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FMB 20202 Mechanics of
Machine
Chapter II Mechanism and
Linkages I
By
Engr. Syed Fawwaz Al-Attas
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Mechanisms
Terminology
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Planar vs. Spatial Mechanisms Planar Mechanisms:
When all the links of a mechanism have plane motion, it is called as a planar mechanism.All the links in a planar mechanism move in planes parallel to the reference plane.
Spatial Mechanisms:
A mechanisms where links move in 3 dimensions.
Examplesof spatialmechanismsA gear train system (for example)
can be a planar or spatial
mechanisms depending on the
configuration of the system.
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PAIRING ELEMENTS
Pairing elements: the geometrical forms ! which twomemers of a mechanism are "oined together, so that the
relative motion etween these two is consistent.
S#ch a pair of links is called Kinematic Pair.
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$o#rtes!:www.technolog!st#dent.com
PAIRING ELEMENTS
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%&'(MA)&$ PA&*S%&'(MA)&$ PA&*S
Base on nat!re o" contact #et$een elements
+i Lo$er pair : )he "oint ! which two memers areconnected has s#rface contact.
A%antages:
)he l#ricant traps etween their enveloping s#rfaces.
)herefore res#lts in low wear and long life
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-ower Pair oints-ower Pair oints
Planar &'() Mechanism Spatial &*() Mechanism
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Name &Sym#ol) (+, -ontains
*evol#te +* //+01 R
)ranslating +Prismatic +P //+02 P
elical+//+01 R
$!lindric +$ 44+01, +02 RP
Spherical +S 33+01, +05, +06 RRR
Planar +7 33+01, +02, +0! RPP
-ower Pair oints-ower Pair oints
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(2amples of Planar +48 -ower Pair oints(2amples of Planar +48 -ower Pair oints
A door "oint to a frame with hinges +revol#te +* pairA piston sliding on c!linder +prismatic +P pair
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&ii) .igher pair:)he contact etween the pairing elementstakes place at a point or along a line.
%&'(MA)&$ PA&*S%&'(MA)&$ PA&*S
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igher Pair ointsigher Pair oints9ear )eeth $am 7ollower Pin;in;Slot -ink against Plane
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Base on relati%e motion #et$een pairing
elements
&a) Siing pair &prismatic pair) /(+, 0 12
) T!rning pair &re%ol!te pair)/(+, 0 12
%&'(MA)&$ PA&*S%&'(MA)&$ PA&*S
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Base on relati%e motion #et$een pairingelements
&c) -ylinrical pair/(+, 0 '2
&) Rolling pair/(+, 0 12
%&'(MA)&$ PA&*S%&'(MA)&$ PA&*S
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Base on relati%e motion #et$een pairing
elements
&e) Spherical pair /(+, 0 *2
(g. =all and socket "oint
&") .elical pair or scre$ pair /(+, 0 12
%&'(MA)&$ PA&*S%&'(MA)&$ PA&*S
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Base on the nat!re o" mechanical constraint
&a) -lose pair
) 3nclose or "orce close pair
%&'(MA)&$ PA&*S%&'(MA)&$ PA&*S
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Kinematic -hain
8efinition: A kinematic chain is an asseml! of links connected together either
"oined together or arranged in a manner that permits them to moverelative to one another, witho#t specif!ing the ase link+i.e., a fixed link
Joints
Binary LinksBinary Links
TernaryTernaryLinkLink
,ig48evices with diverse link components.
56lin7 7inematic
chain
)hat is, when)hat is, when allalllinkages in a s!stem are moval! and connectedlinkages in a s!stem are moval! and connectedtogether !together !"oints"oints, the! are said to form a, the! are said to form a kinematic chainkinematic chain..
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-
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)!pes of -inks in a %inematic $hain
%inematic chains might contain different t!pes of links and "oint.%inematic chains might contain different t!pes of links and "oint.
-inks containing onl! 4 par element connections are called-inks containing onl! 4 par element connections are calledbinary linksbinary links??
)hose having 3 are called)hose having 3 are called ternary linksternary links,,
)hose having @ are called)hose having @ are called uaternary linksuaternary links, and so on, and so on
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=inar!=inar!
linklink=inar!=inar!
linkslinks
)ernar! link)ernar! link
,ig4Mechanism with diverse link t!pes.
Binary LinksBinary Links
TernaryTernary
LinkLink
,ig48evices with diverse link components.
Joints
)!pes of -inks in a %inematic $hain
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-losevs.
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+pen -hain Mechanisms: A 7inematic chain that is not close
&has no close loops) is an open kinematic chain4
An open mechanism o" more than one lin7 $ill
al$ays ha%e more than one (+,4
Re9!ires as many act!ators &motors) as (+,4
P3MA Ro#ot:*6lin7 open chain mechanism
Skeleton
Real ro#ot
*oot sim#lation
$losed vs. +penkinematic chains
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MechanismsDefinition:Definition:A mechanism is a kinematic chain where one of its linkages
does not move (such link is fixed and its called the base link).
A mechanism is a constrained kinematic chain.
Motion of any one link in the kinematic chain will give a definite and predictale motion relative to
each of the others. !sually one of the links of the kinematic chain is fixed in a mechanism
,ixelin7 or #ase lin7
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Some -ommon Types o" Mechanisms
@;ar mechanism
B;ar C;ar mechanisms
Slider;crank mechanism
$am;follower mechanism
9ear )rains mechanism
(tc.
,ig!re4+a Slider crank mechanism.
+ Skeleton representation.
slider
crank
,ig!re4Slider crank
mechanism with offset.
,ig!re49ear train.
$am 8isk
7ollower
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-inks &ndivid#al parts of machines or mechanisms
are also referred to as links.
)!pes of -inks: -inks can e non!rigid: cales and elts. -inks can also e rigid bodies: cranks, levers, wheels, ars or
gears.
'on;rigid link:
timing elt
*igid links:
p#lle!s,
cam,
crank, etc.
(2ample:
-inks
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7o#r;=ar Mechanism
@;ar mechanisms are among the most common and #sef#l mechanisms:
$omponents in a @;ar mechanism:
&t has @ ars +links
A stationar! or #ase lin7 +link " and 3 moving links.
)he cran7+link # or link $ rotates ao#t a ase pivotD"oint +%#or %$ and
move the mechanism. A co!pler +link & connects the crankto the o#tp#t link.
,ig!re4 Skeleton
representation.
,ig!re4(2ample @;ar
mechanism.
Ang!larAng!lar
isplacementsisplacements
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$omple2 mechanisms can e #ilt from simple mechanisms ! adding more links.
7&9. @;ar mechanism
Skeleton.
7&9. $omple2 mechanism
7&9. @;ar mechanism #sed in a
washing machine.
1'
* 5
Gears
This gear ri%es the agitator
to pro%ie the $ashing action
7o#r;=ar Mechanism
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Slider;crank mechanism
,ig!re4Slider crank mechanism with offset.
)his mechanism incorporates B main
elements:
/.A stationar!ase link +link ". )he otherlinks can move relative to the ase link .
4.)he crank+link # rotates ao#t a asepivotD"oint.
3.)he sliderorpiston+link $ moves in a linearmotion.
@.A co#pler+link & connects the crankto theslider.
B.)he line of action is the straight;line path ofthe center of theslider.
)he slider;crank mechanism might have anoffsetetween the line of actionand the baseline.
,ig!re4Slider;crank mechanism.
slier
cran7
co!pler
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Skeleton of a Mechanism
Askeletonis a highl! simplified drawing of a
mechanism.
>se:
Skeletons are #se for anal!Eing themotions of the mechanism.
theoretical
)he dimensions in the skeleton diagramare critical for determining motions.
)he skeleton incl#des linksand'oints:
oints are represented with a s!mol thatdepends on the t!pe of "oint.
-inks are, in general, represented !straight lines +regardless of the actual
shape of the real link.
,ig!re4+a Slider crank mechanism.
+ Skeleton representation.
slider
crank
"oints
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$ompo#nd Mechanisms A compound mechanismis s!stemDmachine
composed of asicDsimple mechanisms
forming a comple2 machine.
)he entire machine can e completel!
anal!Eed ! independentl! anal!Eing all the
individ#al +simple mechanisms comprising
the overall s!stem.
...
$!Bar mechanism
$!Bar mechanism
$!Bar mechanism
Example:compound
mechanism xca*atorCompound
mechanism
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Tho!gh all machines are mechanisms8 allTho!gh all machines are mechanisms8 allmechanisms are not machinesmechanisms are not machines
Machines
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Mechanisms
(egrees o" ,reeom(DOF)
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8
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Translationalandotational8
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(2amples of root leg mechanisms with 4 3 8
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1ontrollablevs. 2ncontrollable8
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'#mer of degrees of freedom of a mechanism is given !
Where,
,G 8egrees of freedom
nG '#mer of links in the mechanism.
lG '#mer of lower pairs, which is otained ! co#nting then#mer of "oints. &f more than two links are "oinedtogether at an! point, then, one additional lower pair is toe considered for ever! additional link.
hG '#mer of higher pairs
9*>=-(*HS $*&)(*&
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7 G 3+n;/;4l;h
ere, n G @, l G @ h G I.
7 G 3+@;/;4+@ G /
i.e., one inp#t to an! one link will res#lt in definite motion of all the links.
(2amples ; 8
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7 G 3+n;/;4l;h
ere, n G B, l G B and h G I.
7 G 3+B;/;4+B G 4
i.e., two inp#ts to an! two links are reF#ired to !ield definite motions in
all the links.
(2amples ; 8
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7 G 3+n;/;4l;h
ere, n G C, l G J and h G I.
7 G 3+C;/;4+J G /
i.e., one inp#t to an! one link will res#lt in definite motion of all the links.
(2amples ; 8
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7 G 3+n;/;4l;h
ere, n G C, l G J +at the intersection of 4, 3 and @, two lower pairs
are to e considered and h G I.
7 G 3+C;/;4+J G /
(2amples ; 8
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7 G 3+n;/;4l;h
ere, n G //, l G /B +two lower pairs at the intersection of 3, @, C? 4,@, B? B, J, K? K, /I, // and h G I.
7 G 3+//;/;4+/B G I
(2amples ; 8
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%inematic 8iagram%inematic 8iagram
A simpli"ie iagram from o"ectDprod#ct.
)he diagram #sed for kinematic anal!sis, s#ch as
mechanism vector, force anal!sis, etc.
)here are * metho to convert from o"ectDprod#ct to
kinematic diagram, which as follows:
/ Kinematic Representation -on%ersion
4 Kinematic (iagram3 (+, (etermination
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1) Kinematic Representation -on%ersion
Lin7 No4 Typical ,orm Kinematic Representation
1
'
*
5
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') Kinematic (iagram
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*) (+, (etermination
7 G 3+n;/;4l;h
ere, n G @, l G @ and h G I.
7 G 3+@;/;4+@
G 1 (+,
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1) Kinematic Representation -on%ersion
Lin7 No4 Typical ,orm Kinematic Representation
1
'
*
5
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') Kinematic (iagram
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*) (+, (etermination
7 G 3+n;/;4l;h
ere, n G @, l G @ and h G I.
7 G 3+@;/;4+@
G 1 (+,
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') Kinematic (iagram
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*) (+, (etermination
7 G 3+n;/;4l;h
ere, n G @, l G @ and h G I.
7 G 3+@;/;4+@
G 1 (+,
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1) Kinematic Representation -on%ersion
Lin7 No4 Typical ,orm Kinematic Representation
1
'
*
5
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') Kinematic (iagram
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*) (+, (etermination
7 G 3+n;/;4l;h
ere, n G @, l G @ and h G I.
7 G 3+@;/;4+@
G 1 (+,
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ExamplesExamples
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1) Kinematic Representation -on%ersionLin7 No4 Typical ,orm Kinematic Representation
1
'
*
5
;
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') Kinematic (iagram
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*) (+, (etermination
7 G 3+n;/;4l;h
ere, n G K, l G /I and h G I.
7 G 3+K;/;4+/I ;I
G 1 (+,
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1) Kinematic Representation -on%ersion
Lin7 No4 Typical ,orm Kinematic Representation
1
'
*
5
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') Kinematic (iagram
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1) Kinematic Representation -on%ersionLin7 No4 Typical ,orm Kinematic Representation
1
'
*
5
;
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