kinematics of machinery

M.P.KEDARNATH / Asst Prof - Mechanical

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MAHALAKSHMI

ENGINEERING COLLEGE

B TIRUCHIRAPALLI – 621213

QUESTION BANK

DEPARTMENT: MECHANICAL SEMESTER: III

SUBJECT CODE: ME2203 SUBJECT NAME: KINEMATICS OF

MACHINERY

UNIT – I: BASICS OF MECHANISMS

PART – A (2 Marks)

1. What is Grashof’s law for a four bar mechanism

and give out its significance (AU Dec 2011) (AU Dec 2009)

2. State the application of an offset slider crank mechanism. (AU Dec 2011)

3. Explain the term kinematic link. Give the classification of kinematic link. (AU Dec 2011)

4. Explain the term: a) Lower pair, (b) Higher pair. (AU Apr 2011,Dec 2006)

5. Define kinematic chain & inversion of kinematic chain. (AU Apr 2011,Dec 2006)

6. Differentiate between a machine and a mechanism. (AU Dec 2010)

7. Write and explain Gruebler’s equation. (AU Dec 2009,Dec 2010)

8. Define degree of freedom and give the DOF for a cam with

roller follower. (AU May 2010, Dec 2009)

9. Define the terms kinematic pair and kinematic chain. (AU May 2010)

10. List out the applications of straight line motion mechanism. (AU May 2010)

11. State Gruebler’s criterion for spatial mechanisms. (AU Dec 2009)

12. State Gruebler’s criterion for planar mechanisms. (AU Dec 2008)

13. State the Kutzbach Criterion. (AU Dec 2009, Dec 2006)

14. What is toggle position? (AU Dec 2009)

15. Define “Mechanical Advantage”. (AU Dec 2009)

16. Give any two inversions of a single slider chain. (AU June 2009)

17. Give out inversions of a double slider crank chain. (AU June 2007)

18. Differentiate between a machine and a structure. (AU Dec 2007)

19. Sketch an exact straight line mechanism, with link properties. (AU Dec 2006)


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PART - B (16 Marks)

1. State and explain the three inversions of a four bar chain? (AU Dec 2011)

2. Using kutzbach Criterion, find the number of degrees of freedom of the two mechanisms

M1 & M2 shown below. (AU Dec 2011)

3. In a crank and slotted lever quick return motion mechanism, the distance between fixed

centres is 240mm and the length of driving crank is 120mm. Find the inclination of the

slotted bar with the vertical in the extreme position and the time ratio of cutting stroke to

return stroke. If the length of the slotted is 450mm, find the length of the stroke if the line

of stroke passes through the extreme positions of free end of the lever. (AU Dec 2011)

4. What is inversion of mechanism? Describe various inversions of

double slider crank mechanism with sketches. (AU Dec 2011, June 2010)

5. Explain the working of toggle mechanism and its application with

a neat sketch. (AU Dec 2010, Dec 2009)

6. Explain the working of pantograph and one indexing mechanism

with a neat sketch. (AU Dec 2010)

7. Explain the working of any two inversions of a single slider crank

chain with neat sketches. (AU Dec 2010, Jun2007)

8. State and explain the various inversions of four bar

chain mechanism. (AU Jun 2010, Dec 2007)

9. Explain with neat sketch the working of crank and slotted lever

quick return motion mechanism. Deduce the expression for length

of stroke in terms of link lengths. (AU Jun 2010)

10. Perform kinematic analysis of following exact straight line

motion mechanisms: (AU Jun 2010)

(a) Peaucellier’s mechanism

(b) Hart’s Mechanism

11. Define Kinematic pair and discuss various types of kinematic

pairs with example. (AU Dec 2009, Jun2007)


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12. Draw a neat sketch and explain any one approximate straight

line generating mechanism. (AU Dec 2009)

13. With a neat sketch, explain the Ackermann steering gear

of an automobile. (AU Dec 2009, Dec 2006)

14. State and explain Whitworth quick return mechanism. Also derive

an equation for ratio of time taken for return strokes and forward strokes. (AU Dec 2009)

15. Define transmission angle. Sketch a drag-link mechanism in

maximum transmission angle positions and explain. (AU Dec 2009)

(a) Explain the Indexing mechanism

16. mechanism in kinematics point of view. (AU Dec 2008)

(b) Ratchet and Pawl Mechanism

17. State and prove the kutzbach criteria for following kinematic chains. (AU Dec 2008)

(a)Cam with roller follower

(b) Three bar chain

(c) Four bar chain

18. Discuss and explain about the straight line generators. (AU Dec 2006)

19. Explain the following (AU Dec 2006)

(a) Mechanical advantage

(b) Grashoff’s law

(c) Mobility of a mechanism


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UNIT 2 - KINEMATIC ANALYSIS


1. For what kind of relative motion, the Coriolis component of acceleration occurs?

Sketch the links to illustrate. (AU Dec 2011)

2. State the relationship between crank angle ‘ѳ’ and connecting rod angle

’φ’ of a single slider crank mechanism. (AU Dec 2011)

3. What is Coriolis component of acceleration? (AU Dec 2011)(AU Dec 2010)

4. Draw a sketch to explain how total acceleration of a link is obtained. (AU Dec 2010)

5. A slider sliding at 100 mm/sec on a link, which is rotating at 60 rpm

is subjected to coriolis acceleration. Find its magnitude. (AU May 2010)

6. Define Rubbing velocity. (AU May 2010) (AU May 2007)

7. Name two mechanisms; one where Coriolis acceleration is encountered

and another where Coriolis acceleration is not encountered. (AU May 2010)

8. How the direction of the angular velocity of the connecting rod is

found out during velocity analysis of a reciprocating engine mechanism

by graphical method. (AU May 2010)

9. What is meant by virtual centre? (AU Dec 2009)

10. Draw an acceleration polygon for a crank rotating at an angular

speed of ‘ω’ rad/sec and angular acceleration of ‘α’ rad/sec2. (AU May 2009)

11. Explain how the direction of coriolis acceleration is obtained. (AU May2009, Dec 2008)

12. Define instantaneous centre of velocity. (AU June 2007)

13. Explain the normal centre of acceleration. (AU Dec 2006)

14. Write the condition for Coriolis component of acceleration. (AU Dec 2006)

15. Illustrate the instantaneous centers of a typical four bar. (AU Jun 2006)

16. What type of link will have only centripetal component of acceleration

and what types of link will have only linear acceleration. (AU Jun 2006)

PART - B (16 Marks)

1. A link AB of a four bar linkage ABCD revolves uniformly at 120rpm in a clockwise

direction. Given AB=75mm, BC=175mm, CD=150mm,DA=100mm and angle BAD equal

to 90°.AD is fixed link. Using graphical approach, find the angular accelerations of links

BC and CD and acceleration of point E on the link BC, if EC = 150mm. (AU Dec 2011)


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2. The lengths of crank and connecting rod of a horizontal reciprocating engine are 100mm

and 500mm respectively. The crank is rotating at 400rpm. When the crank has turned

30° from the inner dead centre, find analytically, the angular velocity and angular

acceleration of the connecting rod. (AU Dec 2011)

3. The following data refers to the lengths of links of a six link mechanism in which the

rotary motion of input link 2 is transformed to horizontal linear motion of output slider 6.

Fixed Link 1, A0B0 -= 60mm, Input link2, AoAr=25mm, Coupler link 3, AB=85mm,

Follower link4, BB0=55mm, Connecting rod5, CD = 60mm.

The pin joint C is at the centre of link BB0.The horizontal line of stroke of the slider passes

through the fixed link pivots A0 and B0. B0A0A is 60°. (AU May 2011)

In this position

(i) Sketch the mechanism and indicate the data.

(ii) Draw the velocity diagram and determine the linear velocity of the slider, if the input link

constant speed is 2 rad/s clockwise.

(iii) Draw the acceleration diagram and determine the linear acceleration of the slider, which

is connected at one end of the connecting rod, CD.

4. A mechanism of a crank and slotted lever quick return mechanism is shown in Fig 1. If

the crank rotates counter clockwise at 120rpm. Determine for the Configuration shown,

the velocity and acceleration of ram D. (AU May 2011)

Also determine the angular acceleration of the slotted lever. Crank, AB=150mm; Slotted

arm , OC = 700mm and link CD = 200mm.


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5. For the mechanism shown in FIG below, determine the velocity of slider 6 and that of

link 3 & 4. (AU May 2011)

6. For the slider crank mechanism shown in fig below, determine (i) the acceleration of

slider B and (ii) acceleration of point C. The crank OA rotates at 180 rpm. OA = 500mm,

AB = 1500mm & AC =250mm. (AU May 2011)

7. The mechanism of a warping machine is shown in figure below. Various dimensions are

as follows: O1A = 100m; AC = 700mm ; BC = 200mm ; BD = 150mm; O2D =200mm;

O2E = 400mm, O3C = 200mm. the crank O1A rotates at a uniform speed of 100rad/sec.

Determine (AU May 2010) (AU May 2007)

(i)Linear velocity of the point E on the bell crank lever

(ii) Angular velocity of link AC & BD.

(iii)Acceleration of the points B & E.


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8. In a slider crank mechanism, the length of the crank is 200mm and length of connecting

rod 825mm. the angular velocity and acceleration of crank is 60rad/s and 1100 rad/s2.

When the crank has turned 120°from the inner dead centre, find : (AU Dec 2009)

(a) The velocity and acceleration of piston

(b) Angular velocity and acceleration of connecting rod.

9. A four bar chain mechanism ABCD with its dimensions is shown in fig below. It is drive

n by the crank AB which rotates at 600 rpm in clockwise direction. The link AD is fixed.

Find the absolute velocity of point C and angular velocity of the links CB and CD.

(AU Dec 2009)

10. In a simple steam engine, the lengths of the crank and the connecting rod are 100mm

and 400mm respectively. The weight of the connecting rod is 50 kg and its centre of

mass is 220mm from the cross head centre. The radius of gyration about the centre of

the mass is 120mm. If the engine speed is 300rpm and the crank has turned 45°from

IDC, determine : (AU Dec 2009) (AU Dec 2006)

(i) The angular velocity and acceleration of the connecting rod

(ii) Kinetic energy of the connecting rod.

11. PQRS is a four bar chain with fixed link PS. The lengths of links are: PQ = 62.5mm,

QR=175mm, RS=112.5mm and PS = 200mm. The crank PQ rotates at 10 rad/s

clockwise. Draw the velocity and acceleration diagram when angle QPS =60° and find

the angular velocity and angular acceleration of the link QR & RS. (AU Dec 2009)

12. A slider crank mechanism has a crank of 30mm length and connecting rod 50mm length.

The angular velocity of the crank is 10rad/sec (ccw).The angular acceleration of the

crank is 1200 rad/sec2 .The crank makes an angle of 90° with the line of stroke.

Determine acceleration of slider, angular acceleration of connecting rod. (AU Dec 2008)

13. Derive the expression for determining the angular position of the coupler link and the

output link of the four bar mechanism. (AU Dec 2008)


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14. The driving crank AD of the quick-return mechanism, as shown in figure below ,

revolves at a uniform speed of 200 r.p.m. Find the velocity and acceleration of the tool-

box R, in the position shown in figure below, when the crank makes an angle of

60°with the vertical line PA.What is the acceleration of sliding of the block at B along the

slotted lever PQ? (AU Dec 2007)

.

15. In a Whitworth quick return mechanism, as shown in figure, crank OA rotates at 30 rpm

in clockwise direction. The dimensions of various links are OA = 150 mm, OC = 100 mm,

CD = 125 mm and DR = 500 mm. Determine the acceleration of the sliding block R and

the angular acceleration of the slotted lever BD. (AU Dec 2007)

16. For the toggle mechanism as shown in figure, the slider D is constrained to move along

horizontal direction. The crank rotates at 180 rpm. The dimensions of various links are

as follows. OA = 180 mm; CB = 240 mm; AB = 360 mm; BD = 540 mm. For the given

configuration determine (i) the velocity and acceleration of the slider (ii) angular velocity

and angular acceleration of links AB, BC and BD. (AU June 2006)

+


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UNIT 3 - KINEMATICS OF CAMS


1. Sketch the shapes of displacement, velocity and acceleration diagrams for uniform

acceleration and retardation motion of a follower. (AU Dec 2011)

2. Why sometimes the axes of translating roller followers, in cam follower

mechanisms are offset form the axis of rotation of cam. (AU Dec 2011)

3. Define pressure angle of cam mechanism and state the best

values of pressure angle (AU Dec 2011) (AU Dec 2009)

4. State the advantage of a tangent cam. (AU Dec 2011)

5. Define tangential cam. (AU Dec 2010)

6. Define undercutting in a cam mechanism. (AU Dec 2010) (AU Dec 2009)

7. What are the different types of follower motions used in

cam – follower mechanism? (AU Dec 2010)

8. What is cam? (AU Jun 2010)

9. What is dwell period of cam? (AU Jun 2010)

10. Name any two types of cams with specified contours. (AU May 2010)

11. What are the different of motion with which a follower can move? (AU May 2010)

12. Define the term pressure angle of a cam mechanism. (AU May 2010)

13. How the maximum velocity of the follower of a cam mechanism is

found out during the lift which takes place with simple harmonic motion? (AU May 2010)

14. Why is roller follower extensively used? (AU Dec 2009)

15. Why is roller follower preferred to knife edge follower? (AU Dec 2009)

16. What is the follower motion used for high speed cams? Why? (AU Jun 2009)

17. Draw atleast four types of a cam with followers (AU Dec 2008)

18. Define pitch curve of the cam. (AU Dec 2008)

19. What is a circular arc cam? (AU May 2008)

20. Construct the displacement diagram for the follower motion to be cycloid.(AU May 2008)

21. What are the classifications of cams based on contact surfaces? (AU Dec 2007)

22. State the basic requirements for high speed cams. (AU Dec 2007)

23. Sketch the displacement, velocity and acceleration diagram

when a follower moves with uniform velocity. (AU Dec 2006)

24. What the advantages of roller follower than knife edge follower? (AU Dec 2006)


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PART - B (16 Marks)

1. A cam with a minimum radius of 25mm and rotating in the CW direction, is to be

designed for a knife edge follower with the following Data: (AU Dec 2011)

- Ascent of the follower through 35mm during 60°cam rotation;

- Dwell for next 40°of the cam rotation ;

- Descent of the follower during the next 90° of the cam rotation;

- Dwell during rest of cam rotation.

The ascent and descent of the cam are with simple harmonic motion and the line of

stroke of the follower is offset 10mm from axis of cam shaft.

(i) Draw the displacement diagram

(ii) Draw the profile of the cam.

(iii) What is the maximum velocity and acceleration of the follower during the ascent and

descent if cam rotates at 150 rpm?

2. The following particulars relate to a symmetrical circular cam operating a flat faced

follower ; least radius =25mm, nose radius = 8mm, lift of the valve = 10mm, Angle of

action of cam = 120°, cam shaft speed =1000rpm (AU Dec 2011)

(i) Find the flank radius

(ii) Determine maximum value of velocity, acceleration and retardation of follower.

(iii) Draw the profile of the cam.

3. A cam with 30mm as minimum diameter is rotating clockwise at a uniform

speed of 1200rpm and has to give the following motion to a roller follower

10mm in diameter: (AU Apr 2011)

(i) Follower to complete outward stroke of 25mm during 120° of cam rotation with

equal uniform acceleration and retardation.

(ii) Follower to dwell for 60°of cam rotation.

(iii) Follower to return to its initial position during 90°of cam rotation with equal

uniform acceleration and retardation.

(iv) Follower to dwell for remaining 90°of cam rotation.

Draw the cam profile if the axis of the roller follower passes through the axis of the cam.

4. Draw the cam profile for the following data: (AU Dec 2010)

Basic circle radius of cam = 50mm, Lift = 40mm, Angle of ascent with cycloidal = 60°,

angle of dwell = 90°, angle of descent with uniform velocity = 90°, speed of cam =

300rpm, Follower offset = 10mm, Type of follower = knife – Edge.


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5. In a symmetrical tangent cam operating a roller follower, the least radius of the cam

30mm and the roller radius is 15mm, the angular of assent is 75°and the total lift is

20mm. The speed of the cam is 600 rpm. Calculate : (AU Dec 2010)

(I)The principal dimensions of the cam.

(II)The acceleration of the follower at the beginning of lift, where straight flank merges

into the circular nose and at apex of the nose.

6. Draw the cam profile for the following data: (AU Dec 2010)

Basic circle radius of cam = 50mm, Lift = 40mm, Angle of ascent with SHM = 90°, Angle

of Dwell = 90°, Angle of descent with uniform acceleration and deceleration = 90°, speed

of cam = 300 rpm, Type of follower = Roller follower (With roller radius = 10mm).

7. Construct a tangent cam and mention the important terminologies on it. Also derive the

expression for displacement, velocity and acceleration of a reciprocating roller follower

when the roller has contact with the nose. (AU May2010)

8. It is required to set out the profile of a cam to give the following motion to the

reciprocating follower with a flat mushroom contact face: (AU May2010)

(i) Follower to have a stroke of 20mm during 120°of cam rotation.

(ii) Follower to dwell for 30° of cam rotation.

(iii) Follower to return to its position during 120° of cam rotation.

(iv) Follower to dwell for the remaining period.

The minimum radius of the cam is 25mm. the outstroke of the follower is performed with

simple harmonic motion and the return stroke with uniform acceleration and retardation.

9. A disc cam used for moving a knife edge follower with SHM during lift and uniform

acceleration and retardation motion during return. Cam rotates at 300rpm clockwise

direction. The line of motion of follower has an offset 10mm to the right angle of cam

shaft axis. The minimum radius of cam is 30mm. The lift of the follower is 40mm. The

cam rotation angles are: lift 60°, dwell 90°, return120°and remaining angle for dwell.

Draw the cam profile and determine the maximum velocity and acceleration during the

lift and return. (AU Dec 2009)

10. A cam is designed for a knife edge follower with following data: Cam lift = 40mm during

90° of cam rotation with SHM, dwell for next 30°, during the next 60°of cam rotation, the

follower returns to its original position with SHM, dwell during remaining 180°. Draw the

profile of the cam when the line of stroke is offset 20mm from axis of cam shaft. The

radius of base circle of cam is 40mm. (AU Jun 2009)


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11. What is tangent cam? Derive the expression for the velocity and acceleration for a roller

follower with tangent cam. (AU Dec 2009)

12. Draw a cam profile for operating the exhaust valve of an oil engine .It is required to give

equal uniform acceleration and retardation during opening and closing of the valve each

of which corresponds to 60°of cam rotation. The valve must remain in the fully open

position for 20°of cam rotation. The valve is 37.5mm and least radius of cam is 40mm.

The follower is provided with a roller of radius 20mm and its line of stroke passes

through the axis of the cam. (AU Jun 2009)

13. A symmetrical circular cam opening a flat faced follower has the following particulars:

(AU Dec 2008)

Minimum radius of the cam = 30mm; Total lift= 20mm; Angle of lift=75°;

Nose radius =5mm; Speed = 600rpm.

Determine: (i) The principal dimensions of the cam.

(ii) Acceleration of the follower at the beginning of lift, at the end of contact

with the circular flank, at the beginning of contact with nose and at the

apex of the nose.

14. A cam drives a flat reciprocating follower in the following manner: (AU Dec 2007)

(i)Follower moves outwards through a distance of 20mm with SHM during first 120°of

cam rotation.

(ii) Follower dwells during next 30° of cam rotation.

(iii)Follower moves inwards with SHM for next 120° of cam rotation.

(iv)The follower dwells for the remaining period.

Draw the profile of the cam, when minimum radius of cam is 25mm. Also calculate the

maximum velocity and acceleration during outward and inward motion of the follower

when the cam rotates with 200 rpm.

15. Construct a tangent cam and mention the important terminologies on it. Also derive the

expression for displacement, velocity, acceleration of a reciprocating roller follower when

the roller has contact with the nose. (AU Dec 2006)


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UNIT 4 - GEARS

PART A (2 Marks)

1. Define the following terms used in a gear: (a) Pressure angle (b) Module. (AU Dec 2011)

2. What are the advantages of planetary gear trains? (AU Dec 2011)

3. State the law of gearing. (AU Dec 2011) (AU June 2010) (AU Dec 2009)

4. What is interference in involute gear and

how it is prevented? (AU Dec 2011) (AU Dec 2009) (AU May 2008)

5. What is the difference between simple gear

train and compound gear train? (AU Dec 2011) (AU June 2010)

6. What is the significance of contact ratio in gears? (AU Dec 2010)

7. What are the advantages of epicyclic gear train? (AU Dec 2010) (AU May2007)

8. What is meant by diametral pitch of gear wheel? (AU June 2010)

9. What is axial pitch of a helical gear? (AU May2010) (AU May2007)

10. What is the role of idlers in gear trains? (AU May2010)

11. Name two curves for use as gear profile, which satisfy the law of gearing. (AU May2010)

12. What is a worm gear drive? Explain with a sketch. (AU May2010)

13. What are the advantages and disadvantages of

involute gear tooth profile? (AU May2009)

14. What are the applications of reverted gear trains? (AU May2009)

15. What are various types of torques in an epicyclic gear train? (AU Dec 2008)

16. Define undercutting in gears (AU May 2008)

17. Define the following terms used in gears: (a) Pitch circle ,

(b) Circular pitch, (c) Diametral pitch and (d) Module. (AU May2007)

PART - B (16 Marks)

1. Two involute gears of 20° pressure angle are in mesh. The number of teeth on pinion is

20 and the gear ratio is 2. If the pitch expressed in module is 5 mm, and the pitch line

speed is 1.2 m/s, assuming addendum as standard and equal to one module, find (i) the

angle turned through by pinion when one pair of teeth is in mesh; and (ii) the maximum

velocity of sliding. (AU Dec 2011)


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2. An epicyclic gear train shown in figure below. (AU Dec 2011)

The internal gear D has 90 teeth and the sun gear A has 40 teeth. The two planet gears B

& C are identical and they are attached to an arm as shown. How many revolutions does

the arm makes,

(i) When’A’ makes one revolution in clockwise and ‘D’ , makes one revolution in

clockwise and ‘D’ makes ½ revolutions in opposite sense.

(ii) When ‘A’ makes one revolution in clockwise and ‘D’ remains stationary.

3. (i) State and prove the law of gearing and thus derive the expression for “Velocity of

sliding”. (AU Dec 2011) (AU May 2010)

(ii)Show that the involute curves as the profiles of mating gears satisfy the law of gearing.

4. Two planet gears B & C having 30 teeth each are attached to the arm E as shown in

figure below and gear A is having 40 teeth instead of 50 , then find the number of

revolutions made by the arm, when:

(i)Gear A makes one revolution clockwise and D makes half a revolution anticlockwise.

(ii)Gear A makes one revolution clockwise and D is stationary. (AU Dec 2010)


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5. The pressure angle of two gears is 20° and has a module of 10mm. The number of teeth

on pinion and gear is same and equal to one module. Determine (i) the number of pairs

of teeth in contact and (ii) the angle of action of pinion and gear and the ratio of sliding to

rolling velocity at the beginning of contact. The pitch circle diameter of the annular gear

in the epicyclic gear train in fig below is 425mm and the module is 5mm. when the

annular gear 3 is stationary, the spindle a makes one revolution in the same sense as

the sun gear 1 for every 6 revolutions of the driving spindle carrying the sun gear . All the

planet gears are of same size. Determine number of teeth on all gears.(AU Dec 2010)

6. Prove that the maximum lengths of arc of contact between a pair of gear tooth to avoid

interference are (r+R) tanφ. (AU Dec 2010)

7. Diagrammatically show the following with reference to a spur gear tooth: Face width,

pitch circle, clearance, tooth thickness, addendum& dedendum. (AU Dec 2010)

8. A pair of spur gears with involute teeth is to give a gear ratio 0f 3:1. The arc of approach

is not to be less than the circular pitch and smaller wheel is the driver. The angle of

pressure is 20°. (AU Dec 2009)

(i) What is the least number of teeth that can be used on each wheel?

(ii) What is the addendum of the wheel in terms of circular pitch?

9. In an epicyclic gear train, an annular wheel A having 54 teeth meshes with a planet

wheel B which gears with a sun wheel C, the wheels A and C being rotated about the

axis of the wheels A &C.If the wheel A makes 20 rpm in a clockwise sense and the arm

rotates at 100rpm in the anticlockwise direction and wheel C. (AU Dec 2009)

10. A pinion of 20 involute teeth and 125 mm pitch circle diameter drives a rack. The

addendum of both pinion and rack is 6.25mm.What is the least pressure angle which

can be used to avoid interference? With this pressure angle , find the length of arc and

the minimum number of teeth in contact at a time. (AU Dec 2008)


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11. In an epicyclic gear train shown in fig below, the pinion A has 15 teeth and is rigidly fixed

in the motor shaft. The wheel B has 20 teeth and gears with A, and also with annular

fixed wheel D. Pinion C has 15 teeth and is integral with B(C, B being a compound gear

wheel). Gear C meshes with annular wheel E, which is keyed to the machine shaft. The

arm rotates about the same shaft on which A is fixed and carries the compound wheel B-

C. If the motor runs at 1000 rpm, find the speed of the machine shaft. (AU Dec 2008)

12. Derive an expression for minimum number of teeth on the wheel in order to avoid

interference (AU Dec 2007)

13. Two mating gears have 20 and 40 involute teeth of module 10mm and 20° pressure

angle .The addendum on each wheel is to be made of such a length that the line of

contact on each side of the pitch point has half of the maximum possible length.

Determine the addendum height for each gear wheel, length of the path of contact, arc

of contact and contact ratio. (AU Dec 2007)

14. Explain the procedure adopted for designing the spur wheels. (AU Dec 2006)

15. A compound epicyclic gear is shown in figure below. The gears A,D & E are free to

rotate on axis P. The compound gears B & C rotate together on the axis Q at the end of

arm F.All gears have equal pitch. The number of external teeth on gears A,B of arm F.All

the gears have equal pitch. The number of external teeth on gears A, Band C are 18,45

and 21 respectively. The gears D & E are annulus gears. The gear A rotates at 100 rpm

in anticlockwise direction and gear D rotates at 450 rpm clockwise .Find the speed and

direction of the arm and the gear E. (AU Dec 2006)


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UNIT 5 – FRICTION

PART A

1. What is limiting angle of friction. (AU Dec 2011)

2. State the functional difference between clutch and a brake. (AU Dec 2011)

3. What is the difference between sliding friction and rolling

friction? Give example? (AU Apr 2011)

4. What are the advantages of V belt drive over flat belt drive? (AU Apr 2011)

5. State the functional difference between clutch and a brake. (AU Apr 2011)

6. What is the role of friction in screw jack? (AU Dec 2010)

7. What is self energizing brake? (AU Dec 2010)

8. Write the various types of brake. (AU Dec 2010)

9. Define sliding friction and rolling friction. (AU Dec 2010)

10. Define virtual coefficient of friction. (AU May 2010)

11. State the condition for maximum power transmission in a

belt drive and deduce the expression for corresponding belt velocity. (AU Apr 2011)

12. What are self locking screws? Why self locking screws

have lesser efficiency? (AU Dec 2009)

13. What are the functions of clutches? (AU Dec 2009)

14. Give the effect of centrifugal tension in belt drives. (AU Dec 2009)

15. What is the apparent coefficient of friction in belt drives? (AU Jun 2009)

16. Distinguish between sliding friction and rolling friction? (AU Jun 2009)

17. Define the term “Limiting friction”. (AU Dec 2008)

18. How centrifugal tension affects the power transmission in belt drive. (AU Dec 2008)

19. What is creep in the case of belt? (AU May2008)

20. Which type of screw thread is preferable in power transmission? (AU May 2008)

21. List any four desirable characteristics of brake lining material. (AU Dec 2007)

22. What are the advantages of wire ropes over fabric ropes? (AU Dec 2007)

23. What are timing belts? (AU Dec 2006)

24. Explain briefly the significance of friction in braking. (AU Dec 2006)

PART - B (16 Marks)

1. Derive an expression for maximum efficiency of a screw jack. (AU Dec 2011)


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2. A single plate clutch has dimensions 300mm outside diameter and 100mm inside

diameter. Both side of the plate are effective. Assuming uniform wear and coefficient of

friction of 0.35, determine the maximum power that can be transmitted at 1500rpm,if the

maximum pressure on the plate is not to exceed 1 MN/m2 .Find also the minimum

intensity of pressure and its location. (AU Dec 2011) (AU Dec 2006)

3. Prove that the limiting ration of tensions in a flat belt drive is given by the equation

2

1

T

T= eµѳ. (AU Dec 2011)

4. A rope drive is required to transmit 230KW from a pulley of 1m diameter running at

450rpm.the safe pull in each rope is 800N and mass of the rope is 0.46Kg/m. The angle

of the lap and groove angle are 160° and 45° respectively. If the coefficient of friction

between the rope and the pulley is0.3, find the number of ropes required. (AU Dec 2011)

5. The mean diameter of the screw jack having pitch of 10mm is 50mm.A load of 20 KN is

lifted through a distance of 170mm.Find the work done in lifting the load and efficiency of

the screw jack when

(i) the load rotates with the screw.

(ii) the load rests on the the loose head which does not rotate with the screw.

The external and internal diameters of the bearing surface of the loose head are 60mm

and 10mm respectively, the coefficient of friction for the screw as well as the bearing

surface may be taken as 0.08. (AU Dec 2011)

6. A rotor is driven by a coaxial motor through a single plate clutch, both sides of the plate

being effective .The external and internal diameters of the plate are respectively 220mm

and 160mm and the total spring load pressing the plates together is 570N.The motor

armature and shaft has a mass of 800kg with an effective radius of gyration of 200mm.

The rotor has a mass of 1300kg with an effective radius of gyration of 180mm.The

coefficient of friction for the clutch is 0.35.The driving motor is brought up to a speed of

1250rpm when the current is switched off and the clutch suddenly engaged.

(AU Dec 2011)

Determine

(i) The final speed of motor and rotor,

(ii) The time to reach this speed

(iii) The kinetic energy lost during the period of slipping


19

7. Prove that the torque transmitted by a cone clutch, when the intensity of pressure is

uniform is given b y, T = sin3

W2 2

2

2

1

3

2

3

1 rr/rr( with usual notations. (AU Dec 2010)

8. An effort of 200N is required to just move certain body up an inclined plane of an angle

15°, the force is acting parallel to the plane. If the angle of inclination of the plane. If the

angle of inclination of the plane is made 20°, the effort required parallel to the plane is

found to be as 230N. Determine the weight of the body and the coefficient of friction.

(AU Dec 2010)

9. A compressor 90KW to operate at 250rpm.The drive is V-belts from an electric motor

running at 750rpm.The diameter of the pulley on the compressor shaft must not be

greater than 1 meter while the center distance between the pulleys is limited to 1.75m.

The belt speed should not exceed 1600m/min.Determine the number of V belts required

to transmit the power if each belt has a cross sectional area of 375 mm2 , density 1000

kg/m3 and an allowable tensile stress of 2.5 Mpa.The groove angle of the pulley is

35°.The coefficient of friction between the belt and the pulley is 0.25.Also calculate the

length of each belt. (AU Dec 2010) (AU Dec 2008)

10. What are block brakes? Derive an expression relating the applied force and breaking

torque in a block brake. (AU May 2010) (AU Dec 2006)

11. The diameter of a block brake is 250mm. The L shaped lever has its longer arm

horizontal. The vertical distance of the pivot (of the lever) from the centre of the drum is

75mm. the horizontal distance of the pivot from the centre of the drum is 200mm.An

effort of 700N (vertical) is applied at a horizontal distance of 400mm from the pivot. The

contact angle of the block is 90 degrees. The coefficient of friction is 0.35.Determine the

breaking torque. (AU May 2010)

12. Derive an expression for the centrifugal tension in belt drives. (AU May 2010)

13. A pulley is driven by a flat belt, angle of lap being 120degrees.The belt weighs 6Nper

meter run. The coefficient of friction is 0.3 and maximum stress in the belt is not to

exceed 200N/cm2 . The belt is 10cm wide and 0.6 cm thick. Find the maximum power

that can be transmitted and the corresponding speed of the belt. (AU May 2010)

14. A single plate friction clutch with both sides of plate being effective is used to transmit

power at an engine speed of 200rpm. It has outer and inner radii 10cm and 8cm

respectively. Find maximum power transmitted and the corresponding axial thrust, if the

maximum intensity of pressure is not to exceed 0.08N/mm2 . Assume coefficient of

friction as 0.25. (AU Dec 2009)


20

15. A flat belt runs on a pulley 1m in diameter and transmits 8kW at 200rpm. Assuming

angle of lap as 170°and coefficient of friction as 0.25.Find the necessary width of belt if

the pull is not to exceed 200N/cm width of the belt.

Neglect centrifugal tension. (AU Dec 2009)

16. Derive the condition for maximum efficiency of screw. (AU Dec 2009)

17. A bicycle and rider of mass 100kg are travelling at the rate of 16km/hr on a level road. A

brake is applied to the rear wheel which is 0.9m in diameter and this is the only

resistance acting. How many turns will it make before it comes to rest? The pressure

applied on the brake is 100N and µ = 0.05 (AU Dec 2009)

18. A rope drive is required to transmit 230kw form a pulley of 1m diameter running at

450rpm.The safe pull in each rope is 800N and the mass of the rope is 0.4kg/meter

length. The angle of lap and the groove is 160°and 45°respectively.If µ = 0.3, find the

number of ropes required. (AU Dec 2009)

19. Derive an expression for the torque required to lift a load by a screw jack, if l is the

length of the arm. (AU Dec 2008) (AU Dec 2007)

20. A leather faced conical clutch has a cone angle of 30°.If the intensity of pressure

between the contact surfaces is limited to 0.35Mpa and the breadth of the conical

surface is not to exceed one third of mean radius, find the dimensions of the contact

surfaces to transmit 22.5kW at 2000rpm.Assume uniform rate of wear and take

coefficient of friction as 0.15. (AU Dec 2008)

21. An open belt drive connects two pulleys 120cm and 50cm diameters on parallel shafts

4m apart .The maximum tension in the belt is 1855N.The coefficient of friction is 0.3.The

driver pulley of diameter 120cm runs at 200rpm.Calculate (i) the power transmitted (ii)

the torque on each of the two shafts. (AU Dec 2008)

22. A band brake acts on the 3/4thof circumference of a drum of 450mm diameter which is

keyed to the shaft. The band brake provides a braking torque of 225 N-m.One end of the

band is attached to a fulcrum pin of the lever and other end to a pin 100 mm from the

fulcrum. If the operating force is applied at 500mm from the fulcrum and the coefficient of

friction is 0.25, find the operating force when the drum rotates in anticlockwise direction.

(AU Dec 2007)

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