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Fourth semester B.E. Degree Examination, I)ecemb er 2ollKinematics of Machines

Time: 3 hrs.Max. Marks:100

Note: Answer any FIW full questions, selectingat least TWO questions ftom eaeh part'

(08 Marks)

b. Explain: i) Lower pairs ii) Higher pairs' (06 Marks)

c. Describe with a neat sketch, the crank and slotted lever mechanism, an inversion of a slider

crack mechanism (06 Marks)

2 a. Explain the Whitworth quick return motion mechanism, with a neat sketch' (10 Marks)

b. Derive the expression for necessary condition of correct steering. Explain with a neat sketch,

the Ackerman steering gear mechanism' (10 Marks)

6

Fis.Q3

4 a. Locate all the instantaneous centres ano frna *re angular velocity of the link BC' The link

dimensions of the mechanism are AB = 300mm, BC = BD:360mm and AD:600mm'

The angle BAD :60". The crank rotates at 100 rpm.lRefer Fig.Qa($l (10 Marks)

3 A single slider crank mechanism shown in Fig.Q3, has the crank cB = 100rnm and connecting

rod BA : 300;, with eeatre of gravity G-ld0mm ftom B. The crankshaft has a speed of

75 radlsecand an angular acceleration of 1200 rad/sec'. Find

i) The velocityof G and the angular velocrty of AB'

ii) The acceleiation of G and angular acceleration of AB. (20 Marks)

PART - A

I a. Define the following, with sketches:

i) Link ii) Mechanism iii) Machine iv) Inversion.

Fig.Qa(a)

b. The lengths of the crank and the connecting rod o{ a reciprocating engine are 200mm and

700mm r"rpr.rir"ly. rrr. crank rotates in clockwise direction at 120 rad/sec' when the

crank is at 30oC to'iDC, by using the Klein's construction, determine

i) The velocity *a u..*f*ration Jf the piston ii)Angular velocity and acceleration of the cR'(10 Marks)

1 of2

a

06ME44

PART - B

The crank and connecting rod of an engine are 0.3m and 1.5 in length respectively.The crankrotates at 180 rpm clockwise. Determine the velocity and acceleration of the piston when thecrank is 40o from TDC. Also determine the position of the crank for zero acceleration of thepiston. (20 Marks)

6 a. Derive the expression for the length of arc of contact in a pair of spur gears in a mesh.(08 Marks)

b. Two mating gears have 20 and 40 involute teeth of module 10mm and 20o pressure angle.The addendum of each wheel is to be made of such a length that the line of contact on eachside of the pitch point has half the maximum possible length. Determine the addendumlength for each wheel, length of path of contact, arc of contact and contact ratio. (12 Marks)

7 a. Explain with a neat sketch the o'Sun & planet wheel" (04 Marks)

b. In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth,respectively. If the arm rotates at 150 rpm in the anticlockwise direction about the centre ofgear A which is fixed, determine the speed of the gear B, if the gear A instead of beingfixed, makes 300 rpm in the clockwise direction. [Refer Fie.Q7(b)].

Ag

8 Construct the profile of a cam to suit the following specifications:

(16 Marks)

Cam shaft diameter = 40mmDiameter of the roller:25mmAngle of fall : 150"

Least radius of cam:25mmAngle of lift - 120"Lift of the follower = 40mm

No. of pauses are two of equal interval between motion.During the lift the motion is SHM. During the fall motion is UARM. The speed of camshaft isuniform. The line of stroke is offset to 12.5mm from the centre of the cam. (20 Marks)

*!t*!*rk

Fie.Q7(b)

2 of2

b.

r

Fourth Semester B.E. Degree Examination, June/July 201,1

Kinematics of Machines

Note: Answer any FIVEfull questions.selecting atleast TWO from each.parl.

06M.E,44

Max. Marks:100

(10 Marks)(10 Marks)

(08 Marks)(08 Marks)(04 Marks)

(20 frIarks)

length of connecting rod isDetermine the velocity and

dead centre, use Klein's(l0lVlarks)(10 Marks)

Time: 3 hrs.

.:

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troo,!NdtHoOts(.)otr-co!La7

u.d

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L (,)

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PART - A

I a. Define:i) Kinematic chain

i) Angular veiocity of links QR and RSii) Angular acceleration,:f link QR and RS.

4 a. In a reciprocating engine the length of crank is 250 mm and1000 mm. The crank rotates an uniform speed of 300 rpm.

acceleration of piston, when the crank is 30' from innerconstruction"

b. Locate all instantaneous benters for the following mechanism.

a.

b.

c.

ii) Machineiii) Structureiv) Self closed pairv) Force closed pair.Sketch and explain any two inversions of four bar chain.

Sketch and explain the following :

Whitworth quick return mechanism.Ratchet and pawl mechanism.Toggle mechanism.

A four bar chain of links PQ, QR and RS are 62.5 mm, 175 mm ancl 120 mm longrespectively, the link PS of chain PQRS is fixed and having iength of 200 mm. The link PQ

makes an angle of 60" rvith PS and rotaies at i0 radl sec ciockwise. Detennine :

PART - B

Explain the significance of loop closure equation, with example. (05 Marks)5a.b. The crank of an engine mechanism is 200 mm long and the ratio of connecting rod length to

the crank radius is 4. Determine the acceleration of the piston when crank has turned through

an angle 45o from inner dead centre and rotatin g at a speed of 240 rpm counter clockwise

Fig. Qa@Xi) Fie. Qa&)(ii)

direction by complex number approach.I of2

(15 Marks)

6a.

b.

06M844

What is interference in involute gears? Derive an expression for the length of arc of contactin a pair of meshed spur gears. (10 Marls)Two gear wheels mesh externally and are to give a velocity ratio of 3 to 1. The teeth are ofinvolute form module:6 mm, addendum: one module, pressure angle = 20". The pinionrotates at 90 rpm. Determine :

i) Minimum no. of teeth on each wheel to avoid interferenceii) The number of pair of teeth in contact.

An epicyclic gear train consist of a sun wheel S, a stationary intemal gear 'E' and threeidentical planet wheels 'P' carried on a stat- shape planet carrier'C'. The size of difterenttoothed wheels are such that the planet carrier C rotates one revolution for every 5revolutions of the sun wheel S. The minimum number of teeth on any wheel (say P) is 16.the driving torque on the sun wheel is 100 N -m. Determinei) Number of teeth on different wheels of the train.ii) Toque necessary to keep the internal gear stationary. (20 Marls)

Fig. Q7

The following data relate to cam profile in which the roller follower moves with SHMduring ascent and uniform acceleration and retardation motion during descent.Minimum radium of cam :30 mm

Offset of follower axis : 12 mm towards right

Roller radiusLift

Angle of ascent

Angle of descent

:8 mm=28mm

:90":60o

(10 Marlis)

and acceleration during(20 Marks)

Angle of dwell between ascent and descent :45oSpeed ofcam :200 rpmDraw the profile of cam and determine the maximum verocitvoutstroke and return stroke.

*****

2 of2

USN

Fourth Semester B.E. Degree Examination, Dec.08

Kinematics of MachinesTime: 3 hrs.

06M844

/ Jan.O9

Max. Marks:100

Note : Answer any FIVE questions selecting ot least two from each part.

Part Aa. Define with suitable examples :

i) Structureii) Machineiii) Mechanismiv) Higher pair

b. Sketch and explain the following:i) Beam engineii) Gnome engine.iii) Ellipticaltrammel.

A double slider crank mechanism is shown in figure Q3. The crank OA rotates

angular velocity of 10 radlsec. The links OA, AB and AC are 100 mm, 200mmlong respectively. By drawing the velocity and acceleration polygons determine:

a. Velocity and acceleration of each slider.b. Angular velocity and angular acceleration of each connecting rod.

a. Sketch the crank and slotted lever mechanism. Indicate the strokes. (06 Marks)

b. Sketch and explain Geneva wheel mechanism. (07 Marks)

c. Sketch Ackremann steering mechanism and obtain condition for correct steering. (07 Marks)

(08 Marks)

(12 Marks)

at a constantand 200 mm

(20 Marks)

-+I,,.!,

..--'/ a. '' .-.

.c112--a- - 4.7..,"'

b.

IFig. Q3

Locate all the instantaneous centers for a

i) Four bar mechanism.ii) Slider crank mechanism.

Determine the velocity and acceleration of the pistonengine to the following specifications:Stroke of piston: 600 mmRatio of length of connecting rod to crank length:5Speed of engine:450 rpm clockwise.Position of crank: 45" with inner dead centre.

?. ',.

.ar10l/

- !f'- *\

1

- ,+i fo-l-r

(10 Marks)

by Kleins construction for a steam

1 of ?

(10 Marks)

obtain loop closure equation ro, u +-u*P,f,.ltn?oir*.

06M.F,44

(04 Marks)Develop equations for the angular velocities and angular accelerations for the links 3 and 4

(16 Marks)as shown in figure Q5 O) using complex algebra method.,tr,,t *-*

r-" -\jg' l 6'3

?-..I ,d/\Ib.'L h

',

l/1 ',

1,.

t0r, *'[---- I d,^n

Fig. Qs (b)

a.

b.

cornpare cycloidal and involute gear tooth profile. (05 Marks)What is rneant by interference? Mention various methods of avoiCing interference in gears.

Two gear wheels have respectively 28 and45 teeth and a standard aaaenoullsf;Tlmodule. The pressure angle is 20" and the module of 6 mm Determine : i) length of pathof contact. ii) contact ratio. (i0 Marks)

Sketch and explain:i) Simple gear train.ii) Epicyclic gear train. (06 Marks)

In an epicyclic gear train of sun and planet type, the pitch circle diameter of the Annularwheel (A) is 425 mm and the module is 5 mm" When the annular wheel is stationary, thespider which carries 3 planet Gears (P) of equal size has to make one revolution for every drevolutions of the driving spindle carryrng sun wheel (S). Determirte the number of teethon all the wheels. (I,l Marks)

Draw the profile of a cam operating a roller reciprocating foilower and with the followingdata: Minimum radius of cam : 25 mm, Lift : 30 mm; Rolter diameter : 15 mm. The cam liftithe follower for 120' with SHM followed by a dweil period of 30", then the follower lcwersdown during 150" of the cam rotation with UARM followed by a dwell period. The camrotates at a uniform speed of 150 rprn (CW direction). The axis of the follower passes throughthe axis of the cam shaft. Calculate the maximum velocity and acceleration of the followerduring the descent period. (20 Marks)

Fourth semester B.E. Degree Examination, June / July 08

Kinematics of MachinesMax. Marks:100

Note z1^. Answer any FIVE full questions'

2. Graphieai questions can be drawn oru drawing sheet'

3. Miising data if any may be suitably assumed'

reduced size drawings.

Sketch and explain tle working of scotch yoke mechanism'

Find the degrees of freedom for the following mechanisms:

uix

Time:3 hrs-

1a.

b.

2a.

Fig. Q2 (a)

b. With neat sketches explain the working of all

If the crank OA rotates at 150 rpm in the antislockwise

tnfiguration the velocity and accelerdtion of slider B and I)'t

K--1€Orayp,

-{

Fig. Q3t of2

Differentiate between: i) Lower pair and higher pair ii) Machine and mechanism'

iiD Constrained and unconstrained motion' (05 Marks)

Jil;;JJ ffiffiire working of pantffih and prove that it reproduces the entarged or(08 Marks)(06 Marks)

(08 Marks)

ME44

the inversit,.ns of dcuble slider mechanism'(12 Marks)

direction, find for the given(20 Marks)

OA: 80 mmAC: CB : CD = 120 mm

4a.b.

M.E44

state and prove Arnold-Kennedy's theorem. (05 Marks)Locate all the instantaneous centers of the mechanism shown. Find the angular velocity oflink AB. oA:200 mm, AB: 1500 mrn, BC:600 mm, cD:500 *m urrd BE:400 mm.OA rotates at 120 rpm clockwise. (15 Marks)

Fig. Qa &)

Ja-b.

Derive an expression for loop closure equation for four bar mechanism. (08 Marks)If the crank and connecting rod are 150 mm and 600 mm long respectively and the crankrotates at constant speed of 100 rpm, determinei) Velocity and acceleration of piston and'ii) Angular velocity and angular acceleration of connecting rod.The angle, which the crank makes with the inner dead centre, is 30". (12 Marks)

Explain and derive the condition for the law of gearing. (08 Marks)A pinion having 30 teeth drives a gear having 80 teeth. The profile of the gears is involutewith 20' pressure angle, 12 mm module and 10 mm addendum. Find the length of path ofcontact, arc ofcontact and contact ratio. (12 Marks)

Figure shows diagrarnmatically a compound epicyclic gear train. Wheels A, D and E are freeto rotate independently on spindle O, while B and C are cornpound and rotate together onspindle P, on the end of arm OP. All the teeth of different wheeli have same module. A has 12teeth, B has 30 teeth and C has 14 teeth cut externally. Find the number of teeth on wheels Dand E, which are cut internally. If the wheel A is driven clockwise at 1 rps while D is drivencounterclockwise at 5 rps, determine the magnitude and direction of angular velocities of armOP and wheel E. (20 Marks)

Fig. Q7

Construct the profile of a cam to suit:Cam shaft diameter : 40 mm; Least radius of cam : 25 mm; Diameter of roller : 25 mm;Angle of lift :120':' Angle of fall: 150"; Lift of the follower: 40 mm;Number of pauses aretwo of equal interval between motions.During the lift the motion is SHM. During the fall the motion is uniform acceleration anddeceleration. The speed of the camshaft is uniform. The line of stroke of the follower is oflset

6a.b.

- r:

12.5 mm from the centre of the cam. (20 Marks)

Ft

*ui*

ME44

(20 Marks)

Fourth semester B.E. Degree Examination, Dec. 07 / Jan. 08

Kinematics of MachinesTime:3 hrs. Max. Marks:100

Note z T.Answer any FIVEfull questions'2.Graphicalsolutionscanbedrawnondrawingsheet.

a. Distinguish between :

i) Complete constraint and successful constraint ii) Open pair and closed pair.

iii) Structure and kinematic chain iv) Ivlechanism and machine. (08 Marks)

b. Explain with neat sketches, three inversions of double slider crank chain. (12 Marks)

With neat proportionate diagrams explain the principle and working of following mechanisms'

a. Whitworth mechanismb. Geneva mechanismc. Toggle mechanismd. Hooke's joint.

point 'C' and link O+ B.

Fig.3 (20 Marks)

The Fig.3 shows Robert's straight line mechinism in which point'C'moves.in ahorizontal

direction. 02 and O+ are tlie fiied points. pzA is a crank 75 mm long and its velocity and

acceleration are Z0 rad./sec and 100 rad/secz respectively, both clockwise. The dimensions of

other links are : AB :75 mm, o+B : 75 mm, l\ozo 4 = 45o, OzO+: 125 mm. The point'c'

traces its path along horizontal line .joininB OzO+. Find the velocities and accelerations of

The mechanism of a wrapping machine, is as shown in Fig4 has the following dimensions:

OrA: 100 mm; AC : 700 mm; BC :200 mm; O:C :200 mm;

OzE:400 mm; OzD:200 mm and BD: 150 mm'

The crank OrA rotates at uniform angular velocity of 100 rad/sec. Find the velocity of the

point E of the bell crank iever by instantaneous centre method.€

1?r

i', !6ti

1 r,i ,srTZ

-:r*J-I

I 1 i!c.c nLw'Fc-i

l

--Fig.4

I of2

(20 Marks)

ME+4

Use kineuatic analysis of the slider- crank by complex numbers and derive the expressions9rveJ99ttrandaccelerationoftheslider*d.o*i.tingrod.]--_-The slider-crank of an internal combustion engine shoil in Fig.s(b) includes a crank of50.8 mm tength and a connecting rod of 203 rin length. Th...rril;p;;J;f;;;*;;;constant at 314 rad/s. Determine the acceleration of tf,e *uss r.ri.. f,gl;f ,h.;"#.;Grod when &e crank angle is 30o. The mass centre 93 is located 50.8 *J rro", ifr. crank pinat A.

6a.b.

c.

what is meant by involute irrtrrr"r.n"lrg'J(o' (10 Marks)

Derive * "*pr"rrion

for the minimum number of teeth on a pinion mating *rh(:'r[[T:avoid interference.

(06 Marks)Two mating involute gears of 20o pressure angle have a gear ratio of 2. The number ofteeth on pinion is 20. The speed of pinion is 250 rpm. Takeirodule as l2 mm.If the addendum on each wheel is such that the path of approach and path of recess oneaeh side are of half the maximum possible length each; find:i) The addendum of pinion and gear ii) The l."gth of*, of contact. (r0 Marks)

The FigT shows an epicyclic gear train. Pinion A has 15 teeth and is rigidly fxed in themotor shaft- The wheel B has 20 teeth and gears with A and also with aniular fixed wheelD' Finion C has 15 teeth qd it integral with B (C and B being a compound wheel). Gear Cmeshes with annular wheel E, which is keyed to the machine shaft. The arm rotates aboutthe same shaft on which A is fixed and carries the compound wheel B - C. If the motorruns at 100 rpm, find the speed of the machine shaft. Find also the torque exerted on themachine shaft if the motor develops a torque of 100 N_m.

a.

Draw the profile of the cam for the following details :

a. Minimun radius of the cam -20 mm.b. Rotation-counter clock-wise at 1000 rpm.c. Oufward stroke - UARM - l}0o.d. Follower- l0 mm dia roller.e. Lift ofthe follower- 20 mm.f. Dwell at tull lift - 60o.g. Retum stroke - SHM during 120o.h. offset - foltrower axis 5 mm to the right of the aris of cam.calculate the maxim,m acceleration during retum stroke.

2 of2

(20 Marks)

Fig.s(b)

Fig.7

(20 Marks)

\-: tr. '.'

Page No... I

USN

NBW SCHEME

Fourth Semester B.E. Degree Examination, July 2007Mechanical Engineerin g

Kinematics of Machines

Time: 3 hrs.l [Max. Marks:i00Note : Answer any FIVE full questions.

I a. Define a kinematic chain. Describe various forms of kinematic chain with examples.(05 Marks)

b. Explain the Grubler's mobility equation for a planar mechanism. Determine themobility of a cam with an oscillating follower fitted with a roller. (05 Marks)

c. Sketch and explain the kinematic chain with three lower pairs. (05 Marks)d. Sketch and explain the elliptical trammel mechanisrn. (05 Marks)

2 a" What is meant by quick-return mechanism? Sketch and explain drag link mechanism"(06 Marks)

b. Sketch and explain Peaucellier straight line motion mechanism. (06 Marks)c. A Hooke's joint is used to connect two shafts whose axes are inclined at 200. The

driving shaft rotates uniformly at 6000 rpm. What are the extreme angular velocitiesof the driven shaft? Find the maximum value of acceleration and state the angle atwhich it will occur? (08 Marks)

3 A double slider-crank rnechanism is shown in Fig.3(a). The crank OA rotates at constantangular velocity of 10 radlsec. The links OA, AB and AC are 100 mm, 200 mm and 200mm long respectively. By drawing the velocity and acceleration polygons, determine :

NIT,44

(10 Marks)a. Velocity and acceleration of each slider,b" Angular velocity and angular acceleration of each connecting rod"

A

Fig.3(a) (20 Marks)

The stroke of,a steam engine is 400 mrn and the length of the connecting rod is 600 mm.The crank roJates at 300 rpm clockwise direction and the crank is inclined at 300 with theinner dead center. The center of gravity of the connecting rod is 240 mm away from thecrank end. By Klein's construction determine the following :

a. Velocity and acceleration of the piston.b. Angularvelocity and angular acceleration of the connecting rod.c. Velocity and acceleration at the center of gravity of the connecting rod. (20 Marks)

Contd.... 2

Page No... 2

An internal combustion engine has a crank of 150 mm length and a connecting rod of600 mm length. The crank rotates at a constant speed of 300 rpm counter clockwise.Determine the position, velocity and acceleration of the slider when the crank angle is450 Iiom the inner dead center position by complex algebra. (20 Marks)

TIie thickness of an involute gear tooth is 4.98 mm at a radius of 50.8 mm and a

pressure angle of 200. Calculate the tooth thickness on the base circie. (05 Marks)

The foilowing data refer to the two mating involute gears of 200 pressure angle :

Number of teeth on pinion is 30, gear ratio is 2, module is 12 mm and the speed ofthe pinion is 600 rpm.

The line of contact on each side of the pitch point is half the maximum possiblelength. Find the height of addendum for each gear wheel and the length of arc ofcontact. Also find the maximum velocity of sliding during approach and excess.

(15 Marks)

Sketch and describe a bevel gear differentiaL used in automobiles. (06 Marks)A fixed annular gear A and a smaller concentric rotating gear B are connected by acompound gear CD. The gear C mesh with gear A and D with B. The compoundgears revolved in a pin on the arm R, which revolves about the axis of A and B. Thenumber of teeth on gears A, B and D are 150, 40 and 100 respectively. Determine thenumber of teeth on gear C, if the gears A and C have twice the module of gears B andD. How many revolutions will B make for one complete revolution of the arm R?

(14 Marks)

A cam with a base circle radius of 35 mm is rotating at a uniform speed of 100 rpm inanti-slockwise direction. Draw the profile for the disc cam with reciprocating knife edgefollower on the center line of the cam shaft for the following follower motion.a. Follower to move upward 3C mm with simple harmonic rnotion in 0.1 sec.b. Follower to dwell in next 0.15 sec.

c. Follower to move upward to another 30 mm u'ith simple harmonic rnotion in0.15 sec.

d. Follower to return to its starting position with uniform acceleration and retardation inthe remaining period of one complete revolution of the cam shaft. However, theacceleration period is twice the retardation period.

Determine the maximum velocity and acceleration of the follower during its outwardstroke. (20 Marks)

MEl41 -; .

.Y:

a.

b.

la.b.

JgJJC