Mechanical KOM sem3

8/13/2019 Mechanical KOM sem3

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$. Terminolog# and Definitions4Degree of +reedom, Mo-ilit#

• (inematics/ The study of motion ?position, 9e'ocity, acce'eration@. ; majorgoa' of understanding 2inematics is to de9e'op the abi'ity to design a systemthat $i'' satisfy specified motion reEuirements. This $i'' be the emphasis ofthis c'ass.

• (inetics/ The effect of forces on mo9ing bodies. #ood 2inematic designshou'd produce good 2inetics.

• Mechanism/ ; system design to transmit motion. ?'o$ forces@ • Machine/ ; system designed to transmit motion and energy. ?forces

in9o'9ed@ • 1asic Mechanisms/ 3nc'udes geared systems, cam%fo''o$er systems and

'in2ages ?rigid 'in2s connected by s'iding or rotating joints@. ; mechanismhas mu'tip'e mo9ing parts ?for eFamp'e, a simp'e hinged door does not Eua'ifyas a mechanism@.

• E5amples of mechanisms/ Tin snips, 9ise grips, car suspension, bac2hoe, piston engine, fo'ding chair, $indshie'd $iper dri9e system, etc.

(e# concepts/

• Degrees of freedom/ The number of inputs reEuired to comp'ete'y contro' asystem. E5amples/ ; simp'e rotating 'in2. ; t$o 'in2 system. ; four%bar'in2age. ; fi9e%bar 'in2age.

• T#pes of motion/ !echanisms may produce motions that are pure rotation, pure trans'ation, or a combination of the t$o. • 6oint/ ; connection bet$een t$o 'in2s that a''o$s motion bet$een the 'in2s.The motion a''o$ed may be rotationa' ?re9o'ute joint@, trans'ationa' ?s'iding or

prismatic joint@, or a combination of the t$o ?ro''%s'ide joint@.• (inematic chain/ ;n assemb'y of 'in2s and joints used to coordinate an

output motion $ith an input motion.• ink or element/

; mechanism is made of a number of resistant bodies out of $hich some may ha9emotions re'ati9e to the others. ; resistant body or a group of resistant bodies $ithrigid connections pre9enting their re'ati9e mo9ement is 2no$n as a 'in2.


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; 'in2 may a'so be defined as a member or a combination of members of amechanism, connecting other members and ha9ing motion re'ati9e to them, thus a'in2 may consist of one or more resistant bodies. ; 'in2 is a'so 2no$n as 6inematic'in2 or an e'ement.

*in2s can be c'assified into 1@ Binary, @ Ternary, 5@ uarternary, etc.

• (inematic 7air/; 6inematic (air or simp'y a pair is a joint of t$o 'in2s ha9ing re'ati9e motion

bet$een them.E5ample/

3n the abo9e gi9en S'ider cran2 mechanism, 'in2 rotates re'ati9e to 'in2 1 andconstitutes a re9o'ute or turning pair. Simi'ar'y, 'in2s , 5 and 5, constitute turning

pairs. *in2 ?S'ider@ reciprocates re'ati9e to 'in2 1 and its a s'iding pair.T#pes of (inematic 7airs/6inematic pairs can be c'assified according toi@ Nature of contact.ii@ Nature of mechanica' constraint.iii@ Nature of re'ati9e motion.

i8 (inematic pairs according to nat3re of contact /a@ *o$er (air: ; pair of 'in2s ha9ing surface or area contact bet$een the members is2no$n as a 'o$er pair. The contact surfaces of the t$o 'in2s are simi'ar.

0Famp'es: Nut turning on a scre$, shaft rotating in a bearing, a'' pairs of a s'ider%cran2 mechanism, uni9ersa' joint.

b@ &igher (air:


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b@ nc'osed pair: degrees of freedom.

A H 7, resu'ts in a statica''y determinate structure.A K 7, resu'ts in a statica''y indeterminate structure.• (inematic Chain/

; 6inematic chain is an assemb'y of 'in2s in $hich the re'ati9e motions of the 'in2s is possib'e and the motion of each re'ati9e to the others is definite ?fig. a, b, and c.@


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3n case, the motion of a 'in2 resu'ts in indefinite motions of other 'in2s, it is a non%2inematic chain. &o$e9er, some authors prefer to ca'' a'' chains ha9ing re'ati9emotions of the 'in2s as 2inematic chains.

• inkage, Mechanism and str3ct3re/; 'in2age is obtained if one of the 'in2s of 2inematic chain is fiFed to the ground. 3fmotion of each 'in2 resu'ts in definite motion of the others, the 'in2age is 2no$n asmechanism. 3f one of the 'in2s of a redundant chain is fiFed, it is 2no$n as a structure.To obtain constrained or definite motions of some of the 'in2s of a 'in2age, it isnecessary to 2no$ ho$ many inputs are needed. 3n some mechanisms, on'y one inputis necessary that determines the motion of other 'in2s and are said to ha9e one degreeof freedom. 3n other mechanisms, t$o inputs may be necessary to get a constrainedmotion of the other 'in2s and are said to ha9e t$o degrees of freedom and so on.The degree of freedom of a structure is Gero or 'ess. ; structure $ith negati9e degreesof freedom is 2no$n as a )3perstr3ct3re.

• Motion and its t#pes/


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

1. Completel# constrained motion : 3f the motion bet$een a pair of 'in2s is 'imited toa definite direction, then it is comp'ete'y constrained motion. 0.g.: !otion of a shaftor rod $ith co''ars at each end in a ho'e as sho$n in fig.

'. Incompletel# Constrained motion / 3f the motion bet$een a pair of 'in2s is notconfined to a definite direction, then it is incomp'ete'y constrained motion. 0.g.: ;spherica' ba'' or circu'ar shaft in a circu'ar ho'e may either rotate or s'ide in the ho'eas sho$n in fig.

)omp'ete'y)onstrained

!otion

(artia''y)onstrained

!otion

3ncomp'ete'y)onstrained

!otion


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%. )3ccessf3ll# constrained motion or 7artiall# constrained motion/ 3f the motionin a definite direction is not brought about by itse'f but by some other means, then it is2no$n as successfu''y constrained motion. 0.g.: Aoot step Bearing.

• Machine :

3t is a combination of resistant bodies $ith successfu''y constrained motion $hich isused to transmit or transform motion to do some usefu' $or2. 0.g.: *athe, Shaper,Steam 0ngine, etc.

• Kinematic chain with three lower pairs3t is impossib'e to ha9e a 2inematic chain consisting of three turning pairs on'y. But itis possib'e to ha9e a chain $hich consists of three s'iding pairs or $hich consists of aturning, s'iding and a scre$ pair.The figure sho$s a 2inematic chain $ith three s'iding pairs. 3t consists of a frame B,$edge ) and a s'iding rod ;. So the three s'iding pairs are, one bet$een the $edge )and the frame B, second bet$een $edge ) and s'iding rod ; and the frame B.

This figure shows the mechanism of a fly press. The e'ement B forms a s'iding $ith ;and turning pair $ith scre$ rod ) $hich in turn forms a scre$ pair $ith ;.


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'. (3t>-ach criterion, !rashoff?s la@(3t>-ach criterion/

• +3ndamental E:3ation for '4D Mechanisms/ ! H 5?* C 1@ C 1 C Can @e int3iti el# deri e (3t>-ach9s modification of !r3-ler9s e:3ation)onsider a rigid 'in2 constrained to mo9e in a p'ane. &o$ many degrees offreedom does the 'in2 ha9eL ?5: trans'ation in F and y directions, rotationabout G%aFis@

• 3f you pin one end of the 'in2 to the p'ane, ho$ many degrees of freedom doesit no$ ha9eL

• ;dd a second 'in2 to the picture so that you ha9e one 'in2 pinned to the p'aneand one free to mo9e in the p'ane. &o$ many degrees of freedom eFist

bet$een the t$o 'in2sL ? is the correct ans$er@ • (in the second 'in2 to the free end of the first 'in2. &o$ many degrees of

freedom do you no$ ha9eL

• &o$ many degrees of freedom do you ha9e each time you introduce a mo9ing'in2L &o$ many degrees of freedom do you ta2e a$ay $hen you add asimp'e jointL &o$ many degrees of freedom $ou'd you ta2e a$ay by addinga ha'f jointL +o the different terms in eEuation ma2e sense in 'ight of this2no$'edgeL

!rashoff?s la@/• !rashoff B4-ar linkage/ ; 'in2age that contains one or more 'in2s capab'e

of undergoing a fu'' rotation. ; 'in2age is #rashoff if: S M * K ( M ?$here:S H shortest 'in2 'ength, * H 'ongest, (, H intermediate 'ength 'in2s@. Both

joints of the shortest 'in2 are capab'e of 587 degrees of rotation in a #rashoff'in2ages. This gi9es us possib'e 'in2ages: cran2%roc2er ?input rotates 587@,roc2er%cran2%roc2er ?coup'er rotates 587@, roc2er%cran2 ?fo''o$er@ doub'ecran2 ?a'' 'in2s rotate 587@. Note that these mechanisms are simp'y the

possib'e in9ersions ?section .11, Aigure %18@ of a #rashoff mechanism.• Non !rashoff B -ar/ No 'in2 can rotate 587 if: S M * I ( M

et9s e5amine @h# the !rashoff condition @orks/• )onsider a 'in2age $ith the shortest and 'ongest sides joined together.

0Famine the 'in2age $hen the shortest side is para''e' to the 'ongest side ? positions possib'e, fo'ded o9er on the 'ong side and eFtended a$ay from the

'ong side@. &o$ 'ong do ( and ha9e to be to a''o$ the 'in2age to achie9ethese positionsL • )onsider a 'in2age $here the 'ong and short sides are not joined. )an you

figure out the reEuired 'engths for ( and in this type of mechanism

%. (inematic In ersions of B4-ar chain and slider crank chains/• Types of Kinematic Chain: 1@ Aour bar chain @ Sing'e s'ider chain 5@ +oub'e

S'ider chain

• +o3r -ar Chain/

The chain has four 'in2s and it 'oo2s 'i2e a cyc'e frame and hence it is a'so ca''edquadric cycle chain . 3t is sho$n in the figure. 3n this type of chain a'' four pairs $i'' be turning pairs.


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• 5. att9s straight line mechanism or Do3-le le er mechanism/ 3n thismechanism, the 'in2s ;B D +0 act as 'e9ers at the ends ; D 0 of these 'e9ers arefiFed. The ;B D +0 are para''e' in the mean position of the mechanism and coup'ingrod B+ is perpendicu'ar to the 'e9ers ;B D +0. On any sma'' disp'acement of themechanism the tracing point J)> traces the shape of number J->, a portion of $hich$i'' be approFimate'y straight. &ence this is a'so an eFamp'e for the approFimatestraight 'ine mechanism. This mechanism is sho$n be'o$.

• '. )lider crank Chain/3t is a four bar chain ha9ing one s'iding pair and three turning pairs. 3t is sho$n in thefigure be'o$ the purpose of this mechanism is to con9ert rotary motion toreciprocating motion and 9ice 9ersa.3n9ersions of a S'ider cran2 chain:There are fo3r in ersions in a single slider chain mechanism. The# are/1@ Reciprocating engine mechanism ?1 st in9ersion@@ Osci''ating cy'inder engine mechanism ? nd in9ersion@

5@ )ran2 and s'otted 'e9er mechanism ? nd in9ersion@@


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; s'otted 'in2 1 is fiFed.


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Therefore, Time to cutting H 587 % H 1-7 C Time of return H Q H Q . 587 C Q

• B. Rotar# engine mechanism or !nome Engine/Rotary engine mechanism or gnome engine is another app'ication of third in9ersion. 3tis a rotary cy'inder = C type interna' combustion engine used as an aero C engine. Butno$ #nome engine has been rep'aced by #as turbines. The #nome engine hasgenera''y se9en cy'inders in one p'ane. The cran2 O; is fiFed and a'' the connectingrods from the pistons are connected to ;. 3n this mechanism $hen the pistonsreciprocate in the cy'inders, the $ho'e assemb'y of cy'inders, pistons and connectingrods rotate about the aFis O, $here the entire mechanica' po$er de9e'oped, isobtained in the form of rotation of the cran2 shaft. This mechanism is sho$n in thefigure be'o$.

• Do3-le )lider Crank Chain/; four bar chain ha9ing t$o turning and t$o s'iding pairs such that t$o pairs of thesame 2ind are adjacent is 2no$n as doub'e s'ider cran2 chain.

• In ersions of Do3-le slider Crank chain/3t consists of t$o s'iding pairs and t$o turning pairs. They are three importantin9ersions of doub'e s'ider cran2 chain. 1@ 0''iptica' tramme'. @ Scotch yo2emechanism. 5@ O'dham>s )oup'ing.

• $. Elliptical Trammel/This is an instrument for dra$ing e''ipses. &ere the s'otted 'in2 is fiFed. The s'iding

b'oc2 ( and in 9ertica' and horiGonta' s'ots respecti9e'y. The end R generates ane''ipse $ith the disp'acement of s'iders ( and .

The co%ordinates of the point R are F and y. Arom the fig. cos H F. (R

and Sin H y. RSquaring and adding (i) and (ii) we get x 2 + y 2 = cos 2 + sinθ 2 θ

(PR) 2 (QR) 2


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x2 + y 2 = 1(PR) 2 (QR) 2The equation is that of an ellipse, Hence the instrument traces an ellipse. Path tracedby mid-point of PQ is a circle. In this case, PR = PQ and so x 2+y 2 =1 (PR) 2 (QR) 2

It is an equation of circle with PR = QR = radius of a circle.• '. )cotch #oke mechanism/ This mechanism, the s'ider ( is fiFed.


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• The eFtreme 9a'ues of the transmission ang'e occur $hen the cran2 'ies a'ongthe 'ine of frame.

. Description of common mechanisms4)ingle, Do3-le and offset slidermechanisms 4 3ick ret3rn mechanisms/• 3ick Ret3rn Motion Mechanisms/

!any a times mechanisms are designed to perform repetiti9e operations. +uring theseoperations for a certain period the mechanisms $i'' be under 'oad 2no$n as $or2ingstro2e and the remaining period is 2no$n as the return stro2e, the mechanism returnsto repeat the operation $ithout 'oad. The ratio of time of $or2ing stro2e to that of thereturn stro2e is 2no$n a time ratio. uic2 return mechanisms are used in machinetoo's to gi9e a s'o$ cutting stro2e and a Euic2 return stro2e. The 9arious Euic2 returnmechanisms common'y used are i@


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1-7.


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• '. !ene a mechanism/ #ene9a mechanism is an intermittent motionmechanism. 3t consists of a dri9ing $hee' + carrying a pin ( $hich engages in a s'otof fo''o$er A as sho$n in figure. +uring one Euarter re9o'ution of the dri9ing p'ate,the (in and fo''o$er remain in contact and hence the fo''o$er is turned by one Euarterof a turn. +uring the remaining time of one re9o'ution of the dri9er, the fo''o$erremains in rest 'oc2ed in position by the circu'ar arc.

• %. 7antograph/ (antograph is used to copy the cur9es in reduced or en'argedsca'es. &ence this mechanism finds its use in copying de9ices such as engra9ing or

profi'ing machines.

This is a simp'e figure of a (antograph. The 'in2s are pin jointed at ;, B, ) and +.;B is para''e' to +) and ;+ is para''e' to B). *in2 B; is eFtended to fiFed pin O. is a point on the 'in2 ;+. 3f the motion of is to be en'arged then the 'in2 B) iseFtended to ( such that O, and ( are in a straight 'ine. Then it can be sho$n that the

points ( and a'$ays mo9e para''e' and simi'ar to each other o9er any path straightor cur9ed. Their motions $i'' be proportiona' to their distance from the fiFed point.*et ;B)+ be the initia' position. Suppose if point mo9es to 1 , then a'' the 'in2s

and the joints $i'' mo9e to the ne$ positions ?such as ; mo9es to ;1 , B mo9es to1, ) mo9es to 1 , + mo9es to +1 and ( to (1 @ and the ne$ configuration of themechanism is sho$n by dotted 'ines. The mo9ement of ? 1@ $i'' be en'arged to((1 in a definite ratio.

• B. Toggle Mechanism/


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the instantaneous centre I does not lie on the axis of the rear axle but on a line parallelto the rear axle axis at an approximate distance of 0.3l above it.


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piston changes. The piston starts from one end, and increases its speed. It reachesmaximum speed in the middle of its travel then gradually slows down until it reachesthe end of its travel.

RAC( AND 7INI*N RATCHET

RAC( AND 7INI*N/ The rac2 and pinion is used to con9ert bet$een rotary and'inear motion. The rac2 is the f'at, toothed part, the pinion is the gear. Rac2 and pinioncan con9ert from rotary to 'inear of from 'inear to rotary. The diameter of the geardetermines the speed that the rac2 mo9es as the pinion turns. Rac2 and pinions arecommon'y used in the steering system of cars to con9ert the rotary motion of thesteering $hee' to the side to side motion in the $hee's. Rac2 and pinion gears gi9e a

positi9e motion especia''y compared to the friction dri9e of a $hee' in tarmac. 3n therac2 and pinion rai'$ay a centra' rac2 bet$een the t$o rai's engages $ith a pinion onthe engine a''o$ing the train to be pu''ed up 9ery steep s'opes.

RATCHET/ The ratchet can be used to mo9e a toothed $hee' one tooth at a time.The part used to mo9e the ratchet is 2no$n as the pa$'. The ratchet can be used as a$ay of gearing do$n motion. By its nature motion created by a ratchet is intermittent.By using t$o pa$'s simu'taneous'y this intermittent effect can be a'most, but notEuite, remo9ed. Ratchets are a'so used to ensure that motion on'y occurs in on'y onedirection, usefu' for $inding gear $hich must not be a''o$ed to drop. Ratchets area'so used in the free$hee' mechanism of a bicyc'e.

*RM !EAR ATCH E)CA7EMENT.

*RM !EAR/ ; $orm is used to reduce speed. Aor each comp'ete turn of the$orm shaft the gear shaft ad9ances on'y one tooth of the gear. 3n this case, $ith at$e'9e tooth gear, the speed is reduced by a factor of t$e'9e. ;'so, the aFis of rotationis turned by 7 degrees. n'i2e ordinary gears, the motion is not re9ersib'e, a $ormcan dri9e a gear to reduce speed but a gear cannot dri9e a $orm to increase it. ;s the

speed is reduced the po$er to the dri9e increases corresponding'y.


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WATCH ESCAPEMENT: The watch escapement is the centre of the time piece. Itis the escapement which divides the time into equal segments. The balance wheel, thegold wheel, oscillates backwards and forwards on a hairspring (not shown) as thebalance wheel moves the lever is moved allowing the escape wheel (green) to rotateby one tooth. The power comes through the escape wheel which gives a small 'kick' to

the palettes (purple) at each tick.

!EAR) CAM +* * ER.

!EAR)/ #ears are used to change speed in rotationa' mo9ement. 3n the eFamp'eabo9e the b'ue gear has e'e9en teeth and the orange gear has t$enty fi9e. To turn theorange gear one fu'' turn the b'ue gear must turn 4/11 or . P Pr turns. Notice that asthe b'ue gear turns c'oc2$ise the orange gear turns anti%c'oc2$ise. 3n the abo9eeFamp'e the number of teeth on the orange gear is not di9isib'e by the number of teethon the b'ue gear. This is de'iberate. 3f the orange gear had thirty three teeth then e9erythree turns of the b'ue gear the same teeth $ou'd mesh together $hich cou'd causeeFcessi9e $ear. By using none di9isib'e numbers the same teeth mesh on'y e9eryse9enteen turns of the b'ue gear.

CAM)/ )ams are used to con9ert rotary motion into reciprocating motion. Themotion created can be simp'e and regu'ar or comp'eF and irregu'ar. ;s the cam turns,dri9en by the circu'ar motion, the cam fo''o$er traces the surface of the camtransmitting its motion to the reEuired mechanism. )am fo''o$er design is importantin the $ay the profi'e of the cam is fo''o$ed. ; fine pointed fo''o$er $i'' moreaccurate'y trace the out'ine of the cam. This more accurate mo9ement is at theeFpense of the strength of the cam fo''o$er.

)TEAM EN!INE.

Steam engines $ere the bac2bone of the industria' re9o'ution. 3n this common designhigh pressure steam is pumped a'ternate'y into one side of the piston, then the otherforcing it bac2 and forth. The reciprocating motion of the piston is con9erted to usefu'rotary motion using a cran2.


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As the large wheel (the fly wheel) turns a small crank or cam is used to move thesmall red control valve back and forth controlling where the steam flows. In thisanimation the oval crank has been made transparent so that you can see how thecontrol valve crank is attached.

K. )traight line generators, Design of Crank4rocker Mechanisms/

• )traight ine Motion Mechanisms/The easiest $ay to generate a straight 'ine motion is by using a s'iding pair but in

precision machines s'iding pairs are not preferred because of $ear and tear. &ence insuch cases different methods are used to generate straight 'ine motion mechanisms:$. E5act straight line motion mechanism.a. (eauce''ier mechanism, b. &art mechanism, c. Scott Russe'' mechanism'. Appro5imate straight line motion mechanismsa. s mechanism, c. Robert>s mechanism,d. Tchebicheff>s mechanism

• a. 7ea3cillier mechanism /The pin Q is constrained to move long the circumference of a circle by means of thelink OQ. The link OQ and the fixed link are equal in length. The pins P and Q are onopposite corners of a four bar chain which has all four links QC, CP, PB and BQ ofequal length to the fixed pin A. i.e., link AB = link AC. The product AQ x AP remainconstant 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 ;BH;AMAB andB(HBAMA(. Subtracting, ;B%B(H ;A%A(H?;ACA(@?;AMA(@ H ; F ;( .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.

• -. Ro-ert9s mechanism/This is also a four bar chain. The link PQ and RS are of eEua' 'ength and the tracing

pint JO> is rigid'y attached to the 'in2 R on a 'ine $hich bisects R at right ang'es.The best position for O may be found by ma2ing use of the instantaneous centre ofR. The path of O is c'ear'y approFimate'y horiGonta' in the Robert>s mechanism.

a. 7ea3cillier mechanism -. Hart mechanism


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2nit II (INEMATIC)

• Jelocit# and Acceleration anal#sis of mechanisms

=e'ocity and acce'eration ana'ysis by 9ector po'ygons: Re'ati9e 9e'ocity andacce'erations of partic'es in a common 'in2, re'ati9e 9e'ocity and acce'erations ofcoincident partic'es on separate 'in2, )orio'is component of acce'eration.=e'ocity and acce'eration ana'ysis by comp'eF numbers: ;na'ysis of sing'e s'idercran2 mechanism and four bar mechanism by 'oop c'osure eEuations and comp'eFnumbers.

L. Displacement, elocit# and acceleration anal#sis in simple mechanisms/

Important Concepts in Jelocit# Anal#sis1. The abso'ute 9e'ocity of any point on a mechanism is the 9e'ocity of that point$ith reference to ground.. Re'ati9e 9e'ocity describes ho$ one point on a mechanism mo9es re'ati9e toanother point on the mechanism.5. The 9e'ocity of a point on a mo9ing 'in2 re'ati9e to the pi9ot of the 'in2 is gi9en

by the eEuation: = H ω r, $here ω H angu'ar 9e'ocity of the 'in2 and r H distancefrom pi9ot.

Acceleration Components• #ormal Acceleration: An H ω r. (oints to$ard the center of rotation • Tan$ential Acceleration: A t H α r. 3n a direction perpendicu'ar to the 'in2 • Coriolis Acceleration: A c H ω ?dr/dt@. 3n a direction perpendicu'ar to the 'in2• Slidin$ Acceleration: A s H d r/dt . 3n the direction of s'iding. ; rotating 'in2 $i'' produce norma' and tangentia' acce'eration components at any

point a distance, r, from the rotationa' pi9ot of the 'in2. The tota' acce'eration ofthat point is the 9ector sum of the components.; s'ider attached to ground eFperiences on'y s'iding acce'eration.; s'ider attached to a rotating 'in2 ?such that the s'ider is mo9ing in or out a'ongthe 'in2 as the 'in2 rotates@ eFperiences a'' components of acce'eration. (erhapsthe most confusing of these is the corio'is acce'eration, though the concept ofcorio'is acce'eration is fair'y simp'e. 3magine yourse'f standing at the center of amerry%go%round as it spins at a constant speed ? ω @. You begin to $a'2 to$ard theouter edge of the merry%go%round at a constant speed ?dr/dt@. 09en though you are

$a'2ing at a constant speed and the merry%go%round is spinning at a constantspeed, your tota' 9e'ocity is increasing because you are mo9ing a$ay from thecenter of rotation ?i.e. the edge of the merry%go%round is mo9ing faster than thecenter@. This is the corio'is acce'eration. 3n $hat direction did your speedincreaseL This is the direction of the corio'is acce'eration. The tota' acce'eration of a point is the 9ector sum of a'' app'icab'e acce'erationcomponents:

A H An MA t MAc MA s

These 9ectors and the abo9e eEuation can be bro2en into F and y components byapp'ying sines and cosines to the 9ector diagrams to determine the F and y

components of each 9ector. 3n this $ay, the F and y components of the tota'acce'eration can be found.


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. !raphical Method, Jelocit# and Acceleration pol#gons /

!raphical elocit# anal#sis/ 3t is a 9ery short step ?using basic trigonometry $ith sines and cosines@ to con9ert thegraphica' resu'ts into numerica' resu'ts. The basic steps are these:

1. Set up a 9e'ocity reference p'ane $ith a point of Gero 9e'ocity designated.. se the eEuation, = H ω r, to ca'cu'ate any 2no$n 'in2age 9e'ocities.5. ('ot your 2no$n 'in2age 9e'ocities on the 9e'ocity p'ot. ; 'in2age that isrotating about ground gi9es an abso'ute 9e'ocity. This is a 9ector that originates atthe Gero 9e'ocity point and runs perpendicu'ar to the 'in2 to sho$ the direction ofmotion. The 9ector, J ; , gi9es the 9e'ocity of point ;.. ('ot a'' other 9e'ocity 9ector directions. ; point on a grounded 'in2 ?such as

point B@ $i'' produce an abso'ute 9e'ocity 9ector passing through the Gero 9e'ocity point and perpendicu'ar to the 'in2. ; point on a f'oating 'in2 ?such as B re'ati9eto point ;@ $i'' produce a re'ati9e 9e'ocity 9ector. This 9ector $i'' be

perpendicu'ar to the 'in2 ;B and pass through the reference point ?;@ on the

9e'ocity diagram.4. One shou'd be ab'e to form a c'osed triang'e ?for a %bar@ that sho$s the 9ectoreEuation: J B H J ; MJ B/; $here J B H abso'ute 9e'ocity of point B, J ; H abso'ute9e'ocity of point ;, and J B/; is the 9e'ocity of point B re'ati9e to point ;.

$&. Jelocit# Anal#sis of +o3r 1ar Mechanisms/• (rob'ems so'9ing in Aour Bar !echanisms and additiona' 'in2s.

$$. Jelocit# Anal#sis of )lider Crank Mechanisms/• (rob'ems so'9ing in S'ider )ran2 !echanisms and additiona' 'in2s.

$'. Acceleration Anal#sis of +o3r 1ar Mechanisms/• (rob'ems so'9ing in Aour Bar !echanisms and additiona' 'in2s.

$%. Acceleration Anal#sis of )lider Crank Mechanisms/• (rob'ems so'9ing in S'ider )ran2 !echanisms and additiona' 'in2s.

$B. (inematic anal#sis -# Comple5 Alge-ra methods/

• ;na'ysis of sing'e s'ider cran2 mechanism and four bar mechanism by 'oopc'osure eEuations and comp'eF numbers.

$ . Jector Approach/• Re'ati9e 9e'ocity and acce'erations of partic'es in a common 'in2, re'ati9e

9e'ocity and acce'erations of coincident partic'es on separate 'in2

$F. Comp3ter applications in the kinematic anal#sis of simple mechanisms/• )omputer programming for simp'e mechanisms

$K. Coincident points, Coriolis Acceleration/• Coriolis Acceleration: A c H ω ?dr/dt@. 3n a direction perpendicu'ar to the

'in2. ; s'ider attached to ground eFperiences on'y s'iding acce'eration.; s'ider attached to a rotating 'in2 ?such that the s'ider is mo9ing in or out a'ongthe 'in2 as the 'in2 rotates@ eFperiences a'' components of acce'eration. (erhaps


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the most confusing of these is the corio'is acce'eration, though the concept ofcorio'is acce'eration is fair'y simp'e. 3magine yourse'f standing at the center of amerry%go%round as it spins at a constant speed ? ω @. You begin to $a'2 to$ard theouter edge of the merry%go%round at a constant speed ?dr/dt@. 09en though you are$a'2ing at a constant speed and the merry%go%round is spinning at a constantspeed, your tota' 9e'ocity is increasing because you are mo9ing a$ay from thecenter of rotation ?i.e. the edge of the merry%go%round is mo9ing faster than thecenter@. This is the corio'is acce'eration. 3n $hat direction did your speedincreaseL This is the direction of the corio'is acce'eration.E5ample/$


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2nit III (INEMATIC) *+ CAM

• Cams/Type of cams, Type of fo''o$ers, +isp'acement, =e'ocity and acce'eration timecur9es for cam profi'es, +isc cam $ith reciprocating fo''o$er ha9ing 2nife edge,ro''er fo''o$er, Ao''o$er motions inc'uding S&!, niform 9e'ocity, niformacce'eration and retardation and )yc'oida' motion.

)ams are used to con9ert rotary motion into reciprocating motion. The motion createdcan be simp'e and regu'ar or comp'eF and irregu'ar. ;s the cam turns, dri9en by thecircu'ar motion, the cam fo''o$er traces the surface of the cam transmitting its motionto the reEuired mechanism. )am fo''o$er design is important in the $ay the profi'e ofthe cam is fo''o$ed. ; fine pointed fo''o$er $i'' more accurate'y trace the out'ine ofthe cam. This more accurate mo9ement is at the eFpense of the strength of the camfo''o$er.

$L. Classifications 4 Displacement diagrams• Cam Terminolog#/

7h#sical components/ )am, fo''o$er, springT#pes of cam s#stems/ Osci'''ating ?rotating@, trans'atingT#pes of joint clos3re/ Aorce c'osed, form c'osedT#pes of follo@ers/ A'at%faced, ro''er, mushroomT#pes of cams/ radia', aFia', p'ate ?a specia' c'ass of radia' [email protected]#pes of motion constraints/ Critical extreme position C the positions of thefo''o$er that are of primary concern are the eFtreme positions, $ith considerab'efreedom as to design the cam to mo9e the fo''o$er bet$een these positions. This isthe motion constraint type that $e $i'' focus upon. Critical path motion C The path

by $hich the fo''o$er satisfies a gi9en motion is of interest in addition to the eFtreme positions. This is a more difficu't ?and 'ess common@ design prob'em.T#pes of motion/ rise, fa'', d$e''!eometric and (inematic parameters/ fo''o$er disp'acement, 9e'ocity,acce'eration, and jer2 base circ'e prime circ'e fo''o$er radius eccentricity pressureang'e radius of cur9ature.

$ . 7ara-olic, )imple harmonic and C#cloidal motions/• Descri-ing the motion/ ; cam is designed by considering the desired motion

of the fo''o$er. This motion is specified through the use of S=; diagrams?diagrams that describe the desired disp'acement%9e'ocity%acce'eration and

jer2 of the fo''o$er motion@

'&. a#o3t of plate cam profiles/


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2nit IJ !EAR)#ears are used to change speed in rotationa' mo9ement.

3n the eFamp'e abo9e the b'ue gear has e'e9en teeth and the orange gear has t$entyfi9e. To turn the orange gear one fu'' turn the b'ue gear must turn 4/11 or . P Prturns. Notice that as the b'ue gear turns c'oc2$ise the orange gear turns anti%c'oc2$ise. 3n the abo9e eFamp'e the number of teeth on the orange gear is notdi9isib'e by the number of teeth on the b'ue gear. This is de'iberate. 3f the orange gearhad thirty three teeth then e9ery three turns of the b'ue gear the same teeth $ou'dmesh together $hich cou'd cause eFcessi9e $ear. By using none di9isib'e numbersthe same teeth mesh on'y e9ery se9enteen turns of the b'ue gear.

'F. )p3r gear Terminolog# and definitions/• )p3r !ears/• 0Fterna'• 3nterna'• +efinitions

'K. +3ndamental a@ of toothed gearing and In ol3te gearing/• *a$ of gearing• 3n9o'utometry and )haracteristics of in9o'ute action• (ath of )ontact and ;rc of )ontact• )ontact Ratio• )omparison of in9o'ute and cyc'oida' teeth

'L. Inter changea-le gears, gear tooth action, Terminolog#/• 3nter changeab'e gears• #ear tooth action• Termino'ogy

' . Interference and 3nderc3tting/• 3nterference in in9o'ute gears• !ethods of a9oiding interference• Bac2 'ash

%&. Non standard gear teeth/ Helical, 1e el, orm, Rack and 7inion gears


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2nit J +RICTI*N

% . )3rface contacts/• Basic 'a$s of friction• (i9ot and co''ar, introduction and types.• (rob'em on f'at pi9ot, (rob'ems on conica' pi9ot.

%F. )liding and Rolling friction/• S'iding contact bearings• Ro''ing contact bearings• (rob'ems in bearings

%K. +riction dri es/• Ariction dri9es• (ositi9e dri9es and S'ip dri9es• Speed ratio

%L. +riction in scre@ threads/• Ariction in scre$ and nut• Ariction in scre$ jac2 • (rob'ems in scre$ jac2


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% . +riction cl3tches/• Sing'e p'ate c'utches and !u'ti%p'ate c'utches• niform $ear theory and niform pressure theory• (rob'ems in c'utches

B&. 1elt and rope dri es/• Be't dri9es, Open be't dri9es and )rossed be't dri9es• *ength of the be't and ;ng'e of 'ap• (o$er transmitted by a be't dri9e• (rob'ems in be't dri9es

B$. +riction aspects in 1rakes/• Bra2es, Types• !echanica' bra2es, band bra2es• Bra2ing torEue ca'cu'ations• Se'f 'oc2ing bra2es• (rob'ems in bra2es

B'. +riction in ehicle prop3lsion and -raking/• =ehic'e dynamics• =ehic'e propu'sions• Bra2ing aspects in 9ehic'es


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Mechanical KOM sem3

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Transcript of Mechanical KOM sem3