chapter 02 - mechanism and linkages_part a

7/24/2019 Chapter 02 - Mechanism and Linkages_Part A

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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

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*

5


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7 G 3+n;/;4l;h


7 G 3+@;/;4+@

G 1 (+,


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7 G 3+n;/;4l;h


7 G 3+@;/;4+@

G 1 (+,


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1

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*

5


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7 G 3+n;/;4l;h


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

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*

5

;


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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

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5


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1) Kinematic Representation -on%ersionLin7 No4 Typical ,orm Kinematic Representation

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*

5

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chapter 02 - mechanism and linkages_part a

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