# Theory of Machines. CH-1: Fundamentals and type of Mechanisms

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1 CH-1: Fundamentals and type of Mechanisms 1. Define kinematic link and kinematic chain. 2. Enlist the types of constrained motion. Draw a label sketch of any one. 3. Define (1) Mechanism (2) Inversion of mechanism 1. Define kinematic pair and state its types. 2. Describe with neat sketch the working of a crank and slotted lever quick return mechanism. 3. Justify with neat sketch elliptical trammel as an inversion of double slider crank chain * 4. Define completely constrained motion and successfully constrained motion with neat sketch. State one example of each *** 5. Explain with neat sketch working principle of Oldham s coupling ** 6. State inversion of double slider crank chain. Explain Oldham s coupling with neat sketch. 7. Draw a labelled sketch of Quick return mechanism of shaper and explain its working. 8. What are the types of kinematic pair? Give its examples. 9. Define : (i) Spherical pair (ii) Higher pair. 10. State any four inversions of single slider crank chain. Describe any one with neat sketch. 11. What is a machine? Differentiate between a machine and a structure ** 12. Describe with neat sketch the working of scotch yoke mechanism. 13. Justify that slider crank mechanism is a modification of the basic four bar mechanism with neat sketch. 14. State the meaning of sliding pair, turning pair, rolling pair and spherical pair with one example each. 8 Marks Questions 1. List out the various inversions of double slider crank chain and explain the working of Oldham s coupling with the help of neat sketch. Page 1

2 CH-2: Velocity & Acceleration in Mechanisms 1. Define (i) Pressure angle (ii) pitch point related to cam. 1. State the formula for calculating: i) velocity ii) acceleration of piston and connecting rod using analytical method. 2. Explain Klein s construction of determine velocity and acceleration of different links in single slider crank mechanism. 3. In a four bar chain ABCD, AD is fixed and is 150 mm long. The crank AB is 40 mm long and rotates at 120 r.p.m clockwise, while the link CD = 80 mm oscillates about D. BC and AB are of equal length. Find the angular velocity of link CD when angle BAD = The crank of a slider crank mechanism rotates clockwise at a constant speed of 300 r.p.m. The crank is 150 mm and the connecting rod is 600 mm long. Determine linear velocity and acceleration of the midpoint of the connecting rod at a crank angle of 45 from inner dead centre position. 5. Define linear velocity, angular velocity, absolute velocity and state the relation between linear velocity and angular velocity. 6. Describe stepwise procedure for determination of velocity and acceleration by Klein s construction with suitable data. 7. PQRS is a four bar chain with PS fixed length of links are PQ = 62.5 mm, QR =175 mm, RS = mm, PS = 200 mm. The crank PQ rotate at 10 rad/sec. in clockwise direction. Determine the angular velocity of point R, graphically by using relative velocity method. 8. Crank OA of a mechanism is hinged at O and rotates at an angular velocity of 20 rad/sec. and angular acceleration of 25 rad/sec2. If crank OA is 50 mm long determine linear velocity, centripetal acceleration and tangential acceleration of a point A. 9. Explain the inter-relation between linear and angular velocity, linear and angular acceleration with suitable example. 10. Explain the Klein s construction to determine velocity and acceleration of single slider crank mechanism. 11. In a slider-crank mechanism, the crank is 480 mm long and rotates at 20 rad/sec in the counter-clockwise direction. The length of the connecting rod is 1600 mm. when the crank turns 60 from the inner-dead centre. Determine the velocity of the slider by relative velocity method. 12. In a slider crank mechanism, crank AB = 20 mm & connecting rod BC = 80 mm. Crank AB rotates with uniform speed of 1000 rpm in anticlockwise direction. Find (i) Angular velocity of connecting rod BC (ii) Velocity of slider C. When crank AB makes an angle of 60 degrees with the horizontal. Draw the configuration diagram also. Use analytical method. Page 2

3 13. Draw the labelled displacement, velocity and acceleration diagrams for a follower when it moves with simple harmonic motion. 14. In a four-link mechanism, the crank AB rotates at 36 rad/sec. The lengths of a link are AB = 200 mm, BC = 400 mm, CD = 450 mm and AD = 600 mm. AD is the fixed link. At the instant when AB is at right angles to AD determine the velocity of : (i) The midpoint of link BC (ii) A point on the link CD, 100 mm from the pin connecting the link CD & AD. 15. 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. The crank speed is 600 rpm close wise. When the crank has turned 45º from the inner dead centre position, determine: (i) Velocity of slider A (ii) Velocity of the point G graphically. Draw the configuration diagram also. 16. Define the terms linear velocity, relative velocity, angular velocity and angular acceleration. 17. For a single slider crank mechanism, state the formulae to calculate by analytical method (i) Velocity of slider (ii) Acceleration of slider (iii) Angular velocity of connecting rod (iv) Angular acceleration of connecting rod. Also, state the meaning of each term. 18. In a four bar chain ABCD, AD is fixed and is 150 mm long. The crank AB is 40 mm long and rotates at 120 rpm clockwise. The link CD = 80 mm oscillates about D.BC and AD are of equal length. Find the angular velocity of link CD when angle BAD = In a single slider crank mechanism, crank AB = 20 mm and connecting rod BC = 80 mm. Crank AB rotates with uniform speed of 1000 rpm in anticlockwise direction. Find (i) angular velocity of connecting rod BC and (ii) Velocity of slider C when crank AB makes angle of 60 with the horizontal. 8 Marks Questions 1. PQRS is a four bar chain with link PS fixed. The lengths of the links are PQ = 62.5 mm; QR = 175 mm; RS = mm and PS = 200 mm. The crank PQ rotates at 10 rad is clockwise. Draw the velocity and acceleration diagram when angle QPS = 60 and Q and R lie on the same side of PS. Find the angular velocity and angular acceleration of links QR and RS. 2. In reciprocating engine the crank is 250 mm long and connecting rod is 1000 mm long. The crank rotate at 150 rpm. Find velocity and acceleration of piston and angular velocity and angular acceleration of connecting rod when the crank makes an angle of 30 to IDC. Use analytical method. 3. In a slider crank mechanism shown in figure 1. Page 3

4 Calculate : (i) The acceleration of the slider at B (ii) The acceleration of point E. (iii) The acceleration of link AB. OA rotates at 20 rad/sec counter clockwise. 4. In a slider crank mechanism, the crank is 480 mm long and rotates at 20 rad/sec in the counter closewise direction. The length of the connecting rod is 1.6 m when the crank turns 60º from the inner-dead centre determine by relative velocity method (i) Velocity of slider (ii) Velocity of a point E located at a distance 450 mm on the connecting rod extended. (iii) Angular velocity of the connecting rod. 5. The crank and connecting rod of a reciprocating engine are 200 mm and 700 mm respectively. The crank is rotating in clockwise direction at 120 rad/s. Draw Klein s construction and find (i) Velocity and acceleration of the piston (ii) Angular velocity and angular acceleration of the connecting rod at the instant when the crank is at 30 to IDC (inner dead centre) Page 4

5 CH-3: Cams & Followers 1. Write the classification of follower. 2. Enlist the different type of follower motion. 3. Define : (i) Radial follower (ii) Off-set follower. 4. State any two types of motion of the follower. 1. Why roller follower is preferred over a knife follower? State two advantages and application of roller follower *** 2. State different types of cam and follower motion. 3. A cam is to be designed for a knife edge follower with the 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 its original position with S.H.M. iv) Dwell during the remaining 18º 4. Draw the profile of the cam when the line of stroke of the follower passes through the axis of the cam shaft. The radius of the base circle of the cam is 40 mm. 5. Draw a neat sketch of radial cam with roller follower and show the following on it : (i) Pitch point (ii) Pressure angle (iii) Prime circle (iv) Trace point. 6. Draw a neat sketch of Radial cam with roller follower and show on it : (i) Base circle (ii) Pitch point (iii) Prime circle (iv) Cam profile. 7. What are the different types of follower motion? Also draw displacement diagram for uniform velocity. 8. Define the following terms as applied to cam with a neat sketch : (i) Base circle (ii) Pitch circle (iii) Pressure angle (iv) Stroke of the follower. 9. Define the following terms related to cams (i) Trace point (ii) Pitch curve (iii) Prime circle (iv) Lift or stroke. 10. Give detailed classification of followers. 8 Marks Questions 1. Construct a cam profile with knife edge follower having an offset of 10 mm for the following data : Outstroke = 60 with SHM Dwell = 30 Return = 60 with uniform velocity and remaining is dwell period. Minimum radius of cam = 50 mm Lift of follower = 25 mm Consider the rotation of cam in clockwise direction. 2. A cam is to be designed for a knife edge follower with the 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 its original position with S.H.M. iv) Dwell during the remaining 18º6 Page 5

6 Draw the profile of the cam when the line of stroke of the follower passes through the axis of the cam shaft. The radius of the base circle of the cam is 40 mm. 3. Draw the profile of cam operating a roller reciprocating follower with the following data : Minimum radius of cam = 25 mm, lift = 30 mm, Roller diameter = 15 mm The cam lifts the follower for 120 with SHM followed by a dwell period of 30. Then the follower lowers down during 150 of the cam rotation with uniform acceleration and deceleration followed by a dwell period. 4. Construct the profile of a cam to suit the following specifications : Cam shaft diameter = 40 mm, least radius of Cam = 25 mm, Diameter of roller = 25 mm, Angle of lift = 120º, Angle of fall = 150º, lift of the follower = 40 mm, number of pauses are two of equal interval between motions. During the lift the motions is SHM. During the fall the motion is uniform acceleration and deceleration. The speed of the cam shaft is uniform. The line of stroke of the follower is off-set by 12.5 mm from the centre of the cam. 5. A cam is to give the following motion to a knife edged follower : (i) Outstroke during 60 of cam rotation. (ii) Dwell for the next 30 of cam rotation. (iii) Return stroke during next 60 of cam rotation. (iv) Dwell for the remaining 210 of cam rotation. The stroke of the follower is 40 mm and the minimum radius of the cam is 50 mm. The follower moves with uniform velocity during both the outstroke and return stroke. Draw the profile of the cam when the axis of the follower passes through the axis of the camshaft. Page 6

7 CH-4: Power Transmission 1. What are the two advantages and disadvantages of chain drive? 2. Define angle of lap and slip in belt drive. 3. State four conditions under which the V belt drive is selected. 4. How are drives classified? 5. Write any two disadvantages of chain drive. 6. What do you mean by crowning of pulleys in flat belt drive? State its use. 7. Define slip and creep in belt drive. 8. State any two advantages of V belt drive over flat belt drive. 1. State one application of each. V-belt drive, flat belt drive, gear drive and chain drive. 2. In a flat belt drive the initial tension is 2000 N. The coefficient of friction between the belt and the pulley is 0.3 and the angle of lap on the smaller pulley is 150. The smaller pulley has a radius of 200 mm and rotates of 500 r.p.m. Find the power in KW transmitted by the belt. 3. State types of gear train and explain any one. 4. Write the equation relating tension on slack and tight side. Explain in brief the term in it in case of flat belt. 5. Compare cross belt drive and open belt drive on the basis of: (i) velocity ratio (ii) application (iii) direction of driven pulley (iv) length of belt drive 6. The central distance between two shaft is 4 m having two pulleys with diameter having 500 mm and 700 mm respectively. Find length of belt required (i) for open belt drive (ii) for cross belt drive. 7. State the type of power transmission chains. Describe any one with its sketch. 8. Explain the phenomenon of slip and creep in a belt drive. State its effect on velocity ratio. 9. Compare cross belt drive and open belt drive on the basis of : (i) velocity ratio (ii) direction of driven pulley (iii) length of belt drive (iv) Application 10. A shaft runs at 80 rpm & drives another shaft at 150 rpm through belt drive. The diameter of the driving pulley is 600 mm. Determine the diameter of the driven pulley in the following cases : (i) Taking belt thickness as 5 mm (ii) Assuming for belt thickness 5 mm and total slip of 4%. 11. Explain epicyclic gear train with neat sketch. 12. State and explain Law of Gearing. 13. Explain steep and creep phenomenon in belts. 14. Define slip and creep with reference to belt drive. Also state their effect on velocity ratio. Page 7

8 15. A pulley rotating at 50 m/s transmits 40 kw. The safe pull in belt is 400 N/cm width of belt. The angle of lap is 170º. If coefficient of friction is 0.24, find required width of belt. 16. State four advantages and four disadvantages of chain drive over belt drive. 17. Draw neat labelled sketch of spur gear terminology. 18. Draw the neat sketch of epicyclic gear train and explain how it works. 19. A casting weighing 9 kn hangs freely from a rope which makes 2.5 turns round a drum of 300 mm diameter revolving at 20 rpm. The other end of the rope is pulled by a man. Taking μ = 0.25, determine (i) the force required by the man (ii) the power to raise the casting. 20. State the formulae to calculate the length of open belt drive and cross belt drive. State the meaning of each term by drawing suitable diagrams in both cases. 21. What is centrifugal tension? State its formula. Explain its effect on power transmitted by a belt drive. 8 Marks Questions 1. Explain with sketch working principle of epicyclic gear trains & Compare flywheel and governor. 2. A belt is required to transmit 10 kw from a motor running at 600 rpm. The belt is 12 mm thick and has a mass density gm/mm3. Safe stress in the belt is not to exceed 2.5 N/mm2, diameter of the driving pulley is 250 mm whereas the speed of the driven pulley is 200 rpm. The two shafts are 1.25 m apart. The coefficient of friction is 0.25, determine (1) Angle of contact at driving pulley (2) The width of the belt 3. (i) Define Gear Train. State its purpose and types of gear train. (ii) Explain the concept of fluctuation of energy related with turning moment diagram with sketch. 4. Two parallel shafts, connected by a crossed belt, are provided with pulleys 480 mm and 640 mm in diameters. The distance between the centre lines of the shafts is 3 m. Find by how much the length of the belt should be changed if it is desired to alter the direction of rotation of the driven shaft. 5. An epicyclic gear train is shown in figure no. 1. The number of teeth on A and B are 80 and 200. Determine the speed of the arm, a (i) if A rotates at 100 rpm clockwise and B at 50 rpm counter-clockwise. (ii) if A rotates at 100 rpm clockwise and B is stationary. 6. Two parallel shafts whose centre line are 4.8 m apart, are connected by open belt drive. The diameter of larger pulley is 1.5 m and that of smaller pulley 1 m. The initial Page 8

9 tension in the belt when stationary is 3 kn. The mass of the belt is 1.5 kg/m length. The coefficient of friction between the belt and pulley is 0.3 Taking centrifugal tension into account, calculate the power transmitted when the smaller pulley rotates at 400 rpm. 7. In a simple band brake, the band acts on the 3/4th of circumference of a drum of 450 mm 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 the other end to a pin 100 mm from the fulcrum. It the operating force is applied at 500 mm from the fulcrum and the coefficient of friction is 0.25, find the operating force when the drum rotates in the (i) anticlockwise direction and (ii) clockwise direction Page 9

10 CH-5: Flywheel & Governors 1. Define fluctuation of speed and fluctuation of energy *** 2. State the function of Governor in an I.C. engine ** 3. State four applications of flywheel. 4. Draw a line diagram of porter governor. 5. Define the sensitivity in relation to governor. State its significance. 6. State the function of flywheel in I.C. Engine. 7. Define stability and hunting of governor. 1. Draw and explain the turning moment diagram of four stroke I.C engine *** 2. Explain with sketch working of hartnell governor. 3. Differentiate between flywheel and governor *** 8 Marks Questions 1. Explain with sketch working principle of epicyclic gear train. 2. Draw the neat labelled sketch of centrifugal governor. Page 10

11 CH-6: Brakes & Dynamometers 1. State type of brakes. 2. Give the classification of dynamometer. State the function of it. 3. State the application of (i) Disc brake (ii) Internal expanding brake. 4. Draw a neat labelled sketch of internal expanding brake. 5. Compare brakes and dynamometers. (Any two points) 1. Explain with neat sketch construction and working of eddy current dynamometer *** 2. Explain working of hydraulic brake dynamometer with sketch. 3. Explain the working of rope brake dynamometer with neat sketch. 8 Marks Questions 1. A band brake acts on the ¾th of circumference of a drum of 450 mm diameter which is keyed to the shaft. The band brake provides a breaking torque of 225 N-M. one end of the band is attached to a fulcrum pin of the lever and the other end to a pin 100 mm from the fulcrum. If the operating force is applied at 500 mm from the fulcrum and the coefficient of friction is Find the operating force when the drum rotates in the i) anticlockwise direction and ii) clockwise direction. 2. A simple band brake is operated by lever 40 cm long. The brake drum diameter is 40 cm and brake band embrance 5/8 of its circumference. One end of band is attached to a fulcrum of lever while other end attached to pin 8 cm from fulcrum. The coefficient of friction The effort applied at the end of lever is 500 N. Find braking torque applied if drum rotates anticlockwise and acts downwards. 3. A simple band brake shown in figure 2 is applied to a shaft carrying a flywheel of mass 250 kg and of radius of gyration 300 mm. The shaft speed is 200 rpm. The drum diameter is 200 mm and the coefficient of friction is The dimensions a and l are 100 mm and 280 mm respectively and the angle β = 135. Determine (i) the brake torque when a force of 120 N is applied at the lever end. (ii) the number of turns of the flywheel before it comes to rest. (iii) the time taken by flywheel to come to rest. Page 11

12 4. A band brake acts on the 34th of the circumference of a drum of 450 mm 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 the other end to a pin 100 mm from the fulcrum. If the operating force is applied at 500 mm from the fulcrum and the coefficient of friction is 0.25, find the operating force when the drum rotates in the (i) anticlockwise direction (ii) clockwise direction. Page 12

13 CH-7: Clutches & Bearings 1. List out various types of clutches used to transmit the power. 2. List out various types of bearings used. 1. State types of clutch and its applications *** 2. Draw a neat labeled sketch of multiplate clutch and state it s working. 3. A single plate clutch with both sides effective, has outer and inner diameter 300 mm and 200 mm respectively. The maximum intensity of pressure at any point in the contact surface is not to exceed 0.1 N/mm2. If the coefficient of friction is 0.3, determine the power transmitted by a clutch at a speed 2500 r.p.m. 4. Explain working principle of clutch. State its location in transmission system of an automobile. 5. A thrust shaft of a ship has 6 collar of 600 mm external diameter and 300 mm internal diameter. The total thrust from the propeller shaft is 100 kn. If the coefficient of friction is 0.12 and speed of engine 90 rpm. Find power absorbed in friction at the thrust block using uniform pressure intensity condition. 6. Explain (i) uniform pressure theory (ii) uniform wear theory in clutches and bearings. 7. A multiplate disc clutch transmits 55 kw of power at 1800 rpm. Coefficient of friction for the friction surfaces is 0.1. Axial intensity of pressure is not to exceed 160 kn/m2. The internal radius is 80 mm and is 0.7 times the external radius. Find the number of plates needed to transmit the required torque. 8. State any four types of friction clutch, along with its application each. 9. Explain with neat sketch working of a centrifugal clutch. 10. A car engine has a single plate clutch having outside diameter of 25 cm and inside diameter of 20 cm. If the axial load exerted by springs is 1500 N, determine the power transmitted by the clutch at 700 rpm. Assume uniform wear μ = What is the necessity of clutch? State its types. 12. Draw the neat sketch of single plate clutch and explain its working ** 13. A vertical shaft 150 mm in diameter and rotating at 100 rpm rests on a flat end footstep bearing. The shaft carries vertical load of 20 kn. Assuming uniform pressure distribution and coefficient of friction equal to 0.05, estimate power lost in friction. 8 Marks Questions 1. An engine of a car has a single plate clutch developed maximum torque 147 N-m. External diameter of clutch plate is 1.2 times its internal diameter. Determine the dimension of clutch plate and axial force provided by the spring. The maximum pressure intensity of the clutch facing 98 kn/m2 and coefficient of friction is 0.3. Assume uniform wear condition. 2. A conical pivot with angle of cone as 100, supports a load of 18 kn. The external radius is 2.5 times the internal radius. The shaft rotates at 150 rpm. If the intensity of Page 13

14 pressure is to be 300 kn/m2 and coefficient of friction as 0.05, what is the power lost in working against the friction? 3. Determine the power lost in a footstep bearing due to friction if a load of 15 kn is supported and the shaft is rotating at 100 rpm. The diameter of bearing is 15 cm and coefficient of friction is Assume : (i) Uniform wear condition (ii) Uniform pressure condition. 4. 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 N/mm2. If the coefficient of friction is 0.3, determine the power transmitted by a clutch at a speed of 2500 rpm. Assume uniform condition. Page 14

15 CH-8: Balancing 1. What is balancing? What are the methods of balancing? 2. Why is balancing of rotating parts necessary for high speed engines? 3. State the adverse effect of imbalance of rotating elements of machine. 4. State any two adverse effects of imbalance. 1. Explain the method of balancing of different masses revolving in the same plane. 2. Four masses A, B, C and D are attached to a shaft and revolve in the same plane. The masses are 12 kg, 10 kg, 18 kg and 15 kg respectively and their radii of rotations are 40 mm, 50 mm, 60 mm and 30 mm. The angular position of the masses B, C and D are 60, 135 and 270 from the mass A. Find the magnitude and position of the balancing mass at a radius of 100 mm. 3. Write the procedure for balancing of a single rotating mass by single masses rotating in the same plane **** 4. Three masses 10 kg, 20 kg and 15 kg are attached at a point at radii of 20 cm, 25 cm and 15 cm respectively. If the angle between successive masses is 60 and 90. Determine analytically the balancing mass to be attached at radius of 30 cm. 5. A rotor having the following properties : m1 = 4 kg r1 = 75 mm Ɵ1 = 45 m2 = 3 kg r2 = 85 mm Ɵ2 = 135 m3 = 2.5 kg r3 = 50 mm Ɵ3 = 240 Determine the amount of the countermass at a radial distance of 75 mm required for the static balance. 6. Four masses are 260 kg, 160 kg, 300 kg and 200 kg. The corresponding radii of rotation 300 mm, 250 mm, 150 mm and 200 mm respectively. The angle between successive masses are, 0º, 45º, 90º and 135º. Find the position and magnitude of balancing mass required, if its radius of rotation is 200 mm by using graphical method. 7. Four masses m1, m2, m3 and m4 are 200 kg, 300 kg, 240 kg, and 260 kg respectively. The corresponding radii of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m respectively and the angles between successive masses are 45, 75 and 135. Find the position and magnitude of balance mass required, if its radius of rotation is 0.2 m. Page 15

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