the

rack and %inion railwa" a central rack between the two rails engages with a %inion on

the engine allowing the train to be %ulled u% ver" stee% slo%es$

>O?M 0EA?: 1 worm is used to reduce s%eed$ &or each com%lete turn of the

worm shaft the gear shaft advances onl" one tooth of the gear$ #n this case, with atwelve tooth gear, the s%eed is reduced b" a factor of twelve$ 1lso, the a4is of

rotation is turned b" RA degrees$


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Unit F?ICION

4@. Sur%ace contacts:

asic laws of friction

Pivot and collar, introduction and t"%es$

Problem on flat %ivot, Problems on conical %ivot$

4. S!idin" and ?o!!in" %riction:

'liding contact bearings

olling contact bearings

Problems in bearings

4G. Friction drives:

&riction drives

Positive drives and 'li% drives

'%eed ratio

4. Friction in scre; threads:

&riction in screw and nut

&riction in screw 0ack

Problems in screw 0ack

4. Friction c!utches:

'ingle %late clutches and !ulti3%late clutches


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143913277 Kinematics of Machinery Lecturer Notes All 5 Units

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Transcript of 143913277 Kinematics of Machinery Lecturer Notes All 5 Units