ME6401 KINEMATICS OF MACHINERY L T P C3 0 0 3OBJECTIVES: To understand the basic components and layout of linkages in the assembly of a system /machine.To understand the principles in analyzing the assembly with respect to the displacement, velocity, and acceleration at any point in a link of a mechanism.To understand the motion resulting from a specified set of linkages, design few linkage mechanisms and cam mechanisms for specified output motions.To understand the basic concepts of toothed gearing and kinematics of gear trains and the effects of friction in motion transmission and in machine components.

UNIT I BASICS OF MECHANISMS 9Classification of mechanisms Basic kinematic concepts and definitions Degree of freedom, Mobility Kutzbach criterion, Grueblers criterion Grashofs Law Kinematic inversions of four-bar chain and slider crank chains Limit positions Mechanical advantage Transmission Angle Description of some common mechanisms Quick return mechanisms, Straight line generators, Universal Joint rocker mechanisms.

UNIT II KINEMATICS OF LINKAGE MECHANISMS 9Displacement, velocity and acceleration analysis of simple mechanisms Graphical method Velocity and acceleration polygons Velocity analysis using instantaneous centres kinematic analysis of simple mechanisms Coincident points Coriolis component of Acceleration Introduction to linkage synthesis problem.

UNIT III KINEMATICS OF CAM MECHANISMS 9Classification of cams and followers Terminology and definitions Displacement diagrams Uniform velocity, parabolic, simple harmonic and cycloidal motions Derivatives of follower motions Layout of plate cam profiles Specified contour cams Circular arc and tangent cams Pressure angle and undercutting sizing of cams.

UNIT IV GEARS AND GEAR TRAINS 9Law of toothed gearing Involutes and cycloidal tooth profiles Spur Gear terminology and definitionsGear tooth action contact ratio Interference and undercutting. Helical, Bevel, Worm, Rack andPinion gears [Basics only]. Gear trains Speed ratio, train value Parallel axis gear trains EpicyclicGear Trains.UNIT V FRICTION IN MACHINE ELEMENTS 9Surface contacts Sliding and Rolling friction Friction drives Friction in screw threads Bearings and lubrication Friction clutches Belt and rope drives Friction in brakes- Band and Block brakes.

0101

OUTCOMES:

TOTAL: 45 PERIODS

Upon completion of this course, the students can able to apply fundamentals of mechanism for

the design of new mechanisms and analyse them for optimum design.TEXT BOOKS:1. Uicker, J.J., Pennock G.R and Shigley, J.E., Theory of Machines and Mechanisms, 3rdEdition, Oxford University Press, 2009.2. Rattan, S.S, Theory of Machines, 3rd Edition, Tata McGraw-Hill, 2009.

REFERENCES:1. Thomas Bevan, "Theory of Machines", 3rd Edition, CBS Publishers and Distributors, 2005.2. Cleghorn. W. L, Mechanisms of Machines, Oxford University Press, 20053. Robert L. Norton, "Kinematics and Dynamics of Machinery", Tata McGraw-Hill, 2009.4. Allen S. Hall Jr., Kinematics and Linkage Design, Prentice Hall, 19615. Ghosh. A and Mallick, A.K., Theory of Mechanisms and Machines", Affiliated East-West Pvt.

Reg. No. :1~~~--~~--~~--~~--~~~

B.E.IB.Tech. DEGREE EXAMINATION,APRILIMAY2008.

Third Semester

Mechanical Engineering

ME 232 -KINEMATIQS OF MACHINES (Common to Mechatronics Engineering)Time: Three hours Maximum: 100 marks

Ad-size drawing sheet is to be provided.

Answer ALL questions. PART A - (10 X 2 = 20 marks)

1. What is Kutzbach criterian for planar mechanism?

2. Sketch an exact straight line mechanism, with link proportions.

3. Illustrate the instantaneous centers of a typical four bar mechanism.

4. State the condition for a link to experience coriolis acceleration.

5. What are the advantages of roller follower than knife-edge follower?

6. Sketch the displacement, velocity and acceleration diagram when a follower moves with uniform velocity.

7. Prove or disprove that pure rolling is possible at one point only, on the line of action, between two meshing gear teeth profiles.

8. Distinguish, with suitable free hand sketches, a non-reverted gear train and a reverted gear train.

9. Prove or disprove that the efficiency of a screw jack is independent of the load raised.

10. State the condition and the equation for the velocity of the belt for the transmission of power in a flat belt drive.

202

PART B - (5 x 16 = 80 marks)

11. Ca) (i) Explain the inversions of four bar chain, with neat sketches. (8)

(ii) Explain with neat sketches the following: (8) (1) Offset slider mechanism.(2) An indexing mechanism.

Or

(b) (i) Explain the inversions of single slider crank chains, with neat sketches.(10)

-(ii) Explain mechanical advantage and transmission angle related toFour- bar mechanisms. (6)

12. (a) In the mechanism shown in Fig. 12(a) the crank OA rotates at a constant speed equal to 20 rpm anticlockwise and gives motion to the slidingblocks Band D. The dimensions of various links are OA = 300 mm;AB = 1200 mm; BC = 450 mm and CD = 450 mm.

For the given configuration, determine:

(i) Velocities of sliders Band D (ii) Angular velocity of link CD (iii) Linear acceleration of D and (iv) Angular acceleration of CD

Fig. 12(a) Or

2 L 1479

303(b) For the Four-bar linkage shown in Fig. 12(b) find the acceleration of A and B and the angular acceleration of links 3 and 4, Crank 2 has a constant angular velocity, (l)2 == 200 radls counter clockwise direction.

Fig. 12(b)

The linkage A02 == 150 mm; BA == 450 mm, B04 == 300 mm,

-0402 == 200 mm.

13.(a)The following data are for a disc cam mechanism with roller follower:

Minimum radius of the cam == 35 mm, lift of the follower == 40 mm

Offset of the follower == 10 mm right, Roller diameter == 15 mm

Cam rotation angles are as mentioned below:

During ascent == 120, Dwell == 80

During descent == 80, Dwell == 80

Cam rotates in clockwise direction and the follower motion IS simple harmonic during both ascent and descent.

(i) Draw the displacement diagram of the follower and indicate the relevant data.

(ii) Draw the cam profile and indicate the relevant data.

Or

(b) Draw the profile of the cam when the roller follower moves with cycloidal motion as given below :

(i) Outstroke with maximum displacement of 44 mm during 180 of cam rotation

(ii) Return stroke for the next 150 of cam rotation. (iii) Dwell for the remaining 30 of cam rotation.The minimum radius of the cam is 20 mm and the diameter of the roller is 10 mm. The axis of the roller follower passes through the cam shaft axis.

3 L 1479

40414. (a) (i) State the advantages of spur gear over helical gear. (3)

(ii) Which type of gear pair is to be used to get very large speed reduction in a single stage? State the reason. (3)

(iii) State and prove the fundamental law of gearing. (7)

(iv) Determine the minimum number of teeth to avoid interference in worst case of meshing with 14to pressure angle. (3)

Or

(b)Two mating gears have 20 and 40 involute teeth of module 10 mm and20 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 the maximum possible length. Determine the addendum height for each gear wheel, length of the path of contact, arc of contact and contact ratio.

15.(a)A screw-jack. has a square thread of mean diameter 60 mm and pitch 8 mm. The co-efficient of friction at the screw thread is 0.09. A load of 3 kN is to be lifted through 120 mm. Determine the torque required and the work done in lifting the load through 120 mm. Find the efficiency

of the jack also.

Or

(b) (i) Prove or disprove the following statement : "AV-belt drive with same Co-efficient of friction and angle of wrap as a flat-belt drive will transmit less power than flat-belt drive". (6)

(ii) Two pulleys, one 450 rnm diameter and the other 200 mm diameter are on Parallel shafts 2.1 m apart and are connected by a crossed belt. The larger Pulley rotates at 225 rpm. The maximum permissible tension in the belt is 1 kN and the coefficient of friction between the belt and the pulley is 0.25. Find the length of the belt required and the power that can be transmitted. (10)

4 L 1479

505

B.E.IB.Tech. DEGREE EXAMINATION, MAY/JUNE 2009.

Fourth Semester

Mechanical Engineering

ME 1252 - KINEMATICS OF MACHINERY (Regulation 2004)(Common to B.E. (Part-Time) Third Semester - Regulation 2005)

Time: Three hours Maximum: 100 marks

Answer ALL questions. Sketches should be drawn neatly.Give brief procedure for graphical constructions.Answer without units and with wrong units will carry less marks. Symbols used in the solutions should be explained atleast once for each answer. Answers without substituting the data in the equations will carry zero marks. A3 size drawing sheet will be supplied on request. Use both sides of the drawingsheet, if necessary.

Fold the drawing sheet to the size of the answer sheet and attach it.

PART A - (10 x 2 = 20 marks)

1. Give any two inversions of a single slider chain.

2. Write Grashoffs law for 4-bar mechanism.

3. Draw an acceleration polygon for a crank rotating at an angular speed of, 0)' rad/sec and angular acceleration of' a' rad/sec''.

4. Explain how the direction of Coriolis acceleration is obtained.

5. What is the significance of pressure angle in cam?

6. What is the follower motion used for high speed cams? Why?

7. What are the advantages and dis-advantages of involute gear tooth profile?

8. What are the applications of inverted gear trains?

606

9. What is the apparent co-efficient of friction in belt drives?

10. Distinguish between sliding and rolling friction.

PART B - (5 x 16 = 80 marks)

11.(a) Explain the working a quick return motion mechanism. Also derive an equationfor the ratio of time taken for return stroke and forward strokes.

Or

(b) Explain the working of a toggle mechanism and its application with a neat sketch.

12. (a) A slider crank mechanism has a crank of 30 mm length and connecting rod 50 mm length. The angular velocity of crank is 10 radlsec(ccw). The angularacceleration of the crank is 1200 rad/sec-. The crank makes an angle of 900- with the line of strike. Determine the acceleration of slider and angular acceleration of connecting rod.

Or

(b) The driving crank AB of a quick-return mechanism shown below revolves at a uniform speed of 200 rpm. Find the velocity of the tool-box R, in the position shown in Fig.l, when the crank makes as angle of 60 with the vertical line AP. Also determine the angular velocity of link PQ.

200m1n1

Fig. 1

2 J 3309

70713. . (a) A cam is to designed for a knife edge follower with the following data:cam lift = 40 mm during 90 of cam rotation with SHM, dwell for the next30, during the next 60 of cam rotation, the follower returns to its

808

original position with SHM, dwell during the remaining 1800

Draw the

profile of the cam when the line of stroke is offset 20 mm from the axis of the cam shaft. The radius of the base circle of the cam is 40 mm.

Or

14.(a)stroke passes through the axis of the cam.A pinion of 20 involute teeth and 125 mm pitch circle diameter drives arack. The addendum of both pinion and rack is 6.25 mm. What is theleast pressure angle which can be used to avoid .interference? With thispressure angle, find the length of the arc of contact and the minimumnumber of teeth in contact at a time.(b)OrIn an epicyclic gear train shown in Fig.2, the pinion A has 15 teeth and is rigidly fixed in the motor shaft. The wheel B has 20 teeth and gearswith A, and also with annular fixed wheel D. Pinion C has 15 teeth and isintegral. with B(C,B being a compound gear wheel). Gear C meshes withannular wheel E, which is keyed to the machine shaft. The arm rotatesabout 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.(b) Draw a cam profile for operating the exhaust valve of an oil engine. It is requiredto 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 200 of cam rotation. The valve is 37.5 mm and the least radius of the cam is 40 mm. The follower is provided with a roller of radius 20 mm and its line of

Fig. 2.

3 J3309

15.(a)A single dry plate clutch transmits 7.5 kW at 900 rpm. The axial

pressure is limited to 0.07 Nzmm-. If the co-efficient of friction is 0.25,

find mean radius and face width of the friction lining assuming the ratio

of the mean radius to the face width as 4 and outer and inner radii of the

clutch plate.

Or

(b) A load of 10 kN is raised by means of a screw jack, having a square threaded screw of 12 mm pitch and of mean diameter 50 m. If a force of100 N is applied at the end of a lever to raise the load, what should be the length of the lever used? Co-efficient of friction = 0.15. What is the mechanical advantage obtained? State whether the screw is self locking or not.

4 J3309

909Reg. No. :

Question Paper Code : T3051

B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2009

Third Semester

Mechanical Engineering

ME 2203 KINEMATICS OF MACHINERY (Regulation 2008)Time : Three hours Maximum : 100 Marks

Sketches to be drawn neatly

A3 size drawing sheet will be issued if required

Answer ALL Questions

PART A (10 2 = 20 Marks)

1. State Grueblers criterion for spatial mechanism.

2. Define Mechanical Advantage.

3. What is coriolis acceleration?

4. What is meant by virtual centre?

5. Why is a roller follower preferred to knife edge follower?

6. Define Under cutting in cam.

7. State the law of gearing.

8. Write the mobility of differential mechanism.

9. What do you mean by self-locking screws?

10. Give the effect of centrifugal tension in belt drives.

1010PART B (5 16 = 80 Marks)

11. (a) (i) Define transmission angle. Sketch a drag-link mechanism inmaximum transmission angle and minimum transmissionangle

positions and explain.(10)

(ii)Sketch and explain Whitworth quick return mechanism.(6)

Or

(b)(i) Describe various inversions of double slider crank-mechanism with sketches. (10)

(ii) Discuss about the straight line generators. (6)

12.(a)In a simple steam engine, the lengths of the crank and the connecting rod

are 100 mm and 400 mm respectively. The weight of the connecting rod is

50 kg and its centre of mass is 220 mm from the cross head centre. The radius of gyration about the centre of mass is 120 mm. If the engine

speed is 300 rpm and the crank has turned 45 from IDC, determine

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

(ii)Kinetic energy of the connecting rod.(16)

Or

(b) PQRS is a four bar chain with a fixed link PS. The lengths of the links are : PQ = 62.5 mm, QR = 175 mm, RS = 112.5 mm and PS = 200 mm. The crank PQ rotates at 10 rad/s clockwise. Draw the velocity and acceleration diagram when angle QPS = 60 and find the angular velocityand angular acceleration of the links QR and RS. (16)

13.(a)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 300 rpm clockwise direction. The line of motion of the follower

has an offset 10 mm to the right angle of cam shaft axis. The minimum

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

rotation angles are: lift 60, dwell 90, return 120 and remaining angle

for dwell. Draw the cam profile and determine the maximum velocity and

acceleration during the lift and return. (16)

Or

(b) What is tangent cam? Derive the expressions for the velocity and acceleration of a roller follower in the tangent cam. (16)

2 T 3051

111114. (a) A pair of spur gears with involute teeth is to give a gear ratio of 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

(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? (16)

Or

(b) 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 rotates about the axis of the wheels A and C. If the wheel A makes 20 rpm in a clockwise sense and the arm rotates at 100 rpm in the anticlockwise direction and the wheel C has 24 teeth, determine the speed and direction of rotation of wheel C. (16)15. (a) (i) Derive the condition for maximum efficiency of screw. (8) (ii) A bicycle and rider of mass 100 kg are travelling at the rate of16 km/hr on a level road. A brake is applied to the rear wheel which is 0.9 m 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 100 N and = 0.05. (8)

Or

(b) A rope drive is required to transmit 230 kW from a pulley of 1 m diameter running at 450 rpm. The safe pull in each rope is 800 N and the mass of the rope is 0.4 kg per meter length. The angle of lap and the groove is 160 and 45 respectively. If = 0.3, find the number of ropesrequired. (16)

3 T 3051

1212Reg. No. :

Question Paper Code: E3130

B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010

Third Semester

Mechanical EngineeringME2203 KINEMATICS OF MACHINERY (Regulation 2008)

Time: Three hours Maximum: 100 Marks

Answer ALL Questions

PART A (10 2 = 20 Marks)

1. Define Degree of Freedom and give the DOF for a cam with roller follower.

2. List out the applications of Straight line motion mechanisms.

3. A slider sliding at 100 mm/sec on a link, which is rotating at 60 rpm is subjected to Coriolis acceleration. Find its magnitude.

4. Define rubbing velocity.

5. Name any two types of cams with specified contours. -

6. What are the different types of motion with which a follower can move?

7. What is axial pitch of a helical gear?

8. What is the role of Idlers in gear trains?

9. Define virtual coefficient of friction.

10. State the condition for maximum power transmission in a belt drive and deduce the expression for corresponding belt velocity.

PART B (5 16 = 80 Marks)

11. (a) Perform the kinematic analysis of the following Exact Straight Line motion mechanisms. (2 8 = 16)

(i) Peaucellier Mechanism. (ii) Harts Mechanism.Or

1413(b) (i) Sketch and explain any three inversions of a double slider crank chain. (9)

(ii)Illustrate a crank and slotted lever mechanism as an inversion of

single slider crank chain. Deduce an expression for length of stroke

12.

(a)

Thein terms of link lengths. (7)

mechanism of a warping machine is shown in the figure given

below. Various dimensions are as follows. O1A = 100 mm; AC =

700 mm;

BC = 200 mm ; BD = 150mm; O2D = 200mm; O2E = 400mm; O3C =200mm . The crank O1A rotates at a uniform speed of 100 rad/sec. D(i)eterLminineearthveelocity of the point E on the bell crank lever

(ii) Angular velocity of link AC and BD.

Or

(b)Derive the expression for determining the angular position of the coupler

link and the output link of a four bar mechanism.

13.(a)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:

(i) Follower to have a stroke of 20 mm 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 25 mm. The outstroke of the follower is performed with simple harmonic motion and the return stroke with equal uniform acceleration and retardation.Or

(b) 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.

14214E 313014. (a) (i) State and prove Law of gearing, and thus derive the expression for Velocity of sliding. (10)

(ii) Prove that the maximum length of arc of contact between a pair of gear tooth to avoid interference is (r + R)tan . (6)

Or

Face width, Pitch circle,Clearance,Tooththickness,Addendum and Dedendum.(6 1 = 6)(b) (i) Diagrammatically show the following with reference to a spur gear tooth:

(ii) An epicyclic gear train is shown in the following figure. How many revolutions does the arm makes when (1) A makes one revolution in clockwise and D makes 1/2 a revolution in the opposite sense and (2) A makes one revolution in clockwise and D remains stationary? The number of teeth in gears A and D are 40 and 90 respectively. (10)

15. (a) (i) Prove that the torque transmitted by a cone clutch, when the

15315E 31302 W

r3 r3

1 2

2 2intensity of pressure is uniform is given by, T

3 sin r1

r2

with usual notations. (8)

(ii) An effort of 200 N is required to just move a 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 is made 20, the effort required parallel to the plane is found to be 230 N. Determine the weight of the body and the coefficient of friction. (8)

Or

(b) A compressor requires 90 kW to operate at 250 rpm. The drive is by V belts from an electric motor running at 750 rpm. 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 1.75 m. The belt speed should not exceed 1600 m/min. Determine the number of V belts required to transmit the power if each belt has a cross sectional area of375 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.

~.IQuestion Pflper CQd~ ~ (j-ai951.. , _'. ' " ' -,.,," , .. " .-,. "-"".,, -_ ..;.~._

13.E.lS.Tec:,:h.DEGREE EXAMINATION? NQVEM13$R!DECEMBER 2010

Thirg Semeste Mechanical EnginlE!rin~ME 2Z0? - KIN~l\1A'l'ICS OF MAClI~tmRY

(Regulation 2008)

(Common to PTME 220a - Kinematics of Machinery for a.E. (Part-Time) Third. Semester Mechanical El1gineering- (Reguiatiol1 2009

Time; Three hours Maximum: 100 MarksAnswer ALL questions

PART A ""7 (10 x 2 = 2Q Marks)

1. .Differentiate between a machine and a l11eCn~msm.2. Write and explain Gruebler's equation.

3. Draw a sketch to explain how total acceleration of a link, is obtained.

4. What is Coriolis component of acceleration?. . .--

, : " " : '~5.Define undercutting in a cam mechanism,' "6. What arEl the different types of follower motions used in cam-follower mechanisms?.

. ",: -.: ',,;, _'," - -': .. ',..- ,7, What is the significance of contactratio in gears?" ","",",

8. What are the l:igyalltages of epicyclic gear train?

1616

"9. What is t}ie.

role of~fr. ict'.ion in: screw jack?

10.

What is self-energizing brake?. !

11. (11) (i)(ii)

12. (a) -Forths m~cMnisin shown in Fig. Q, 12 (a), determine the velocity of the slider 6 and Iinks 3 and 4,

r651

125

Fig. Q. 12 (a) Or(b) For the slider-crank mechanism shown in Fig. Q. 1.2(b), determine (i) theacceleration qf slider B and (ii)' acceleration of point C. The crank OArotates at l8() rpm. OA ::;:5:0Q mm, AB :;::1500 mm and AC ::;:2:50 mm,

Fig. Q. 1~ (b)

13.(a)Draw the cam profile for the follpwing, data: Base circle radius of

cam > 50 mm, Lift = 40 mm, Angle of ascent, with Cycloidal ::; 600, Angle

of dwell ::; 900, Angle of descent with uniform velocity = 900, Speed ofcam= 300 rpm, Follower offset > 10 mm,' Type of follower Knife-edge. '

Or(b)! -Draw .the cam profile for, the following data: base circle radius of cam::; 50 mm, Lift 40 mm, Angle of ascent with SliM = 90, Angle of dwell= 900, Angle of descent with uniform acceleration and deceleration 90,'$}:leed.of ~m:::;; 300 rpm, TyPe of follower Roller follower (with rollerradius? 10 mm),

2 53195

1717

14.(~) ThE! pressure angle of two gears is 20 and has a module of 10 mm, The numberof teeth on pinion is 24 and is on gear 60. The addendum ofpinion and gear is same and equal to one module. Determine (i) thenumber of pairs of teeth in contact (ii) the angle of action of pinion andgear and the ratio of sliding to rolling velocity at the beginning of contact.

Or

(b)The pitch circle diameter of the annular gear in the epicyclic gear train in Fig. Q. 14 (P) is 425 mm and the module is Q mm. When the annular gear 3 is stationary, the spindle A makes one revolution in the same sense as the sun gear I for every 6 revolutions of the driving spindlecarrying the sun gear. All the planet gearS are of the same size. Determine the number of teeth on all gears,

Fig. Q. 14 (b)

. '. .'15.(a) An open belt drive is used to connect two parallel shafts 4 m apart. The diameterof bigger pulleyis 1.5 m and that of the smaller pulley 0.5 m . The mass of the belt is 1 kg/m length. ThE! maximum tension is not to exceed 1500 N. The coefficient of friction is 0.25. The bigger pulley which is the driver runs at 250 rpm' Due to slip, the speed of the driven pulley is 725 rpm. Calculate the power transmitted, and power lost in friction.

Qr

(b)(i)A verticil I shaft140 mm diameter rotating at 120 rpm rests on a

flat end footstepbearing, The shaft carries a vertical load of 30 kN.

The co-efficient of friction is 0,06. Estimate the power lost in frictionassuming (1) uniform Pressure and (2) uniform wear. (10)

(ii) A Conical pivot supports a load of 20 kN, the cone angle being 120, and thJ;lintensity of normal pressure does notexceed 0.25 MPa. The externalradius is twice the internal diameter, Find the outer and inner radii of the bearing surface. If the shaft rotates at 180 rpm and the coefficient of friction is 0,15, find the power lost in friction, assuming uniform pressure. (6)

53195

18

18

1919Re g. No. : I~

l_--'---'--'--

j_-,----,-----,---,----,--I jl

Question Paper Code: 10408

B.E.lB.Tech. DEGREE EXAMINATION, MAY/JUNE 2012.

Third/Fourth Semester

Mechanical Engineering

ME 2203/113302/ME 35/10122 ME 404/ME 1202/080120010 - KINEMATICS OF MACHINERY

(Common to PTME 2203 - Kinematics of Machinery for B.E. " )Third Semester Mech. - Regulations 2009)

(Regulation 2008)

Time : Three hours Maximum: 100 marks

Answer ALL questions. PART A - (10 x 2 = 20 marks)

1.Sketch and define Transmission angle of a four-bar mechanism. What are the worst values of transmission angle?

2. What is the condition for correct steering of an automobile?

3. What is a configuration diagram? What is its use?

4. Define rubbing velocity in a pin joint and write the equation fOTcalculating the same.

5. Which type of cam follower motion is used in high speed engines? Why?

6. Why large pressure angle is not preferred in cam curves?

7. Define the following terms used in Gear(a) Pressure angle(b) Module .

. 8. What are the roles of "Idlers" in gear trains?

9. Differentiate between self locking and overhauling of screw.

10. State the functional difference between a clutch and a brake.

PAlfr B - (5 x 16 = 80 marks)

11..(a)(i)ExplainKutzbachcriterionfor themobilityof amechanismwith

suitableexample.(4)

(ii)

M2M1

M3 M4

Dimensions are in em

Ml, M2, M3 and M4 are four-bar linkages as shown in figure. The numbers on the figure indicate the respective link lengths in ern. Identify the nature of the mechanism, i.e. whether double crank,crank rocker or double rocker. Give reasons in brief. (4 x 3 = 12)

Or

(b) (i) 'Explain, with a neat sketch, how an offset slider crank mechanism can be used as a quick-return motion mechanism. Derive an expression to find the quick-return ratio. (10)

(ii)With a suitable diagram,explainhow a pantographworks.What

are its uses?(6)

12. (a) A four bar chain is represented by a quadrilateral ABCD in which AD is fixed and is 0.6 m long. The crank AB = 0.3 ill long rotates in a clockwisedirection at 10 rad/s and with an angular acceleration of 30 rad/s-, both clockwise.

The crank drives the link CD (= 0.36 m) by means of the connecting link BC (= 0.36 m). The angle BAD = 60. Using graphical method, determine the angular. velocities and angular accelerations of CD and BC. (16)

Or

2 10408

2020(b)

A four-bar mechanism, with O2 A as the input link, is shown in figure.

(i).Using analytical method, derive the equations for theangular

velocity of the output link and of the connecting link ~.(8)

(ii) If the coordinates of the pin joints are O2 (0,0), A (-15, 26), B(75, 70) and 04(50,0) and the input link rotates at 2 rad/s counter-clockwise, find the angular velocities of AB and of 04B. (8)

13. (a) A cam is to be designed for a knife edged follower with the following data:

(i) Follower lift is 4.0 mm with SHM, during 90 of cam rotation

(ii) Dwell for the next 30

(iii) Follower return to: its original position with SHM, during next 60of cam rotation

(iv) Dwell for the remaining cam rotation.

The line of stroke of the follower passes through the axis of the cam shaft. Radius of the base circle of the cam is 40 mm.

2121(1) Draw the displacement diagram. (2) Draw the profile of the cam.

(4)

(8)

(3) Determine the maximum velocity and acceleration of the follower during forward and return strokes, if the cam rotates at 200 rpm: in CW direction. . (4)

Or

(b) . The following particulars relate to a symmetrical.circular camoperating,a flat faced follower: Least radius = 25 mm, Nose radius = 8 mrn, Lift of the valve = 10 min, Angle of action of cam = 120, Cam shaft speed =1000 r.p.m. -(i) Find the flank, radius. (4)

(ii)Determine the maxim um retardationof the follower.(iii) Draw the profile of the cam.

values of velocity, acceleration and(3)(9)

3 104,08

14.(a)(i)Two unequal gears of involute profile are to give required gear

ratio. Derive an expression for the minimum number of teeth

(ii)required for the pinion in order to avoid interference. (12)

Two gear wheels mesh externally to give a velocity ratio of 3 to 1.

The involute teeth has 6 mm module and 20 pressure angle.Addendum is equal to one module, Determine the number of teethon pinion to avoid interferenceandthe correspondingnumber on

the wheel.(4)

Or

(b)A reverted compound gear train is used as back gear of a lathe, It is required to give a reduction from cone-pulley speed to spindle speed of approximately 9 to 1. The module of the teeth on the high-speed pair is4 111mand of those on low-speed pair is 5 mm. The centre distance is180 mm. Determine the number of teeth on' each of the four wheels, if the pinions are to have as nearly as possible equal numbers of teeth. Also sketch a line diagram and show the gear train. (16)

15. (a) (i) A single plate clutch, with both sides effective, has outer and inner diameters 300 mm and 200 mm respectively. The maximum' intensity of pressure at any point in the contact surface is not to exceed 0.1 Nzmm". If the coefficient of friction is 0.3, determine the power transmitted by a clutch at a speed 2500 rpm for two types of assumptions, that is; for uniform pressure and for uniform wear.(10)

(ii) The following data related to a screw jack; Pitch of the thread screw= 8 mm, diameter of the screw thread = 40 mrn, Coefficient of friction between screw and nut = 0,1, load = 20 kN. Assuming thatthe load rotates with screw, determine:

-(1) the ratio of torques required to raise and lower the load.

2222

(2)

,the efficiency of the machine.

(6)

Or

(b) (i) Two pulleys, one 450 mm diameter and the other 200 mm diameter are on parallel shafts 2.1 m apart and are connected by a belt, as a cross belt drive. The, larger pulley rotates at 225 r.p.m. The maximum permissible tension in the belt is 1kN and the coefficient of friction between the belt and the pulley is 0.25. Find the power that can be transmitted. (8)

(ii)In a simple band brake, one end of the band is attached to the fulcrum of a lever. The other end is attached at a distance of b from the fulcrum. The effort is applied at the end of the lever. Derive an expression for braking torque, in terms of the 'effort, (8)

4 10408

!_ - _.

2323Reg.No.: LI _J

~_L_J

i L_J

~_L

L_~~

Question Paper Code : 11519

B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2012.

Third Semester

Mechanical Engineering

ME 2203/113302IME 35/10122 ME 404!ME 1202 Al080120010 - KINEMATICS OF:MACHINERY

(Common to PTME 2203 - Kinematics of Machinery for B.E. (Part-Time) ThirdSemesterMech. - Regulations 2009)

(Regulation 2008)

Time: Three hours . Maximum: 100 marks

Answer ALL questions. PMT A- (10 x 2 = 20,marks)

1. Write Grashoffs lawford-bar mechanism.

2. What is meant by Indexing mechanism? Where do we use it?

3. What is a configuration diagram? What-is its use?

4. Define rubbing velocity. What will be the expression forrubbing velocity at a pin joint when the two links rotate in opposite direction?

5. State the expressions for maximum acceleration of a follower moving with cycloidal motion.

6.'Why sometimes theaxes of translating roller followersincam follower

mechanisms are offsetfrom the axis of rotation of cam?

7. Define the term 'arc of contact' in gears.

8. Name two applications of reverted gear train.

9. Why self locking screws have lesser efficiency?

10. What is meant by a self-locking and a self-energised brake?

PART B - (5 x 16 = 80 marks)

1l. (a) Sketch and explain the four inversions of Single-slider crank chain. (16) Or(b) (i) What are straight-line mechanisms? Sketch the Peaucellier straight-linemotion mechanism and prove that the generating point moves in straight line. (8)

(ii)Sketch a Hooke's joint and derive the condition for equal speeds of driving and driven shafts. (8)

12.(a)In a four bar chain ABCD, AD is fixed and is 120 mm long. The crank

AB is 30 mm long and rotates at 100 rpm clockwise while the linkCD = 60 mm oscillates about D; BC ::: 120 mm. Using graphical method,

find the angular velocity and angular acceleration of link BC when angle

BAD = 60. (16)

Or

(b) (i) Derive the expressions for the velocity and acceleration of the piston of a reciprocating engine mechanism. (8)

(ii)In a reciprocating engine mechanism, the lengths of the crank and connecting rod are 150 mm and 600 mm respectively. The crank position is 60 from inner dead centre. The crank shaft speed is450 r.p.m. (clockwise)".Using analytical method, determine

2424

(1) velocity of the piston

(2) acceleration of the piston

(2) (2)

(3) crank angle for maximum velocity of the piston and the corresponding velocity. (4)

13. (a) A cam with a minimum radius of 25 mm, rotating clockwise at a uniform speed is to be designed to give motion to a roller follower, at the end of a valve rod, as described below: .

(i) To raise the valve through 50 mm during 120 rotation of the cam.

(ii) To keep the valve fully raised through next 30. (iii) ';['0 lower the valve during next 60 and(iv) To keep the valve closed during rest of the revolution.

2 11519

The diameter of the roller is 20 mm and the diameter of the cam. shaft is 25 mm. The line of the stroke is offset by 15 mm from. the axis of the cam shaft. The displacement of the valve, while being raised and lowered is to take place with SHM.

(1) Draw the displacement diagram. Sketch roughly the shapes of velocity and acceleration diagrams. (6)(2) Draw the 'profile of the cam. (10) Or

(b)In a symmetricaltangent cam operating a roller follower, the least radius of the cam is 30 mm and roller radius is 17.5 mm. The angle of ascent is75 and the total lift is 17.5 mm. The speed of the cam shaft is 600 rpm. Assume that there is no dwell between ascent and descent.

(i) Calculate the principal dimensions of the cam. (6) (ii) Find the acceleration of the follower at the beginning of the lift. (2).(iii) Draw the profile of the cam.. (8)

14. (a) (i) State and prove the law of gearing. (10)

(ii)Show that the involute curves as the profiles of mating gears satisfy the law of gearing. (6)

Or

(b) A compound gear train using spur gears 1S required to give a total reduction ratio of 250 to 1 in four steps. The modules of the gears are5 mm for the first step, 7 mm for the second, 10 mm for the third and16 mm for the fourth.

(i)Arrive at the individual speed ratios, if a tolerance of 0.2% is allowed in the total reduction ratio. (4)

(ii) Find the numbers of teeth of all gears, if the minimum number of teeth for any pinion is 20. (4)

(iii) Find the pitch circle diameters of all gears and the centre distances.(4)

(iv) Sketch a line diagram showing the gear train. (4)

3 11519

252515. (a) (i) In a thrust bearing, the external and internal diameters of the contacting surfaces are 320 mm and 200 mm respectively. The total axial load is 80 kN and the intensity of pressure is 350 kN/m2. The shaft rotates at 400 rpm. Taking the coefficient of friction as 0.06, calculate the power lostin overcoming the friction and the number of collars required. (8)

(ii)A screw-jack has a square thread of mean diameter 60 mm and pitch 8 mrn. The co-efficient of friction at the screw thread is 0.09. A load of 3 kN is to be lifted through 120 mm. Determine the torque required and the work done in lifting the load through 120 mm. Find also the efficiency of the jack. (8)

Or

(b)(i)Derive an expression for the centrifugaltension in a belt passing

round a pulley rim.(6)

(ii) A leather belt is required to transmit 7.5 kW from a pulley 1.2 m in diameter, running at 250 rpm. The angle embraced is 1650 and the coefficient offriction between- the belt and the pulley is 0.3. The safe working stress for the leather belt is 1.5 MPa; the density of leather is 1000 kg/m" and thickness of belt is 10 mm. Determine the width of the belt taking centrifugal tension into account. (10)

4 11519

2626

Question Paper Code: 21559

B.E.IB.Tech. DEGREE EXAMINATION, MAY/JUNE 2013.

Third Semester

Mechanical Engineering

ME 2,2031ME 35/10122 ME 404JME 1202 NOS0120010 - KINEMATICS OF MACHINERY

(Regulation 200S/2010)

(Common to PTME 2203 - Kinematics of Machinery for B.B. (Part-Time) ThirdSemester Mechanical Engineering - Regulation 2009) .

Time: Three hours Maximum: 100 marks

Answer ALL questions.

PART'A - (10 x :2.= 20 marks)

1.What is meant by Kinematic Pair?

2.State the difference between mechanism and structure.

3.Write about rubbing velocity.

4.Write down the expression for finding the number of instantaneousa mechanism.centres in

5.What are the major types of cams? .

6.Define Angle of dwell.

7.List down the common forms of teeth.

8.What is the condition stated by the law of gearing] .

9.List down the laws of friction.

10. Distinguish between open and cross belt drive in terms of its application.

2727PART B - (5 x 16 = 80 marks)

282811. (a) Explain the inversions of Four bar chain with examples.

Or

(b)Sketch and explain the following: (i) Elliptical trammel(ii) Scotch yoke mechanism.

(8)

(8)

12. (a) The following data refer to the' dimensions of the links of a. four-bar mechanism:AB = 50 mm; Be = 66 mm; CD = 56 mm and AD (fixed link)= 100 mm. At the instant when L DAB = 60, the link AB has anangular velocity of 10.5 rad/s in the counter clockwise direction. Determinethe velocity of point C, velocity of point E on the link BC whileBE = 40 mm and the angular velocities of the links BC and CD. Alsosketch the mechanism and indicate the data.

Or

. (b) A single slider-crank mechanism is shown in Fig. 12 b. Determine the accelerationat B & EJ and the angular acceleration of the link AB. The crank rotates at 20 rad/s counter-clockwise.

,

Fig. 12 (b)

13. (a) A cam with a minimum radius of 25 mm, rotating clockwise at uniform speed of 300 rpm is to he designed to give motion to a flat faced mushroom follower as detailed below:

(i) To raise through a distance of 25 mm in 120 rotation of the cam

(ii) To remain at rest for the next 30

(iii) To lower during further 120 rotation of the cam

(iv) To remain in the same position during rest of the revolution .

. The raising of the follower takes place with cycloidal motion and the loweringwith uniform acceleration and retardation. However, the uniformacceleration is 2/3rd of the uniform retardation. Draw the displacementdiagram and profile of the cam.

Or

/' 2 21559

(b) A circular cam operating a flat faced follower has a least diameter of

2929

40 mm. The lift is 12mm and angle of action is 1600

The Speed of

rotation is 500 'rpm. If the period of acceleration of the follower is 60% 'Of the retardation during the lift, determine the following: ,

(i) The principal dimensions of the cam

(ii) The acceleration at the main points.

Also determine the maximum acceleration and deceleration during thelift. .

14. (a) With the help of a neatly drawn sketch of a spur gear, explain elaborately the nomenclature of gears.

Or

(b) An epicyclic gear, train is shown in Fig. 14(b). The input S has 24 teeth.Gears P and C constitute a compound planet having 30 and 18 teeth respectively. If all the gears are of the same pitch, fmd the speed ratio of the gear train assuming A to be fixed.

A

o

Fig. 14 (b)

15. (a) (i) A friction clutch of multi-plate type is meant for transmitting a power of 55 kW at 1800 rpm. Coefficient of friction for the friction surfacesis 0.1. Axial intensity of pressure is not to exceed160 kN 1m2 The internal radius is 80 mm and is 0.7 timesthe external tadius. Determine the number of plates needed to transmit the required torque. (10)

(ii) A vertical shaft of 100 mm diameter rotating at 150 rpm, rests on a flat end foot step bearing. The coefficient of friction is equal to 0.05, and shaft carries a vertical load of 15 kN. ,Find the power lost in friction assuming the following conditions:

(1) Uniform pressure

(2) Uniform wear.

(3) (3)

Or

3 21559

(b) (i) Find the power transmitted by a belb running over a pulley 700 mm, diameter at 300 rpm, fl. = 0.3 and angle of lap rEWo and maximumtension in the belt is 2.453kN. (6)

(ii) A simple brake as shown in Fig 15 (b) (ii) is used on a shaft carrying, a flywheel of mass 450 Kg. The radius of gyration of the flywheel is500 mm, and runs at 320 rpm. The coefficient of friction is 0.2 and the diameter of brake drum is 250 mm, Determine the following:

(1) ,Torque applied due to a hand load of 150 N (4)

(2) The number of turns of the wheel before it is brought to rest.(4)

(3) The time required to bring it to rest from the moment of application of the brake. (2)

3030....- 100 mm - ~ ... ----

300mm

100N '

T,

Fig. 15 (b),(ii)

4 21559

Question Paper Code: 31559

B..E.lB.Tech. DEGREE EXAMINATION, N0_yEMBER/DECEMBER 2013.

Third Semester

Mechanical Engineering

ME 2203iME 35/10122 ME 404/ME 1202 Al080120010 - KINEMATICS OF MACHINERY

(Regulation 2008/2010)

(Common to PTME 2203 .; Kinematics of Machinery for B.E. (Part-Time) ThirdSemester - Mechanical, Engineering _ Regulation 2009)

Time: Three hours Maximum: 100 marks

Answer ALL questions. PART A- (10 x 2 = 20 marks)1. Define sliding connectors.

2. Differentiate rotation and translation.

3. Define number ofinstantaneous centre.

4. Wh,at is low degree of complexity?

5. Define pressure angle.

6. Write the procedure to draw the earn. profile.

7. Define gear ratio. I

8. Write short notes on differentials.

9'. Define anti -friction bearing.

10. Differentiate multiplate clutch and cone clu.tch.

3131PART B - (5 x 16 = 80 marks)

11. . (a) (i) What is kinematic inversion? Explain the four different inversions of slider crank mechanism. (10)

(ii) Determine the degree of freedom for following linkages. (Fig. 1) (6)5'

F~g.1Or

(b) (i) Find the maximum and minimum tranamission angles for the mechanismsshown in fig.2. The figureaindicate the dimensions in standardunits of length. (8)'

9 c

.&

9JL ~A.~

Fig. 2

(ii) Write short notes on toggle mechanism. (8)

12.(a)(i)The crank AB of four bar mechanism shown in figu:re. 3. Rotatesat

60 rpm clockwise. Determine the relative angular velocities ofthe

coupler to the crank and the lever to the coupler. Find also therubbing velocities al the surface of pins 25 mm radius and the joints13 and C. . (8)

Fig. 3

31559

3232(ii) Locate the instantaneous centre's of the slider crank mechanism shown in fig.4. Find the velocity of the slider. (8)

,{$I' "-

trr

......

,",.. ~ -1!ltt

\j,~JlsI I~

(b) (i)~

Fig. 4OrFig.S shows the configuration of a whit worth quick return mechanism. The lengths of the fixed lin): OA ana the crank OP are200 mm and 300mm respectively. Other lengths are AR=200 mm and RS=400 mrn. Find the velocity of the ram using instantaneous. centre method when the crank makes a angle 0[120 with the fixed link and rotates, at 10 rad/s. .

Fig. 5

(ii)Differentiate lowdegreeand highdegreeof complexitywith

suitable sketch.(6)

13. (a) A cam operates on offset roller follower. The least radius of the cam is50 mrn, rollerdiameter is 30 rom, and offset is 20 mm, the cam rotates at360 rpm, The angle of ascent is 480, angle of dwell is 420, and angle of ldescent is 600, The motion is to be SHM during ascent and uniform acceleration and deceleration during decent. Draw the cam profile, . (16)Or

3 315.59

33

33

3434(b) (i)

A flat faced mushroom follower is operated by a symmetrical cam with circular arc flank and nose profile the axis of tappet passed through the cam axis. Total angle of action 'is 162, lift 10 mm and base circle diameter 40 mm. period of acceleration is half the period of retardation during the lift. The cam rotates at 1200 rpm. Determine

14.

, .

. (ii) (a) (i) (ii)

List the various methods to be used to reduce the pressure angle. (4) Explain the various pitches of helical gears with, sketch. (10) Two 15 mm module 20 pressure angle spur gears have addendum

U)The nose and flank radii and(2)The maximum acceleration and retardation during Iift;(12)equal to one module. The pinion has 25 teeth and the gear 50 teeth.Determine whether interference will occur or not. If it 'occurs, to what valve should the pressure angle be changed to eliminate interference? (6)Or

(b)(i) An epicyclic gear train consists of three gears I, 2 and 3 as shown in fig.6 the internal gear 1 has 72 teeth and gear 3 has 32 teeth. The gear 2 meshes with both gear .1 and gear 3 arid is carried on an arm A. 'which rotates about the centre 02 at 20.rpm. If the gear 1 is fixed, determine the speed of gears 2 and 3. (12)

'(ii)15. (a) (i)

eii)

(b) (i)

Fig. 6Write short notes on speed ratio of a planetary gear train. (4) Derive the force analysis of a body resting on an inclined plane with force inclined to the plane. (12)List the various types of friction. (4) OrA veztical shaft 140 mm diameter rotating at. 120 rpm rests on a flat end foot step bearing. The shaft carries a vertical load of 30 KN. The coefficient of friction is 0.06. Estimate the power lost is friction, assuming uniform pressure and uniform wear. .(8)

(ii) A multi-plate disc olutch transmits 55 KW of power at 1800 rpm.'Coefficient of friction for the friction surface is 0.1. Axial intensity of pressure is not to exceed 160 KN/m2. The internal radius is80 mm and 0.7 times the external radius. FInd the number of plates needed to transmit the required torque. (8)

4 31559

Reg. No. I

Question Paper Code: 51622 J

B.EJB.Tech. DEGREE EXAMINATION, MAY/JUNE 2014.

Third Semester

Mechanical Engineering

ME 2203IME 35IME 1202 Al080120010/10122 ME 404 - KINEMATICS OF MACHINERY

(Regulation 2008/2010)

(Common to PTME 2203-KinematicS' of Machinery for B.E. (Part-Time) Third Semester - Mechanical Engineering - Regulation 2009)

Time: Three hours Maximum: 100 marks

Note: A-3 Drawing Sheet is to be Supplied to the ExaminationAnswer ALL questions. PART A - (10 x 2 = 20 marks)1. Differentiate the machine and structure.

2. Classify the constrained motion. ,

3. Define instantaneous centre.

4. What" is the expression for coriolis component of acceleration?

5. Define tangent cam.

6. What are the different motions of the follower?'

7. State the law of gearing.

8. What are the methods to avoid interference?-9. Define velocity ratio.

10. What is themaximum efficiency ofthe screw jack?PART B - (5 x 16 = 80 marks)

11. (a) Explain the working of two different types of quick return mechanisms.Derive an expression' for the ratio of time taken in forward and return stroke for one of these mechanisms. (16)

Or

(b) Sketch and explain any three kinematic inversion of four-bar chain.

353512. . (a) (i) Derive an expression for the relationship between the angular velocities of links in terms of known link lengths, angular positions of links and angular velocity of input link, for a four-bar linkage. (6)(ii)In a slider crank mechanism, the length. of crank OB and connecting rod AB are 125 mm and 500 mm respectively. The centre of gravity G of the. connecting rod is 275 mm from the slider A. The crank speed is 600 rpm clockwise. When the crank has turned 45 from the inner dead centre position, determine velocity of the slider A, Velocity of the point G and Angular velocity of the connecting rod AB (10)Or

(1)By analytical method, Derive the velocity and acceleration for the reciprocating steam engine mechanism.

13.(a)A cam is designed for a knife edge follower with following data:(i) Cam lift = 40 mm during 90 of cam rotation with SHM

(ii) Dwell for the next 30

(iii) During the next 60 of cam rotation, the follower returns to original

position with SHM(iv) Dwell for the remaining 180

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

(b)In a cam with translating roller follower, the follower axis is offset to the right of Cam hinge by 12 mm. The roller radius is 10 mm and the cam rotates in the counter clock-wise direction. Layout the rise portion of the

cam profile to meet the following specifications: Rise takes place during

180 of cam rotation of which for. the first 90 the rise is with constant

acceleration and the rest is with constant retardation. Take seven stationpoints only. The lift of the cam is 30 rom and 'the least radius of the cam is 25 mm.

14.(a)Two gear wheels mesh externally to give a velocity ratio of 3 to 1. The

involute teeth has 6 mm module and 20 pressure angle. Addendum is

equal to one module. The pinion rotates at 90 rpm. Determine

3636

(i)

(ii) (iii) (iv)

Number of teeth on pinion to avoid corresponding number on the wheel;The length of path and are of contactContact ratio andThe maximum velocity of sliding.Or

interference and the(4) (4) (4) (4)

(b)(i)Derive an expression to determine the length of path between two spur gears of different size.of contact(10)

(ii)Briefly explain the sub-classification of compound gear neat sketches.trains with(6)

2 51622

15.. (a)Two pulleys, one 450 mm diameter and the other 200 mm diameter are in

parallel shafts 1.95 m apart and are connected by a crossed belt. Find thelength of the belt required and the angle of contact between the belt and

each pulley. What power can be transmitted by the belt when the larger

pulley rotates at 200 rpm if the maximum permissible tension in the beltis 1 kN and tbe co-efficient of friction between the belt and pulley is0,25? (16)

Or

(b)(i) Derive an expression for the effort required to raise a load with screw jack taking friction into consideration. (8)

(ii) A 150 mtn diameter value, against a steam pressure of 2 MN/m2 is acting, is closed by means of a square threaded screw50 mm in' external diameter with 6 mill. pitch. If the co-efficient offriction is 0.12, find torque required to turn the handle. (8)

..

3 51622

3737ME6401- Kinematics of Machinery

41

Part A questions:

UNIT 1 - BASICS OF MECHANISMS

1. What is Kinematics?

Kinematics is the study of motion (position, velocity, acceleration). A major goal of Understanding kinematics is to develop the ability to design a system that will satisfy Specified motion requirements. This will be the emphasis of this class.

2. What is Kinetics?

Kinetics is the study of effect of forces on moving bodies. Good kinematic design should produce good kinetics.

3. Define Link.

A link is defined as a member or a combination of members of a mechanism connecting other members and having relative motion between them. The link may consist of one or more resistant bodies. A link may be called as kinematic link or element. Eg: Reciprocating steam engine.

4. Define Kinematic Pair.

Kinematic pair is a joint of two links having relative motion between them. The types of kinematic pair are classified according to Nature of contact (lower pair, higher pair)

Nature of mechanical contact (Closed pair, unclosed pair)

Nature of relative motion (Sliding pair, turning pair, rolling pair, screw pair, spherical pair)

5. Define Kinematic Chain

When the kinematic pairs are coupled in such a way that the last link is joined to the first link to transmit definite motion it is called a kinematic chain.Eg: The crank shaft of an engine forms a kinematic pair with the bearings which are fixed in a pair, the connecting rod with the crank forms a second kinematic pair, the piston with the connecting rod forms a third pair and the piston with the cylinder forms the fourth pair. The total combination of these links is a kinematic chain. Eg:Lawn mower.

38

6. Define Degrees of Freedom.

It is defined as the number of input parameters which must be independently controlled in order to bring the mechanism in to useful engineering purposes.It is also defined as the number of independent relative motions, both translational and rotational, a pair can have.

7. Define Pantograph.

Pantograph is used to copy the curves in reduced or enlarged scales. Hence this mechanism finds its use in copying devices such as engraving or profiling machines.

8. What is meant by spatial mechanism?

Spatial mechanism have a geometric characteristics in that all revolute axes are parallel and perpendicular to the plane of motion and all prism lie in the plane of motion.

9. Classify the Constrained motion?

Constrained motions are classified into three types

1. Completely constrained motion.

2. Incompletely constrained motion.

3. Successfully constrained motion.

10. What is Toggle position?

It is the position of a mechanism at which the mechanical advantage is infinite and the sine of angle between the coupler and driving link is zero.

11. What are the important applications of a single slider crank mechanism?

1. Rotary or Gnome engine.

2. Crank and slotted lever mechanism.

3. Oscillating cylinder engine.

4. Bull engine and

5. Hand pump.

12. Give some examples for kinematic pairs.

1. Crank and connecting rod,

2. Connecting rod and piston rod, and

3. Piston and engine cylinder.

39

13. What is meant by transmission angle?

In a four bar chain mechanism, the angle between the coupler and the follower

(driven) link is called as the transmission angle.

14. What are the applications of inversion of double slider crank chain mechanism?

It consists of two sliding pairs and two turning pairs. There are three important inversions of double slider crank chain. 1) Elliptical trammel. 2) Scotch yoke mechanism. 3) Oldhams coupling. Give some examples for kinematic pairs.

15. Write down the Grashofs law for a four bar mechanism?Grashofs law states that the sum of the shortest and longest links cannot be greater than the sum of the remaining two links lengths, if there is to be continuous relative motion between two members.

40

UNIT 2 - KINEMATICS OF MOTION

Part A questions:

1. What are the important concepts in velocity analysis?

1. The absolute velocity of any point on a mechanism is the velocity of that point with reference to ground.2. Relative velocity describes how one point on a mechanism moves relative to another point on the mechanism.

2. Define Instantaneous centre.

Instantaneous centre of a moving body may be defined as that centre which goes on changing from one instant to another.

3. Define Instantaneous centre

Instantaneous axis is a line drawn through an instantaneous centre and perpendicular to the plane of motion.

4. How to represent the direction of linear velocity of any point on a link with respect to another point on the same link?The direction of linear velocity of any point on a link with respect to another point on the same link is perpendicular to the line joining the points.

5. Define Kennedys theorem.

The Kennedys theorem states that if three bodies move relatively to each other, they have three instantaneous centers and lie on a straight line.

6. Define displacement.

It may be defined as the distance moved by a body with respect to a fixed certain fixed point. When there is no displacement in a body it is said to be at rest and when it is being displaced, it is said to be in motion.

7. What are the types of motions?

1. Rectilinear motion.

2. Curvilinear motion.

3. Circular motion.

41

8. What are the methods for determining the velocity of a body?

Important methods for determining the velocity of a body are:

1. Graphical method: i) Relative velocity method

ii) Instantaneous centre method

2. Analytical method.

9. Define velocity.

Velocity may be defined as the rate of change of displacement of a body with respect to the time. Since the velocity has both magnitude and direction, therefore it is a vector quantity.

10. Define speed.

Speed may be defined as the rate of change of linear displacement of a body with respect to the time. Since the speed is irrespective of its direction, therefore it is a scalar quantity.

11. What is deceleration?

The negative acceleration is also known as deceleration or retardation.

12. Define Acceleration.

The rate of change of velocity with respect to time is known as acceleration.

13. Define coincident points.

When a point on one link is sliding along another rotating link, then the point is known as coincident point.

14. Define centrode.

The locus of all instantaneous centres (i.e., I1, I2,) is known as centrode.

15. Define Axode.

The locus of all instantaneous axis is known as axode.

16. Define Body centrode.

The locus of all instantaneous centre relative to the body itself is called the body centrode.

4242UNIT 3 - KINEMATICS OF CAMS

Part A questions:

1. What is cam?

A cam is a rotating machine element which gives reciprocating (or) oscillating motion to another element known as follower

2. Define tangent cam?

When the flanks of the cam are straight and tangential to the base circle and nose circle, the cam is known as tangent cam.

3. Distinguish radial and cylindrical cams.

Radial camCylindrical cam

In this cam, the follower reciprocates (or) oscillates

in a direction perpendicular to the axis.In this the follower reciprocates (or) oscillates in a

direction parallel to the cam axis.

4. What are the different motions of the follower? (i) Uniform motion,(ii) Simple harmonic motion,

(iii) Uniform acceleration and retardation, and

(iv) Cycloidal motion.

5. Compare Roller and mushroom follower of a cam.

S.NoRoller FollowerMushroom Follower

1.Roller followers are extensively used where

more space is available.The mushroom followers are generally used

where space is limited.

2.It is used in stationary gas engines, oil engines

and aircraft valves in engines.It is used in cams which operate the valves in

automobile engines.

6. Explain offset follower.

When the motion of the follower is along an axis away from the axis of the cam centre, it is called offset follower.

43437. Define trace point in the study of cams.

It is a reference point on the follower and is used to generate the pitch curve. In case of knife edge follower the knife edge represents the trace point and the pitch curve corresponds to the cam profile. In a roller follower the centre of the roller represents the trace point.

8. Define pressure angle with respect to cams.

It is the angle between the direction of the follower motion and a normal to the pitch curve. This angle is very important in designing a cam profile. If the pressure angle is too large, a reciprocating follower will jam in its bearings.

9. Define Lift (or) Stroke in cam.

It is the maximum travel of the follower from its lowest position to the topmost position.

10. Define undercutting in cam. How is occurs?

The cam profile must be continuous curve without any loop. If the curvature of the pitch curve is too sharp, then the part of the cam shape would be lost and thereafter the intended cam motion would not be achieved. Such a cam is said to be undercut. Undercutting occurs in the cam because of attempting to achieve too great a follower lift with very small cam rotation with a smaller cam.

11. What do you know about Nomogram?

In Nomogram, by knowing the values of total lift of the follower (L) and the cam rotation angle () for each segment of the displacement diagram, we can readdirectly the maximum pressure angle occurring n the segment for a particular choice of prime circle radius (R0).

12. What are the classifications of cam based on the follower movement?

1) Rise-Return-Rise (R-R-R) cams,

2) Dwell-Rise-Return-Dwell (D-R-R-D) cams,

3) Dwell-Rise-Dwell-Return-Dwell (D-R-D-R-D) cams,

4) Dwell-Rise-Dwell (D-R-D) cams.

444413. What are the different types of cams?

1. Wedge (or) flat cams

2. Radial (or) Disc cams

3. Spiral cams

4. Cylindrical (or) Barrel (or) Drum Cams

5. Conjugate cams

6. Globoidal cams

7. Spherical cams

14. What do you know about gravity cam?

In this type, the rise of the cam is achieved by the rising surface of the cam and the return by the force of gravity of die to the weight of the cam.

15. Define Trace point.

It is a reference point on the follower to trace the cam profile. In case of a knife edge follower, the knife edge itself is a tracing point and in roller follower, the centre of the roller is the tracing point.

16. Define pressure angle.

It is the angle between the direction of the follower motion and a normal to the pitch curve. This is very important in cam design as it represents steepness of the cam profile. If the pressure angle is too large, a reciprocating follower will jam in its bearings.

17. Define Prime circle.

The smallest circle drawn tangent to the pitch curve is known as the prime circle.

18. Define Angle of Ascent.

The angle of rotation of cam from the position when the follower begins to rise till it reaches its highest position is known as angle of ascent. It is also known as out stroke and is denoted by 0.

19. What is meant by Simple Hormonic Motion?When a body rotates on a circular path with uniform angular velocity, its projection on the diameter will have simple harmonic motion. The velocity of the projection will be maximum at the centre of and zero at the ends of the diameter. In case of

45

47acceleration and retardation, the values will be zero at the centre and maximum at the ends of diameter.

20. What are the different shapes of high speed cams?

1. Circular Arc cam with flat faced follower

2. Tangent cam with reciprocating roller follower

21. Define cam angle.

It is the angle of rotation of the cam for a definite displacement of the follower.

22. What are the classifications of follower based on the follower movement?

i) Reciprocating (or) translating follower. ii) Oscillating (or) rotating follower.

23. Define Pitch curve.

The locus of the tracing point is known as the pitch curve. For the purpose of laying out the cam profiles, it is assumed that the cam is fixed and the follower rotates around it.

24. What are the classifications of the follower based on the path of motion of the follower?a) Radial follower. b) Offset follower.

25. What are the classifications of cam base on the constraint of the follower?

a) Pre-loaded spring cams. b) Positive drive cams.c) Gravity cams.

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UNIT 4 - GEARS

Part A questions:

1. State law of Gearing.

The law of gearing states that for obtaining a constant velocity ratio, at any instant of teeth the common normal at each point of contact should always pass through a pitch point, situated on the line joining the centre of rotation of the pair of mating gears.

2. Define normal and axial pitch in helical gears.

Normal pitch is the distance between similar face of adjacent teeth, along a helix on the pitch cylinder normal to the teeth.

Axial pitch is the distance measured parallel to the axis between similar faces of a adjacent teeth.

3. What is the maximum efficiency in worm and worm gear?

max = 1-sin/1+sin

4. What are the advantages and limitations of gear drive? Write any two.

Advantages:

1. Since there is no slip, so exact velocity ratio is obtained.

2. It is more efficient and effective means of power transmission.

Limitations:

1. Manufacture of gear is complicated.

2. The error in cutting teeth may cause vibration and noise during operation.

5. Define interference.

The phenomenon when the tip of tooth undercuts the roots on its mating gear is known as interference.

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6. Define cycloidal tooth profile and involute tooth profile.

A cycloid is the curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line.

Involute profile is defined as the locus of a point on a straight line which rolls without slipping on the circumference of a circle.

7. Define circular pitch and diametral pitch in spur gears.

Circular pitch (pc) : It is the distance measured along the circumference of the pitch circle from a point on one teeth to the corresponding point on the adjacent tooth.

pc=D/T

Diametral pitch (pD) : It is the ratio of number of teeth to the pitch circle diameter.

PD=T/D=/pc

8. Define Backslash.

It is the difference between the tooth space and the tooth thickness along the pitch circle.

Backslash = Tooth space Tooth thickness

9. What is gear train of train of wheels?

Two or more gears re made to mesh with each other to transmit power from one shaft to another. Such a combination is called a gear train or train of wheels.

10. Write velocity ratio in compound train of wheels?

Speed of last follower - Product of teeth on drivers

Speed of first driver Product of teeth on followers.

11. Define simple gear train.

When there is only one gear on each shaft, it is known as simple gear train.

12. What is reverted gear train?

When the axes of the first and last wheels are co-axial, the train is known as reverted gear train.

484813. Where the epicyclic gear trains are used?

The epicyclic gear trains are used in the back gear of lathe, differential gears of the automobiles, pulley blocks, wrist watches, etc.

14. Write down the difference between involute and cycloidal tooth profile.

S.NoInvolute Tooth ProfileCycloidal Tooth Profile

1.Variation in centre distance does not affect the velocity ratio.The centre distance should not vary.

2.Pressure angle remains constant throughout the teeth.Pressure angle varies. It is zero at the pitch point and maximum at the start and end of engagement.

3.Interference occurs.No interference occurs.

4.Weaker teeth.Stronger teeth.

15. Define Contact Ratio.

It is the ratio of the length of arc contact to the circular pitch is known as contact ratio. The value gives the number of pairs of teeth in contact.

16. What is an angle of obliquity in gears?

It is the angle between the common normal to two gear teeth at the point of contact and the common tangent at the pitch point. It is called as pressure angle.

17. What is bevel gearing? Mention its types.

When the non-parallel (or) intersecting but coplanar shafts connected by gears, they are called bevel gears and the arrangement is bevel gearing. It is of two types namely skew bevel gearing and spiral gearing.

18. What are the methods to avoid interference?

1. The height of the teeth may be reduced.

2. The pressure angle may be increased.

3. The radial flank of the pinion may be cut back (undercutting).

19. What is the advantage when arc of recess is equal to arc of approach in meshing gears?

4949When arc of recess equal to arc of approach, the work wasted by friction is minimum and efficiency of drive is maximum.

20. What do you know about tumbler gear?

Tumbler gears are those which are used in lathes for reversing the direction of rotation of driven gears.

21. What you meant by non-standard gear teeth?

The gear tooth obtained by modifying the standard proportions of gear teeth parameters is known as non- standard gear teeth.

22. What is meant by compound gear train?

When there are more than one gear on shaft, it is called a compound gear train.

23. What is the advantage of a compound gear train over a simple gear train?

The advantage of a compound gear train over a simple gear train is that a much larger speed reduction from the first shaft to the last shaft can be obtained with small gears.

24. State the methods to find the v