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Mechanics of MachineryMechanics of Machinery

. .


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1. ! " #$ %&'(). !*" +$ % ,'(

-. % /01"2 !3 4'( 4''(

4. A5t65r 7. 8r9man:7;oran9@M; 6anism 9;si nt6;sisE FoC5m; 4G? )n9 89itiM 7raHIJiCC? 4KK4


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!Z [1"21 %\ ] ^c # "_


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Mechanism AnalysisMechanism Analysis

Kinematics motion position velocity acceleration

Kinetics F=ma

Mechanics

DynamicsStatics

MechanismMechanism

AnalysisAnalysis

Object is inObject is inmotionmotion

Object isObject is

motionless ormotionless ormovin

g with a = 0moving with a = 0


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Object types

1. Particle a point mass, m2. Rigid body a finite body that is not

fle ible.

3. !le ible body " a finite body that isfle ible, not considered in this class.

#ote$ %n this class, &e &ill loo' at ho& a particleand a rigid body mo(e in t&o dimensionalspace)2*+ or plane.


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Motion types in 2D

4. jransCation ` 3 Z # `%"\ l Z lc #Z 0! 02" p2cq ; tiCin;ar transCation ` 3Z #

`%"\ l Z lc #Z0 `*d 1!!` 3 #Z lcq V5r iCin;ar transCation I ` 3Z #

`%"\ l Z lc #Z0 `*d 1!!` 3 %3#Z lc). otation `%"\ l Z lZ l 2+2 b #0 0

/ !1 + l# \0 %b%#Z l\l l


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Translation motion !


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"otational motion


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echanism ynthesis

"e&'ire$ Motion

#omponents types

('mber)si*e)shape

MechanismSynthesis(design)

Mechanisms are the basis of allmachine design


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echanism synthesis

%n some de(ices, e.g. instr0ments, controlmechanisms the correct motion is the mostimportant thing. he po&er )force+ transmitted issmall and so strength si e of parts is not theprime concern.

%n other machines, the 'inematic analysis is onlyone step in the design process. 7nce &e ha(e&or'ed o0t ho& parts sho0ld mo(e together &em0st then calc0late the forces that areprod0ced. he re80ired strength and si e shapeof parts can then be determined


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+asicMechanisms


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9in'agesSli$er,#ran-.in- / frame )reference+.in- 2 cran'.in- connecting"rod )con"rod+.in- 1 slider

4 " Reciprocating motion)bac' : fore+

2 " Rotation

Kinematic $iagrams simpli3ie$ b't acc'rate!$iagrams showing geometry o3 motion

#ran-,"oc-er .in- / frame )reference+.in- 2 cran'.in- connecting"rod )con"rod+.in- 1 roc'er


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4"bar lin'age e amples

/ran'"roc'er *o0ble"roc'er
http://var/www/apps/conversion/tmp/scratch_6/C:%5CMonsak%5CMachinery%5CAnimation%5Cdoublerocker_assembly.avihttp://var/www/apps/conversion/tmp/scratch_6/C:%5CMonsak%5CMachinery%5CAnimation%5Cgrashof_crank_rocker.avi


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lider"cran' e amples

%n(ersiontandard slider"cran'
http://var/www/apps/conversion/tmp/scratch_6/C:%5CMonsak%5CMachinery%5CAnimation%5Cinverted_sc_assembly.avihttp://var/www/apps/conversion/tmp/scratch_6/C:%5CMonsak%5CMachinery%5CAnimation%5Cslidercrank_assembly.avi


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/am

(+4 A cam can only p'sh the 3ollower not p'll!the ret'rn action re&'ires spring)gravity etc5

#am rotates at constant ang'lar velocityFollower moves 'p an$ $own


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/am"follo&er e amples

!lat faced translating follo&er !lat faced reciprocating follo&er
http://var/www/apps/conversion/tmp/scratch_6/C:%5CMonsak%5CMachinery%5CAnimation%5Cflat_faced_cam.avihttp://var/www/apps/conversion/tmp/scratch_6/C:%5CMonsak%5CMachinery%5CAnimation%5Cff_translating_follower.avi


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;ears

;ears are 0sed to transmit motion from one shaftto another &ith a constant ang0lar (elocity ratio)gear ratio+.

;ears trains canbe 0sed &hen alarge o(erall gearratio is re80ired

driver

driven
http://var/www/apps/conversion/tmp/scratch_6/C:%5CMonsak%5CMachinery%5CCt%20&%20Br.avi


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;ears


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De3initions


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9in'

< rigid body ha(ing t&o or more pairing elements )=oints+ thatconnect to other bodies for the p0rpose of transmitting force ormotion

+ell,#ran- < simple lin' ha(ing threeconnections 0sed to formotion red0ction


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!rameFi6e$,.in-4 re3erence 3rame7 .in- no5 /not always shown as a lin-!

>oint )?inematic pair+#onnection o3 2 or more lin-s allowing relative

motion


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?inematic pairs)>oints or connections+

@a(e 2 basic types$ .ower pair a =oint connected 2 members

ha(ing s0rface contact )e.g. b0sh, pin+ 8igher pair a connection that ta'es place at

a point or along a line )ball bearing, gearteeth, cam+

These classifications are not really important forkinematic analysis


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ypes of pairs )=oints+

"evol'te pair/ $o3!

9rismatic sli$ing! pair/ $o3!

"olling pair / $o3!, witho't slip

#ams 2 $o3!,with slip

Lower pairs

higher pairs


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2-

ype of >oints, @igher Pairs%ears sliding and rotation motion bet&een t&o teeth, 2 *7!


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ype of >oints, @igher Pairs+elt an$ p'lley no sli$ing! or chain an$ sproc-et 1 *7!

Spring no effect on mechanism *7!


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/ommon types of >oint


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*egrees 7f !reedom )dof+ obility )!+

The n'mber o3 motion variables 's'ally joint variables s'ch as angles! which canbe controlle$ in$epen$ently to bring the$evice to a partic'lar positioncon3ig'ration!

:3 F = / the mechanism can be $riven by asingle inp't motion

:3 F = 2 the mechanism re&'ires twoseparate inp't motions to pro$'ceconstraine$ $e3inite! motion


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obility of planar machanisms

#0mber of lin'sn A 6

#0mber of =ointf 1 A

/an &e calc0late themobility from thisinformationB


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link ! " dof # links ! " x# !$ dof

# links % &oint ! " x#' #x ! ( dof

'dof'&oint


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2 ?? ?????????

)x ,y *

1

link ! " dof

)x ,y * )x#,y#*

12

# links ! " x# !$ dof

)x ,y * )x#,y#*

1

#'dof'&oint

# links % &oint ! " x#' x ! + dof


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!orm0la for dof

! A 3)n"1+ 2f 1 f 2

! A obility )dof+

n A n0mber of lin's

f 1 A n0mber of =oints &ith 1 dof

f 2 A n0mber of =oints &ith 2 dof

To calc'late the total n'mber o3 $o3 3or aplanar mechanism4

K't*bach;s criteriaOr %r'bler;s criteria


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D amplesn = 7 3 / = 7 3 2 = 0F = 0 motion is impossible$ mechanism formsa str0ct0re

F = n,/! 23 / 3 2

n = 17 3 / = 17 3 2 = 0F = / mechanism can be dri(en by a singleinp0t motion$ constrained mechanism

n = 17 3 / = 17 3 2 = 0F = / mechanism can be dri(en by a singleinp0t motion$ constrained mechanism


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f f f

f 3 / = ?

3 2 = 0

F = >,/!,2 ?,0

F = 2

D f F d DOF! h h


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Degrees of Freedom DOF! trench hoe#0mber of lin's, n A 12, #0mber of one *7! =oints, f 1 A 12 )pins+ E 3 )slider+ A 15,

#0mber of t&o *7! =oints, f 2 A

! A 3)n

1+ 2f 1 f 2 A 3)12"1+ "2)15+ A 3

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