BHARATHIDASAN ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING ME6401- KINEMATICS OF MACHINERY QUESTION BANK

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1 1 BHARATHIDASAN ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING ME6401- KINEMATICS OF MACHINERY QUESTION BANK Unit 1-BASICS OF MECHANISMS PART-A 1) Differentiate between a machine and a structure? Oct / Nov ) State and sketch any two inversions of a double slider crank mechanisms. Oct/Nov 02;May/June ) Name any four common mechanisms with specific applications. May/June ) How many inversions are possible from a four-bar kinematic chain? Name them based on their input-output motions. April/May ) What are the conditions to obtain a four bar crank rocker mechanism? April/May ) State at least one similarity and one difference between a helical pair and a cylindric pair. Nov/Dec ) Define transmission angle of a four bar mechanism. What are the worst values of transmission angle? Nov/Dec 2003/11;May/June ) State any four types of kinematics pairs according to the types of relative motion between them. Nov/Dec ) Explain with neat sketch,the centrode and body centrode. Nov/Dec ) What is a machine? Give to examples. Also differentiate between a machine and a structure. May 2005April 11) Explain Grubbler s criterion for determining degree of freedom for spatial mechanism. April/May 2005/ Nov/Dec ) Describe Grashof s Law for a four bar mechanism? Nov/Dec 2007/12; April/May 2008/09 13) What is the significance for Grashof s Law for a four bar mechanism? Nov/Dec ) Define Kutzbach criterion for planar mechanism. April/May ) State Grubbler s criterion for planner mechanisms. April/May 2005; Nov/Dec 2005/08/10 16) Define kinematic chain. Nov/Dec 2005; April/May ) Define lower pair and higher pair, give two examples for each pairs. Nov/Dec 2005/11; April/May ) Draw a four bar mechanism and show that as one degree of freedom as pair kutzbeach criterion. May/June ) Define inversion of mechanism. May/June ) Identify the possible motion(s) and name of the kinematic pairs of the following combinations: (a) members of a scissor (b) a two pin plug inserted in s two pin socket. 21) State the differences between a crank rocker mechanism and a drag link mechanism. May/June06 22) Define kinematic pair and illustrate any two types of constrained pair. Nov/Dec 06;Apr/May10 23) Define kinematic link or element. Nov/ Dec 2011; May/June ) Differentiate between a machine and a structure. Oct/Nov 2002;Apr/May 2005; May/June 2007/13/14;Nov/Dec ) Classify the constrained motions. May/June 2014

2 2 26) Illustrate any two types of constrained pair. Nov/Dec ) Give the DOF for a shaft in a circular hole. Nov/Dec ) Give the DOF for a cam with roller follower. Apr/May 2010; 29) Define sliding connectors. Nov/Dec ) Define mechanical advantages of a mechanism. Nov/Dec 2008/09 31) What is the use of offset slider-crank mechanism? Nov/Dec ) What are indexing mechanisms? Nov/Dec ) Sketch the Geneva wheel indexing mechanism and state its application. Nov/Dec 2012; Apr/May 2007 PART-B 1. 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. (May/June 2014) 2. Sketch and explain any three kinematic inversion of four-bar chain. (May/June 2014); Nov/Dec What is kinematic inversion? Explain the four different inversions of slider crank mechanism. (Nov/Dec 2013)(Oct/Nov 2002) 4. Write short notes on toggle mechanisms. (Nov/Dec 2013) 5. Explain the inversion of four bar chain with examples. (May/June 2013) 6. Sketch and explain the following: (i) Elliptical trammel (ii) Scotch yoke mechanism. (May/June 2013) 7. a) Describe different types of Link. (8) b) Classify and explain the Kinematic pair. (8) 8. Describe inversion of four bar chain. 9. Explain the inversion of Single Slider Crank Chain. Nov/Dec Explain the inversion of Double Slider crank chain. Nov/Dec a) Explain the offset slider crank mechanism. (8) b) Explain Straight line mechanism with neat sketch (8)Nov/Dec 2012; Nov/Dec Describe the working of Oldham s coupling with a neat sketch and state its applications. 13. Discuss the steering gear mechanism with neat sketch. 14. Explain the working of Whitworth quick return mechanism with a neat sketch. 15. Explain the working of crank and slotted lever quick return motion mechanism with a neat sketch 16.a)Design a four-bar crank rocker quick return mechanism to give a time ratio of 1.25 with rocker swing angle as 75 clockwise. Assume the output link (rocker) length as 50 mm and in the left extreme position it is vertical. b) Sketch our-bar crank rocker mechanism in (1) Maximum transmission angle position and (2) toggle position where mechanical advantage is infinity.

3 3 Unit 2- KINEMATICS OF LINKAGE MECHANISMS PART-A 1. Write about rubbing velocity. (May/June 2013) 2. Define number of instantaneous center. (May/June 2013) (Nov/Dec 2013) 3. What is the low degree of complexity? (Nov/Dec 2013) 4. Define instantaneous center. (May/June 2014) 5. What is the expression for Coriolis component of the acceleration? (May/June 2014) 6. Write the relation between the number of instantaneous center and the number of links in a mechanism. (April/May 2015) 7. Depict all the directions of Coriolis component of acceleration that arise in a completed cycle of quick return motion of the crank mechanism. (April/May 2015) 8. Define kinematic analysis? 9. Explain Klien s construction. 10. Name the various types of kinematic pairs. 11. Differentiate between complexity and incomplete constrained motion. 12. Illustrate the properties of instantaneous center. 13. Explain Freudnstein s equation for four bar mechanism. 14. Define Kennedy s theorem. 15. Describe low degrees of complexity. Nov/Dec Describe the expression for velocity and acceleration of piston of reciprocating engine. 17. Define rubbing velocity. Nov/Dec 2004/05/12; May/June 2007/10; Apr/May Deduce the expression for coriolis component of acceleration Nov/Dec 2007/09/10/12; May/June List out the various possible instantaneous center in a four bar chain mechanism. 20. Classify the types of instantaneous center. Apr/May Define virtual center. May/June 2014; Nov/Dec 2002/03/ Describe angular velocity ratio theorem? 23. Illustrate the space centrode and body centrode. 24. Explain normal component of acceleration. 25. Describe configuration diagram?what is the use? May/June 2012; Nov/Dec Explain body centrode? 27. Compare the two components of acceleration. Nov/Dec Differentiate between rotation and translation. Nov/Dec What do you mean by coupler curve? May/June illustrate the instantaneous centres of a typical four bar. May/June write the equation to determine the number of instantaneous centres of a mechanism. Nov/Dec 2003/13; May/June 2007/ How the direction of coriolis component of acceleration is determined? May/June 2009 PART-B 1. (i) Drive the expression for the relationship between the angular velocities of links in terms of known link lengths, angular positions of links and angular velocity of the input link, for a four bar linkages. (May/June 2014) (ii) In a slider crank mechanism, the length of crank OB and connecting rod AB are 125 mm and 500 mm respectively. The center 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 o from the inner

4 dead center position, determine velocity of the slider A, Velocity of the point G and angular velocity of the connecting rod AB. (May/June 2014) 2. By analytical method, derive the velocity and acceleration for the reciprocating steam engine mechanism. (May/June 2014) 3. (i) draw the velocity polygon for the four bar mechanism shown in fig. and determine VBA, VCB and VCD. Also find the ωab, ωbc, ωcd. 4 In this four bar chain ABCD, AD is the fixed. The crank AB rotates at 120 rpm clockwise. (Nov/Dec 2013) (ii) Locate all instantaneous centers of the slider crank mechanism as shown in fig. The lengths of crank OB and connecting rod AD are 200 mm and 800 mm respectively. If the crank rotates clockwise with an angular velocity of 10 rad/s, find 1. Velocity of the slider A and 2. Angular Velocity of the connecting rod AB. (Nov/Dec 2013) 4. In a whitworth quick return mechanism, as shown in figure, crank OA rotates at 30 rpm in clockwise direction.

5 5 The dimension of various links are OA = 150 mm, OC = 100 mm, CD = 125 mm and DR = 500 mm. determine the velocity of the sliding block R, VAB, VRD and the angular velocity of the link BC. (Nov/Dec 2013) 5. The following data refer to the dimension of the links of four bar mechanism: AB = 50 mm; BC 66 mm; CD = 56 mm and AD (fixed link) = 100 mm. At the instant when <DAB = 60o, the link AB has an angular velocity of 10.5 rad/s in the counter clockwise direction. Determine the velocity of point C, velocity of point E on the link BC while BE = 40 mm and the angular velocities of the links BC and CD. Also sketch the mechanism and indicate the data. (May/June 2013) 6. A single slider crank mechanism is shown in fig. Determine the acceleration at B & E and the angular acceleration of the link AB. The crank rotates at 20 rad/s counter clockwise. (May/June 2013) 7. The Crank of a slider crank mechanisms rotates clockwise at a Constant speed of 300 r.p.m. The crank is 125 mm and connecting rod is 600 mm long. Determine 1. Linear velocity and acceleration of the mid Point of the connecting rod, and 2. Angular velocity and angular acceleration of the connecting rod, at a crank angle of 45 from inner dead centre position. 8. In a four link mechanism, the dimensions of the links are AB=200 mm, BC=400mm, CD=450 mm and AD=600mm. At the instant when DAB=90, the link AB has angular velocity of 36 rad/s in the clockwise direction. Determine (i) The velocity of point C, (ii) The velocity of point E on the link BC When BE =200 mm (iii) the angular velocities of links BC and CD, iv) acceleration of link of link BC.

6 9. The dimensions of the various links of a mechanism, as shown in fig. are as follows: OA=300 mm; AB=1200; BC=450 mm and CD=450 mm. if the crank OA rotates at 20 r.p.m. in the anticlockwise direction and gives motion to the sliding blocks B and D, find, for given configuration: (1) Velocity of sliding at B and D, (2) Angular velocity of CD (3) Linear acceleration of D and (4) angular acceleration of CD. 10. a)derive the expressions for Velocity and acceleration of piston in reciprocating steam engine mechanism with neat sketch (8) b).derive the expression for Coriolis component of acceleration with neat sketch (8) 11. In a slider crank mechanism, the length of the crank and the connecting rod are 100 mm and 400 mm respectively./ The crank [position is 45 from IDC, the crank shaft speed is 600 r.p.m. clockwise. Using analytical method Determine (1)Velocity and acceleration of the slider, and (2) Angular velocity and angular acceleration of the connecting rod. 12. Locate all instantaneous centers of the slider crank mechanism; the length of crank OB and Connecting rod AB are 125 mm and 500 mm respectively. The crank speed is 600 rpm clockwise. When the crank has turned 45 from the IDC. Determine (i) velocity of. slider A (ii)angular Velocity of connecting rod AB. 13. In the mechanism shown in figure, the crank OA rotates at 20 rpm anticlockwise and gives motion of sliding blocks B and D. The dimensions of various links are OA = 300mm, AB = 1200 mm, BC = 450 mm and CD = 450 mm. For the given configuration determine i) velocities of sliding at B and D, ii) angular velocity of CD iii) Linear acceleration of D and iv) angular acceleration of 6 CD. 14. The crank and connecting rod of a theoretical steam engine are 0.5 m and 2m long respectively. The crank makes 180 rpm in the clockwise direction. When it has turned 450 from the inner dead centre position, determine : a) Velocity of piston b) Angular velocity of connecting rod. C) Velocity of point E on the connecting rod 1.5m from the gudgeon pin. D) velocity of rubbing at the pins of the crank shaft, crank and crank cross head when the diameters of their pins are 50mm and 60mm and 30mm respectively.

7 15. A four-bar mechanism has the following link length in mm. Input, A0A = 25, AB = 70, output B0B= 45 and frame A0B0 = 60. Coupler point A is above and B is below the horizontal frame link A0B0, respectively. When the input link is in an angular position of 1050 counter clockwise from the frame link, draw the four bar mechanism and locate all the instantaneous centers. If the input link rotates with a constant angular velocity of 2.5 rad/sec clockwise, determine the linear velocity of B of the output link and the angular velocity of the output link. 16. In a steam engine mechanism shown in figure a) the crank AB rotates at 200 rpm. The dimensions of various links are AB = 12cm, BC = 48cm, CD = 18cm and DE =36cm, EF = 12 cm and FP = 36cm. Find the velocities of C,D,E,F and P. 7

8 8 Unit 3- KINEMATICS OF CAM MECHANISMS PART-A 1. Define angle of dwell & what are the major types of cams? (May/June 2013) 2. Define pressure angle. (Nov/Dec 2013) 3. Write procedure to draw the cam profile. (Nov/Dec 2013) 4. What are the different motion of the follower? (May/June 2006/14); (Nov/Dec 2008/14) 5. Define tangent cam. (May/June 2014) 6. Draw the displacement, velocity and acceleration diagrams for a follower when it moves with simple harmonic motion. (April/May 2015) 7. Why a roller follower is preferred to that of a knife edged follower? (April/May 2015) 8. Define cam? State the advantages of cam mechanisms over linkage mechanisms. (April/May 2003) 9. Classify various types of cam based on contact surfaces? (Nov/Dec 2006) (May/June 2013) 10. Define tangent cam and state its advantages. 11. Point out the different motions of the follower? 12. Criticize, high surface stress in flat faced follower be minimized? 13. Evaluate the suitable follower for high speed cam with reason. 14. Define dwell period, pitch circle, cam angle? May/June 2013) 15. Explain offset follower. 16. Define prime circle. What is the radial distance between the prime circle and base circle for a cam with knife edge follower? (May/June 2007) 17. Define pressure angle with respect to cams. 18. Define undercutting in cam. How it occurs? 19. Summarize about nomogram? 20. Define undercutting in cam and how to prevent it? (May/June 2006); Nov/Dec 2009/10; April/May 2003) 21. Describe the basic requirements for high speed cam? May/June 2007; Nov/Dec 2006) 22. Write the procedure to draw the cam profile. 23. Write the different types of follower with cam arrangement? Nov/Dec 2004/05/08;Oct/Nov Explain base circle? 25. Define trace point? 26. Define pitch curve? (April/May 2008) 27. What is the follower motion used for high speed cams? Why? (May/June 2009/12) 28. State the expression for maximum velocity and acceleration of a follower moves with cyloidal motion. (Nov/Dec 2007/12); May/June 2007 PART-B 1. A cam is designed for a knife edge follower with the following data: (i) Cam lift = 40 mm during 90 o of cam rotation with SHM (ii) Dwell for next 30 o (iii) During the next 60 o of cam rotation, the follower return to original position with SHM. (iv) Dwell for the next 180 o Draw the profile of the cam when the line of the stroke is offset 20 mm from the axis of the

9 9 cam shaft. (May/June 2014) 2. In a cam with the 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 specification: Rise takes place during 90 o of cam rotation with constant acceleration and retardation and the next 90 o of rotation, the follower return to original position with CAR and remaining in a well. The lift of the cam is 30 mm. (May/June 2014) 3. A cam operates on offset roller follower. The least radius of the cam is 50 mm, roller diameter is 30 mm and offset is 20 mm, the cam rotates at 360 rpm. The angle of ascent is 48 o, and angle of descent is 60 o. The motion is to be SHM during ascent and uniform acceleration and deceleration during decent. Draw the cam profile. (Nov/Dec 2013) 4. A cam with 30 mm as minimum diameter is rotating clockwise at a uniform speed of 1200 rpm and has to give the following motion to a roller follower 10 mm in diameter: (i) Follower to complete outward stroke of 25 mm during 120 o of cam rotation with equal uniform acceleration and retardation; (ii) Follower to dwell for 60 o of cam rotating; (iii) Follower to return to its initial position during 90 o of cam rotation with equal uniform acceleration and retardation; (iv) Follower to dwell for the remaining 90 o of cam rotation. Draw the cam profile if the axis of the roller follower passes through the axis of the cam. Determine the maximum velocity of the follower during the outstroke and return stroke and also the uniform acceleration of the follower on the out stroke and the return stroke. (April/May 2015) 5. A cam with a minimum radius of 25 mm, rotating clockwise at uniform speed of 300 rpm is to designed to give motion to a flat faced mushroom follower as detailed below: (i) To raise through a distance of 25 mm in 120 o rotation of the cam (ii) To remain at rest for the next 30 o (iii) To lower during further 120 o 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 lower with uniform acceleration and retardation. However, the uniform acceleration is 2/3 rd of the uniform retardation. Draw the displacement diagram and profile of the cam. (May/June 2013) 6. A cam is to give the following motion to a knife edged follower: (a) Outstroke during 60 of cam rotation (b) Dwell for the next 30 of cam rotation (c) Return stroke during next 60 of cam rotation and (d) Dwell for the remaining 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 strokes. Draw the profile of the

10 cam when (a) the axis of the follower passes through the axis of the cam shaft, and (b) the axis of the follower is offset by 20 mm from the axis of the cam shaft Draw the profile of a cam operating a Knife-edged follower from the following data: (a) Follower to move outward through 40 mm during 60 of a cam rotation; (b) Follower to dwell for the next 45 (c) Follower to return its original position during next 90 (d)follower to dwell for the rest of cam rotation. The displacement of the follower is to take place with simple harmonic motion during both the outward and return strokes. The least radius of the cam is 50mm. If the cam rotates at 300 r.p.m., determine the maximum velocity and acceleration of the follower during the outward stroke and return stroke. (16) 8. A cam, with a minimum radius of 50 mm, rotating clockwise at a uniform speed, is required to giver a knife-edged follower the motion as described below: (a) To move outwards through 40 mm during100 rotation of the cam; (b) to dwell for next 80 (c) To return to its starting position during next 90 and (d) To dwell for the rest period of revolution. Draw the profile of the cam (i) When the line of stroke of the follower passes through the centre of the cam shaft and (ii) When the line of stroke of the follower is to take place with Uniform acceleration and uniform retardation. Determine the maximum velocity and acceleration of the follower when the cam shaft rotates at 900 r.p.m. (16) 9. Draw the profile of a cam operating a roller reciprocating follower and with the following data: Minimum radius of cam =25 mm; lift=30mm; Roller diameter= 15mm. The cam lifts the follower for 120 with SHM, followed by a dwell period of 30. Then the follower lowers down during 150 of cam rotation with uniform acceleration and retardation followed by a dwell period. If the cam rotates at a uniform speed of 150 RPM. Calculate the maximum velocity and acceleration of follower during the descent period. (16) 10. 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 surface: (i) Follower to have a stroke of 20 mm during 120 of cam rotation, (ii) Follower to dwell for 50 of cam rotation, (iii) Follower to return to its initial position during 90 of cam rotation, (iv) Follower to dwell for remaining period of cam rotation. The minimum radius of the cam is 25 mm. The out stroke of the follower is performed with SHM and return stroke with equal uniform acceleration and retardation.(16) 11. A tangent cam to drive a roller follower through a total lift of 12.5 mm for a cam rotation of 75.The cam speed is 600 rpm. The distance between cam centre and follower centre at full lift is 45 mm and the roller is 20 mm in diameter. Find the cam proportions and plot displacement, velocity and acceleration for one full cycle. 12. Construct a tangent cam and mention the important terminologies on it. Also derive the expression for displacement, velocity, acceleration of a reciprocating roller follower when the roller has contact with the nose.

11 13. Layout the profile of a cam operating a roller reciprocating follower for the following data. Lift of follower = 30mm; Angle during the follower rise period =1200; angle during the follower after rise =300; angle during the follower return period = Angle during which follower dwell after return= 600; minimum radius of cam = 25mm; Roller diameter =10mm. The motion of follower is uniform acceleration and deceleration during the rise and return period. 14. Design a cam to raise a valve with simple harmonic motion through 15mm is 1/3rd of a revolution, keep it fully raised through 1/12th of a revolution and to lower it with SHM in 1/6th of a revolution. The valve remain closed during the rest of the revolution. The diameter of the roller is 20mm and the minimum radius of the cam is 25mm. The axis of the valve rod passes through the axis of the cam shaft. If the cam shaft rotates at uniform speed of 100 rpm; find the maximum velocity and acceleration of the valve during raising and lowering. Also draw the profile of the cam Classify with neat sketches the cam follower according to their shape, location and motion. State also their advantages, if any, with respect to other followers b). Sketches neatly the displacement, velocity and acceleration curves of a cycloidal motion follower.why is it superior over other motion curve Unit 4 GEARS AND GEAR TRAINS PART-A 1. Define velocity ratio. (Nov/Dec 2013) 2. Write short notes on differentials. (Nov/Dec 2013) 3. What are the methods to avoid interference? (May/June 2014) 4. Differentiate between the involute profile and cycloidal profile. (Nov/Dec 2014) 5. What do you understand by the term interference as applied to gears? (April/May 2015) 6. What are the special advantages of epicyclic gear trains? (April/May 2015) 7. Define (A) narmal pitch (B) axial pitch relating to helical gears. May/June 2007; April/May 2010; Nov/Dec State the advantages of helical gears over spur gears. Nov/Dec What is a worm gear drive? April/May Define the arc of contact gears. Nov/Dec Advantages and disadvantages of involute gear tooth profile? Nov/Dec 03/06; May/June Define angle of obliquity in gear.

12 Describe undercutting in gears. April/May Define arc of approach and arc of recess. 15. Define module of gear and give it relation with circular pitch 16. Distinguish velocity and sliding velocity in a spur gear ratio. Nov/Dec 13;May/Ju06/ Define law of gearing & significance contact ratio in gears? Nov/Dec 2004/05/08/09; May/June 2007/13/ Write short note on differential. 19. Explain the term interference as applied to gears. April/May 2008; Nov/Dec List out the methods to avoid interference? 21. Analyze the reason for choosing cast iron in manufacturing gears. 22. List out the externally applied torques used to keep the gear train in equilibrium? 23. Define interference & Backlash. 24. Distinguish between cycloidal tooth profile and involute tooth profile. 25. List out the non-metallic materials used in gear manufacturing. 26. Define simple gear train and compound gear train 27. Define reverted gear train. And write applications April/May 2003; Nov/Dec Compare epicyclic gear train over a simple gear train? Nov/Dec Where the epicyclic gear trains are used and list out its advantages Nov/Dec12; May/June Classify the types of gear trains? 31. Formulate the velocity ratio in compound train of wheels? 32. A pitch circle of a spur gear is 120 mm, module 4 mm, calculate number of teeth on the gear.

13 13 PART-B 1. Two gear wheels mesh externally to give. The involute teeth has 6 mm module and 20 o pressure angle. Addendum is equal to one module. The pinion rotates at 90 rpm. Determine (i) Number of teeth on the pinion to avoid interference and the corresponding number on the wheel; (ii) The length of path and arc of contact (iii) Contact ratio and (iv) The maximum velocity of sliding. (May/June 2014). 2. (i) Drive the expression to determine the length of path of contact between two spur gears of the different size. (May/June 2014) (ii) Briefly explain the sub-classification of compound gear trains with neat sketches. (May/June 2014) 3. (a) calculate: (i) Length of path of contact (ii) Arc of contact and (iii) The contact ratio when a pinion having 23 teeth drives a gear having teeth 57. The profile of the gears is involute with pressure angle 20 o, module 8 mm and addendum equal to one module. (April/May 2015) 4. In an epicyclic gear train a gear C is keyed to the driving shaft A which rotates at 900 rpm. Gear D and E are fixed together and rotate freely on a pin carried by the arm M which is keyed to the driven shaft B. gear D is in mesh with gear C while the gear E is in mesh with a fixed annular wheel F. the annular wheel is concentric with the driven shaft B. if the shafts A and B are collinear and number of teeth on gears C, D, E, F are respectively 21, 28, 14 and 84. Determine the speed and sense of the rotation of the driven shaft B. (April/May 2015) 5. An epicyclic gear train is shown in fig. The input S has 24 teeth. Gears P and C constitute a compound plant having 30 and 18 teeth respectively. If all the gears are of the same pitch, find the speed ratio of the gear train assuming A to be fixed. (May/June 2013) 6. a) Two mating spur gear with module pitch of 6.5 mm have 19 ad 47 teeth of 20 pressure angle and 6.5 mm addendum. Determine the number of pair of teeth and angle turned through by the larger wheel for one pair of teeth in contact. Determine also the slidin g velocity at the instant (i) engagement commences (ii) engagement terminates. When the pitch line velocity is 1.2 m/s. (8) b) The number of teeth on each of the two spur gears in mesh is 40. The teeth have 20 involute profile and the module is 6mm. If the arc of contact is 1.75 times the circular pitch. Find the addendum. (8)

14 14 7. a) Two 20 involute spur gears have a module of 10 mm. The addendum is one module. The larger gear has 50 teeth and pinion 13 teeth. Does the interference occur? If it occurs, to what value should the pressure angle be changed to eliminate interference? (8) b) Two mating involute spur gears 16 pressure angle have a gear ratio of 2. The number of teeth on the pinion is 15 and its speed is 240 rpm. The module pitch of the teeth is 5 mm. if the addendum on each wheel recess on each side are half the maximum possible length each, find (1) the addendum for pinion and gear wheel (2) the length of arc of contact (3) the maximum velocity of sliding during approach and recess. Assume pinion to be driver. (8) 8. a) A pair of spur gear with involute teeth is to give a gear ratio of 4:1. The arc of approach is not be less than the circular pitch and the smaller wheel is the driver. The angle of pressure is 14.5 What is the least number of teeth can be used on each wheel? What is the addendum of the wheel in terms of circular pitch? (8) b)a pair 20 full depth involute spur gear having 30 and 50 teeth respectively module 4 mm arc in mesh, the smaller gear rotates at 1000 rpm. Determine (a) Sliding velocities at engagement and disengagement of a pair of teeth and (b) Contact ratio. (8) 9. Two gear wheels mesh externally and are to give a velocity ratio of 3 to 1. The teeth are of involute form; module=6mm, addendum=one module, pressure angle 20. The pinion rotates at 90 rpm. Determine (1) the number of teeth on the pinion to avoid interference on it and the corresponding number of teeth on the wheel, (2) The length of path and arc of contact, (3) the number of pairs of teeth in contact.(4) Maximum velocity of sliding (16) 10. The arm of an epicyclic gear train rotates at 100 rpm in the anticlock wise direction. The arm carries two wheels A and B having 36 and 45 teeth respectively. The wheel A is fixed and the arm rotates about the centre of wheel A. Find the speed of wheel B. What will be the speed of B, if the wheel A instead of being fixed, makes 200 rpm (clockwise). 11. In a reverted epicyclic train, the arm A carries two gear B and C and a compound gear D-E. WheelB meshes with gear E and gear C meshes with gear D. The number of teeth on gear B, C and D are75, 30, and 90. Find the speed and direction of gear C, when gear B is fixed and arm A makes 100rpm clockwise. 12. A compound epicyclic gear is shown in figure. The gears A, D and E are free to rotate on axis P. The compound gears B and C rotate together on the axis Q at the end of arm F. All the gears have equal pitch. The number of external teeth on gears, A B and C are 18, 45 and 21respectively. The gears D and E are annulus gears. The gear A rotates at 100 rpm in anticlockwise direction and the gear D rotates at 450 rpm clockwise. Find the speed and direction of the arm and the gear E. 13. The sun planet gear of an epicyclic gear train, the annular D has 100 internal teeth, the sun gear A has 50 external teeth and planet gear B has 25 external teeth. The gear B meshes with

15 gear D and gear A. The gear B is carried on arm E, which rotates about the centre of annular gear D. If the gear D is fixed and arm rotates at 20 rpm, then find the speeds of gear A and B. 14. An epicyclic gear train for an electric motor, is shown in figure. The wheel S has 15 teeth and is fixed to motor shaft rotating at 1450 rpm. The planet P has 45 teeth, gears with fixed annular A and rotates on a spindle carried by an arm which fixed to output shaft. The planet P also gears with the sun when S. Find the speed of output shaft. If motor is transmitting 2 KW find the torque required to fix the annular An epicyclic gear train as shown in figure is composed of a fixed annular wheel A having 150 teeth. The wheel A is meshing with wheel B which drives wheel D through an idle wheel C, D being concentric with A. The wheels B and C are carried on an arm which revolves clockwise at 100 rpm about the axis of A and D. If the wheels B and D have 25 and 40 teeth respectively, determine the number of teeth on C and speed and sense of rotation of wheel C.

16 16 Unit 5- FRICTION IN MACHINE ELEMENTS PART-A 1. List down the law of dry friction. (May/June 2013(April/May 2003) 2. Define anti-friction bearing. (Nov/Dec 2013) 3. Distinguish between sliding and rolling friction. (April/May 2010); Nov/Dec 2011/12; May/June Differentiate multi plate clutch and cone clutch. (Nov/Dec 2013) 5. Define velocity ratio. (May/June 2014) 6. What is the maximum efficiency of the screw jack? (May/June 2014) 7. What is centrifugal tension in a belt? How does it affect the power transmitted? (April/May 2015) 8. Distinguish between brakes and dynamometers. (April/May 2015) 9. Define anti-friction bearing. Differentiate multi plate clutch and cone clutch 10. What do you mean friction angle? May/June 2007; Nov/Dec State the laws of fluid friction. 12. What is the condition for self-locking in screws? Nov/Dec 2005; April/May What do you mean self-locking screws? May/June 2009; Nov/Dec Define angle of repose? 15. Grade the advantage and disadvantages of V-belt over flat belt drive. (April/May 2010); (Nov/Dec 2011) 16. Define Co-efficient of friction. 17. Compare the advantage of wire rope over fabric rope. 18. Explain the significance of friction in braking. May/June What is the minimum force required to slide a body on a rough horizontal plane? Nov/Dec 2004/ List out the functions of clutches? 21. Distinguish between cone clutch, centrifugal clutch and multiplate clutch? Nov/Dec Explain crowning in pulley? 23. List out the belt materials? 24. Explain velocity ratio. 25. State the law of belting. 26. Explain the term slip & creep? 27. Define wipping? 28. Explain self energizing brake. Nov/Dec 2010/ State the centrifugal effect in belt drive? Nov/Dec 2009;Oct/Nov Why is the cross belt used instead of open belt? PART-B 1. 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 the length 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 belt is 1 kn and the co-efficient of friction between the belt and pulley is 0.25? (May/June 2014)

17 17 2. (i) Derive an expression for the effort required to raise a load with screw jack tacking friction into consideration. (May/June 2014) (ii) A 150 mm diameter value, against a steam pressure of 2 MN/m 2 is acting, is closed by means of a square threaded screw 50 mm in external diameter with 6 mm pitch. If the coefficient of friction is 0.12, find torque required to turn the handle. (May/June 2014) 3. A flat belt, 8 mm thick and 100 mm wide transmits power between two pulleys, running at 1600 m/min. the mass of the belt is 0.9 kg/m length. The angle of lap in the smaller pulley is 165 o the coefficient of friction between the belt and pulley is 0.3. If the maximum permissible stress in the belt is 2 MN/m 2, Find: (i) Maximum power transmitted; and (ii) Initial tension in the belt (April/May 2015) 4. The spindle of a screw jack has single start square threads with an outside diameter of 45 mm and a pitch of 10 mm. the spindle moves in a fixed nut. The load is carried on a swivel head but is not free to rotate. The bearing surface of the swivel head has a mean diameter of 60 mm. the coefficient of friction between the nut and screw is 0.12 and that between the swivel head and the spindle is Calculate the load which can be raised by efforts of 100 N each applied at the end of the two levers each of effective length of 350 mm. also determine velocity ratio and the efficient of the lifting arrangement. (April/May 2015) 5. (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 surface 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. Determine the number of plates needed to transmit the required torque. (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 caries a vertical load of 15 kn. Find the power lost in friction assuming the following condition: (1) Uniform pressure (2) Uniform wear (May/June 2013) 6. (i) Find the power transmitted by a belt running over pulley 700 mm diameter at 300 rpm, µ = 0.3 and angle of lap 160o and maximum tension in the belt is 2.453kN. (ii) A simple brake as shown in fig. is used on a shaft carrying a flywheel of mass 450 kg.

18 18 The radius of gyration of the flywheel is 500 mm. and runs at 320 rpm. The coefficient of friction is 0.2 and the diameter of the brake drum is 250 mm, determine the following: (1) Torque applied due to hand load of 150 N (2) The number of turns of the wheel before it is brought to rest. (3) The time required to bring it to rest from the moment of application of the brake. (May/June 2013) 7. a) For a flat belt, prove that T1/T2=eμ_ Where T1 and T2= Tension in the tight and slack sides of the belt, _= Angle of contact between the belt and the pulley, and μ= Coefficient of friction between the belt and the pulley. (8) b) An open belt running over two pulley of 1.5 m and 1.0 m diameters connects two parallel shafts 4.8 m apart. The initial ten in the belt is 3000 N. The smaller pulley is rotating at 600 rpm. The mass of belt is kg/m length. The coefficient of friction between the belt and pulleys is 0.3. Find (1) the exact length of the belt required (2) the power transmitted taking centrifugal tension into account. (8) 8. a) A multi plate disc clutch transmits 55 KW of power at 1800 rpm. Coefficient of friction for the friction surfaces is 0.1. Axial intensity at 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) b) A rope drive is required to transmit 230 KW from a pulley of 1m 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 groove angle 1600 and 450 respectively. If coefficient of friction is 0.3, find the number of ropes required. (8) 9. The mean diameter of the screw jack having pitch of 10 mm is 50 mm. A load of 20 KN is lifted through a distance of 170 mm. Find the work done in lifting the load and efficiency of the screw jack when (i) the load rotates with the screw, and (ii) the load rests n the loose head which does not rotate with screw. The external and internal diameter of the bearing surface of the loose head is 60 mm and 10mm respectively. The coefficient of friction for the screw as well as the bearing surface may be taken as (16)

19 a).a leather belt is required to transmit 7.5 kw from a pulley 1.2 m in diameter, running at 250 rpm. The angle entranced is 165 and the coefficient of friction between the belt and the pulley is 0.3. If safe working stress for the leather belt is 1.5 MPa, density of leather is 1 kg/ m3 and thickness of belt is 10 mm. Determine the width of the belt taking Centrifugal tension into account. (8) b).two pulley one 450 mm diameter and other 200mm diameter are on parallel shaft 2.1 m apart and are connected by a cross 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 Find the length of the belt required and the power can be transmitted. (8) 11. Two shaft whose centers are 1m apart are connected by a V belt drive. The driving pulley is supplied with 100 KW and has an effective diameter of 300 mm. It runs at 375 rpm. The angle of groove on the pulley is 400 The permissible tension in 400 mm2 cross sectional area of the belt is 2.1 MPa. The density of the belt is 1100 kg/ mm3 coefficient of friction is Estimate number of belts required. (16) 12. a) Prove or disprove the following statement Angle of friction is equal to angle of repose b) Briefly explain the following: 1) Slip of the belt 2) Creep of the belt. 13.A conical pivot bearing supports a vertical shaft of 200mm diameter. It is subjected to a load of 30KN. The angle of cone is 1200 and the co-efficient of friction is Find the power lost in friction when the speed is 140 rpm assuming i) Uniform pressure and ii) Uniform wear. 14. (i)a single plate clutch is required to transmit 8 KW at 1000 rpm. The axis pressure is limited to 70KN/m2. The mean radius of the plate is 4.5 times the radial width of the friction surface. If both the sides of the plate are effective and the coefficient of friction is Find a) the inner and the outer radius of the plate and the mean radius, b) the width of the friction lining. (ii)a shaft has a number of collars integral with it. The external diameter of the collars is 400mm and the shaft diameter is 250mm. If the uniform intensity of pressure is 0.35N/mm2 and its coefficient of friction is 0.05, estimate i) power absorbed in overcoming friction when the shaft runs at 105 rpm and carries a load of 150KN and ii) number of collars required. 15.a) Derive an expression for braking torque on the drum of simple band brake. b.) Deduce the expression for the friction moment of a collar thrust bearing, stating clearly the assumption made.

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