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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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    1-

    /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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    2

    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

    /2 //

    /0

    @?

    >