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

Third Semester

Mechanical Engineering ME2203 — KINEMATICS OF MACHINERY

(Regulation 2008) Time: Three hours Maximum: 100 Marks

Answer ALL Questions

PART A — (10 x 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 x 16 = 80 Marks) 11. (a) Perform the kinematic analysis of the following Exact Straight Line

motion mechanisms. (2x8= 16) (i) Peaucellier Mechanism. (ii) Hart's Mechanism.

Or (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 in terms of link lengths. (7) 12. (a) The 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. Determine the (i) Linear velocity of the point E on the bell crank lever (ii) Angular velocity of link AC and BD.

(b) Derive the expression for determining the angular position of the coupler link and the output link of a four bar mechanism

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

of pressure is uniform is given by, T= 3

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 of 375 mm2; density 1000 kg/m3 and an allowable tensile stress of 2.5 MPa. The groove angle of the pulley is 35°. The coefficient of friction between the belt and the pulley is 0.25. Also calculate the length of each belt.



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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 x 2 = 20 Marks)

1. State Gruebler's 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 dp you mean by self-locking screws? 10. Give the effect of centrifugal tension in belt drives.

PART B — (5 x 16 = 80 Marks) 11. (a)(i) Define transmission angle. Sketch a drag-link mechanism in maximum transmission angle and minimum transmission angle £ 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 ram, 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 velocity and angular acceleration of the links QR and RS. (16)



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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) 14. (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 of 16 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 H 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° arid 45° respectively. If // = 0.3, find the number of ropes required. : (16)



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

Fourth Semester Mechanical Engineering

. \ ME 1252 — KINEMATICS OF MACHINERY

(Common to Third Stemester Mechatronics Engineering)

(Regulation 2004) (Common to B.E. (Part-Time -Third Semester - Regulation 2005)

Time : Three hours Maximum : 100 marks

Answer ALL questions.

PART A — (10x2 = 20 marks)

1. Define the terms 'Kinematic pair' and 'Kinematic chain'. 2. Sketch and indicate the 'Transmission angle' of a four-bar mechanism. 3. Name two mechanism ; one where 'Coriolis Acceleration' is encountered and another

where 'Coriolis Acceleration' is not encountered. 4. How the direction of the angular velocity of the connecting rod is found out during

velocity analysis of a reciprocating engine mechanism by graphical method? 5. Define the term 'Pressure Angle' of a cam mechanism. 6. How the maximum velocity of the follower of a cam mechanism is found out during the

lift which takes place with Simple Harmonic Motion? 7. Name two curves for use as gear profile, which satisfy the law of gearing. 8. What is a 'Worm gear drive'? Explain with a sketch. 9. Briefly explain the term 'Rolling friction'. 10. Make a brief comparison of 'Flat belt drive' and 'V-belt drive'.

PART B — (5 x 16 = 80 marks)

11. (a) Give step-by-step method of design of a crank-rocker mechanism. The inputs parameters, the graphical or analytical method and also the verification of design are to be included. (6 + 7 + 3)

Or (b) Sketch and explain the four inversions of a single - slider crank'chain. Mention also the application of each inversion. .(4x4= 16) 12. (a) In a four - bar chain ABCD, A and D are fixed pivots 120 mm apart. The driving crank AB = 60 mm. At a certain instant, AB makes t60 degree with AD. The driven link CD and the coupler BC are each 95 mm long. The driving crank makes 10 r.p.m. clockwise. (i) Draw the velocity diagram with suitable scale. . (4) (ii) Find the velocity of the point C. (2) (iii) Find the magnitude and direction, of the angular velocity of the linkBC. (2) (iv) Draw the acceleration diagram with suitable scale. (6) (v) .Find the acceleration of the point C. , (2)



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Or

(b) A petrol engine has a stroke of 300 mm and its connecting rod is 900 mm long. The crank rotates at a uniform speed of 1000 r.p.m. For the position . when the crank has rotated 30 degrees from the inner dead centre position, the following are required. (i) Draw the velocity diagram with suitable scale. (4) (ii) Find the velocity of the piston. (2) (iii) Find the magnitude and direction of the angular velocity of the connecting rod. (iv) Draw the acceleration diagram with suitable scale. (6) (v) Find the acceleration of the piston. (2) 13. (a) A flat-faced mushroom follower is operated by a uniformly rotating cam. " The follower is raised through a distance of 25 mm in 120° rotation of the cam, remains at rest for the next 30° and is lowered during further 120° rotation of the cam. The raising of the follower takes place with SHM and the lowering with uniform acceleration and deceleration. However, the uniform acceleration is 2/3 of the uniform deceleration. The least radius of the earn is 25 mm and this rotates at 300 r.p.m. Draw the (i) Displacement diagram and (ii) Cam profile. (5+11)

Or

(b) A cam with a minimum radius of 25 mm, rotating clockwise at a uniform speed is to be designed for a roller follower at the end of valve rod. The valve rod is raised through 50 mm during 120° rotation. The angle of dwell is 30°. The valve is lowered through next 60°. The valve is closed during the rest of revolution. The diameter of roller is 30 mm and the diameter of cam shaft is 25 mm. Draw the

(i) Displacement diagram and (ii) Cam profile.

When the line of the stroke is offset 15 mm from the axis of the cam shaft. The displacements take place with SHM. (5 + 11) 14. (a) A pinion of 20 teeth and modulo 4 mm having involute profile drive's n rack. The addendum of both pinion and rack is (6 mm). (i) What is the least pressure angle which can be used to avoid undercutting?(4) (ii) Derive the formula used for finding the pressure angle. (6) (iii) Find the length of air of contact. (3) (iv) Find the number of pairs of teeth in contact at a time. (3)

Or

(b) In an epicyclic gear of the "Sun and Planet" type, the pitch circle diameter of the internally toothed ring gear is to be around 220 mm as nearly as possible. The module is 4 mm. When the ring gear is stationary, the arm which carries three planet wheels of equal size is to make one revolution for every five of the driving spindle carrying the sun gear. (i) Determine suitable numbers of teeth for all gears. (9)



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(ii) Find the exact diameter of pitch circle of the ring gear. (2) (iii) If a torque of 20 N.m. is applied to the spindle carrying the sun gear, what torque will be required to keep the ring gear stationary? 15. (a) (i) What are Block Brakes? Derive an expression relating the applied force and breaking torque in a Block Brake. (6) (ii) The diameter of a block brake is 250 mm. The L-shaped lever has its longer arm horizontal..The vertical distance of the pivot (of the lever) from the centre of the drum is 75 mm. The horizontal distance of the pivot from the centre of the drum is 200 mm. An effort of 700 N (vertical) is applied at a horizontal distance of 400 mm from the pivot. The contact angle of the block is 90 degrees. The coefficient of friction is 0.35. Determine the breaking torque. (10)

. Or (b) (i) Derive an expression for the centrifugal tension in belt drives. (6) (ii) A pulley is driven by a flat belt, angle of lap being 120 degrees. The belt weighs 6 N per metre run. The coefficient friction is 0.3 and maximum stress in the belt is not to exceed 200 N/cm2. The belt is 10 cm wide and 0.6 cm thick. Find the maximum power that can be transmitted and the corresponding speed of the belt. (10)



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

Fourth Semester



(Common to Third Semester-Mechatronics Engineering) (Also common to B.E. (Part-time)

Third Semester Mechanical Engineering - Regulation 2005) (Regulation 2004)

Time : Three hour Maximum : 100 marks

Sketches to be drawn neatly. Give brief procedure for graphical constructions. A3 size drawing sheet will be issued, if required.


PART A — (10 x 2 = 20 marks)

1. What is Grashoffs law for a four bar linkage? 2. Sketch an offset slider crank mechanism. 3. How angular velocity of a link is calculated from a velocity diagram? 4. Write the name of the mechanism shown in figure.

5. In context with Cam, define Pitch point. 6. What is high speed cam? 7. What is interference in involute teeth? 8. Define velocity ratio of an epicyclic gear train. 9. What is friction angle? 10. State the condition for self locking of screw jack.

PART B — (5 x 16 = 80 marks)

11. (a) (i) In a whitworth quick return mechanism, driving crank is 15 cm long. The distance between the fixed center is 10 cm. The line of stroke of ram passes through the center of rotation of slotted lever, whose free end is connected to the ram by a connecting link. Determine the ratio of time of cutting to time of return. (8) (ii) Determine the number of degree of freedom of the following mechanisms, shown



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in the figure 1. (4x2 = 8)

(b) (i) Sketch the following straight line generators and show the path traced by the point. (2x4 = 8) (1) Peaucillier mechanism (2) Pantograph linkage. (ii) Explain with sketches any two inversions of a double slider crank mechanism(8). 12. (a) In a four bar linkage, link AD is fixed and crank AB rotates at 10 rad/sec constants, (clockwise). The lengths of various links are AB = 60 mm; AD = 120 mm; BC = CD = 70 mm; ZDAB = 60°. Both B and C lie on the same side of AD. Determine. (i) Angular velocities of link BC and CD (ii) Angular accelerations of link BC and CD.

Or | (b) The dimensions of various links of a mechanism as shown in the figure 2 are as follows. AB = 25 mm; BC = 175 mm; CD = 60 mm; AD = 150 mm; BE = fyQ EC; EF = PG = 100 mm; Z.DAB = 135°. The crank AB rotates at 200 rpm. Determine (i) Velocity of G (ii) Angular velocity of link EF (iii) Velocity of sliding of EF in the swivel block S.



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13. (a) (i) Sketch a plate cam mechanism with roller follower and mark. (8) (1) Pitch curve (2) Cam profile (3) Base circle (4) Prime circle (5) Rise (6) Return (7) Dwell. (ii) Derive equation of motion and its derivatives for a tangent cam with roller follower on straight surface. (8)

Or (b) Draw the profile of cam when the follower moves with cycloidal motion for both out stroke and return stroke as detailed below. (i) Outstroke with maximum displacement of 48 mm during 180° of cam rotation (ii) Return stroke for the next 100° of cam rotation (iii) Dwell for the remaining period. . The minimum radius of the cam is 30 mm and diameter of roller is 15 mm. The axis of the follower passes through the axis of the cam shaft. 14. (a) (i)Derive an expression for minimum number of teeth on pinion to avoid interference. (8) (ii) An epicyclic gear train, as shown in figure 3 is composed of a fixed annuLir 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. (8)



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. Or (b) Two 20° involute spur gears mesh externally and gave a velocity ratio of 3.0. Module of both gears is 3 mm and the addendum is equal to one module. If the pinion rotates at 150 rpm, determine (i) Minimum number of teeth on each wheel to avoid interference (ii)Number of pair of teeth in contact (iii) Maximum velocity of sliding at engagement, disengagement and at the point of contact. 15. (a) (i) Derive an expression for braking effort required in a band brake. (8) (ii) An open belt connects two pulleys The smaller pulley is 300 mm in diameter and runs at 200 rpm. The angle of lap on this pulley is 160° and coefficient of friction is 0.25. The belt is in point of slipping when 4 kW is being transmitted. Which of the following two alternatives would be more effective in increasing the power rating? . (1) Increasing the initial tension by 10% (2) Increasing the coefficient of friction by 10%. (8)

Or

(b) (i) A multiple disc friction clutch operating in oil is required to transmit 5 kW at 760 rpm. The effective inner and outer radii of the friction surfaces are 40 mm and 70 mm respectively. Determine the minimum number of discs required, if the permissible average pressure for the friction surfaces is 0.35 MPa and coefficient of friction is 0.1. Assume uniform wear theory is applicable. (8) (ii) Derive an expression for effort to be applied at the end of a lever of length I m to lift a load of W kN in a screw jack. (8)



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B.E./B.Tech. DEGREE EXAMINATION, MAY/JUNE 2009. Fourth Semester



(Regulation 2004) (Common to B.E. (Part-Time) Third Semester - Regulation 2005)


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 drawing sheet, 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 Grashoff s law for 4-bar mechanism. 3. Draw an acceleration polygon for a crank rotating at an angular speed of 'co' rad/sec and

angular acceleration of α rad/sec2. 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? 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 equation for 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 rad/sec(ccw). The angular acceleration of the crank is 1200 rad/sec2. The crank makes an angle of 90°~ with the line of strike. Determine the acceleration of slider and angular acceleration of connecting rod.

Or



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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.

13, (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 next 30°, during the next 60° of cam rotation, the follower returns to its original position with SHM, dwell during 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. The radius of the base circle of the cam is 40 mm.

Or (b) Draw a cam profile for operating the exhaust valve of an oil engine. It is required to give equal uniform acceleration and retardation during opening and closing of the valve each of which corresponds to 60° of cam rotation. The valve must remain in the fully open position for 20° of cam rotation. The valve is 37.5 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 stroke passes through the axis of the cam. 14. (a) A pinion of 20 involute teeth and 125 mm pitch circle diameter drives a rack. The addendum of both pinion and rack is 6.25 mm. What is the least pressure angle which can be used to avoid interference? With this pressure angle, find the length of the arc of contact and the minimum number of teeth in contact at a time.

Or (b) In 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 gears with A, and also with annular fixed wheel D. Pinion C has 15 teeth and is . integral with B(C,B being a compound gear wheel). Gear C meshes with annular wheel E, which is keyed to the machine shaft. The arm rotates about the same shaft on which A is fixed and carries the compound wheel B-C. If the motor runs at 1000 rpm, find the speed of the machine shaft.



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15. (a) A single dry plate clutch transmits 7.5 kW at 900 rpm. The axial pressure is limited to 0.07 N/mm2. 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 50mm. If a force of 100 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.



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B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2008. Fourth Semester (Regulation 2004)



(Common to B.E. (Part-Time) Third Semester Regulation 2005)

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 x 2 = 20 marks)

1. Define DOF of a mechanism. 2. State Grubbler's criterion for planar mechanisms. 3. Define "Actual Mechanical advantage". 4. How the direction of coriolis component of acceleration is determined? 5. Draw at least any four types of cam with followers. 6. What are the different types of motion with which a follower can move? 7. State "Law of gearing". 8. What are various types of torques in an epicyclic gear train? 9. How centrifugal tension affects the power transmission in belt drive? 10. Define the term "Limiting friction".

PART B — (5 x 16 = 80 marks)

11. (a) (i) Explain the following mechanisms in kinematics point of view (1) Ratchat and pawl mechanism. (6) (2) Indexing mechanism. (6) (ii) State and prove the Kutzbach criteria for the following kinematic chains (1) Cam with roller follower. (2) (2) Two bar chain. (2)

Or (b) (i)Sketch and explain any three inversions of a double slider crank chain(8). (ii) In a crank and slotted lever quick return motion mechanism, the distance between the fixed centers is 240 mm and the length of the driving crank is 120 mm. Determine the inclination of the slotted bar with the vertical in the extreme position and the time ratio of cutting stroke to the return stroke. (8) 12. (a)Derive the expression for determining the angular position of the coupler link and the output link of a four bar mechanism.

Or (b) The mechanism of a warping machine is shown in the fig.Q.12.b. Various dimensions are as follows. O1A = 100 mm; AC = 700 mm; BC = 200 mm;BD = 150 mm; O2D = 200mm; O2E = 400 mm; O3C = 200 mm. The crank O1A rotates at a uniform speed of 100 rad/sec. Determine (i) Linear velocity of the point E on the bell crank lever (ii) Acceleration of the points B and E (iii) Aneiilar acceleration of the bell crank lever.



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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. Draw the profile of the cam.

Or (b) A symmetrical circular cam operating a flat faced follower has the following particulars : Minimum radius of the cam = 30 mm; Total lift = 20 mm; Angle of lift = 75°; Nose radius = 5 mm; Speed = 600 rpm. Determine : (i) The principal dimensions of the cam. (ii) Acceleration of the follower at the beginning of lift, at the end of contact with the circular flank, at the beginning of contact with the nose and at the apex of the nose. 14. (a)(i)Derive an expression for minimum number of teeth on the wheel in order to avoid interference. (8) (ii) Two mating gears have 20 and 40 involute teeth of module 10 mm and 20° pressure angle. The addendum on each wheel is to be made of such a length that the line of contact on each side of the pitch point has half of the maximum possible length. Determine the addendum height for each gear wheel, length of the path of contact, arc of contact and contact ratio.(8)

Or (b) (i)Explain the procedure adopted for designing the spur wheels. (6) (ii) A compound epicyclic gear is shown in fig. 1. 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 21 respectively. 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. (10)



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15. (a) (i) Derive an expression for the torque required to lift a load by a screw jack, if I is the length of the arm. (8) (ii) A leather faced conical clutch has a cone angle of 300. If the intensity of pressure between the contact surfaces is limited to 0.35 MPa and the breadth of the conical surface is not to exceed one-third of the mean radius, find the dimensions of the contact surfaces to transmit 22.5 kW at 2000 rpm. Assume uniform rate of wear and take coefficient of friction as 0.15.(8)

Or (b) (i) 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 1.75m. 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 of 375 mm2; density 1000 kg/m3 and an allowable tensile stress of 2.5 MPa. The groove angle of the pulley is 35°. The coefficient of friction between the belt and the pulley is 0.25. Also calculate the length required for each belt. (10) (ii) Derive an expression for braking torque on the drum of Simple band brake.(6)



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B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2008.

Fourth Semester

(Regulation 2004)




Time : Three hours Maximum : 100 mark

Sketches to be drawn neatly.

Give brief procedure for graphical constructions.



PART A — (10 x 2 = 20 marks)

1. Define degree of freedom. 2. Define Grashoffs law. 3. Explain the coriolis component of acceleration. 4. What is higher pair? 5. Define pitch curve of the cam. 6. Define undercutting in Gears. 7. Define interference in Gears. 8. Define pressure angle and explain the effect of different pressure angle. 9. What is creep in the case of belt? 10. Which type of screw thread is preferable in power transmission?

PART B — (5 x 16 = 80 marks)

11. (a) The crank of a slider crank mechanism is 15 cm and the connecting rod is 60 cm long. The crank makes 300 rpm in the clockwise direction. When it has turned 45° from the inner dead centre position determine : (i) Velocity of slider (ii) Angular velocity of connecting rod (iii) Linear velocity of the mid point of the connecting rod. (16)

Or (b) In a four bar mechanism, the crank QA rotates at 36 rad/s. The lengths of the links are AB = 200 mm; BC = 400 mm; CD = 450 mm and AD = 60 mm. AD is the fixed link. At the instant when AB is at right angle to AD, determine the velocity of (i) the mid point of the link BC (ii) a point on link CD, 100 mm from the pin connecting the links CD and AD. 12. (a) What is the importance of finding acceleration of various points in a mechanism? Name the two different methods of finding acceleration in a mechanism.(16)

Or (b) What do you mean by coriolis component of acceleration? When it will exist? Prove that the component of acceleration is equal to 2 vco where v = linear velocity of slider co = angular velocity of link.



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13. (a) From the following data draw the profile of a cam in which the follower moves with SHM during ascent while it moves with uniformly-accelerated and decelerated motion during descent. Least radius of the cam = 50 mm Angle of ascent = 48° Angle of dwell = 42° Angle of descent = 60° Lift of the follower = 40 mm Diameter of the roller = 30 mm If the cam rotates at 360 rpm anticlockwise find the maximum velocity and acceleration of the follower during descent. (16)

Or

(b) A symmetrical tangent cam with a least radius of 25 mm operates a roller follower of radius 10 mm. The angle of ascent is 60° and total lift is 15 mm. If the speed of the cam is 400 rpm, then calculate : The principal dimensions of the cam (i.e) the distance between the cam centre and nose centre; nose radius and angle of control of cam with straight flank. (16) 14. (a) What do you mean by pitch point, circular pitch, module, addendum and pressure angle? Explain in detail. (16)

Or

(b) State and prove the law of gear tooth action for constant velocity ratio and show how the involute teeth profile satisfies the condition. Derive an expression for the velocity of sliding between a pair of involute teeth. State the advantages of involute profile as a gear tooth profile. (16) 15. (a) An open belt drive connects two pulleys 120 cm and 50 cm diameters on parallel shafts 4 m apart. The maximum tension in the belt is 1855 N. The coefficient of friction is 0.3. The driver pulley of diameter 120 cm runs at 200 rpm. Calculate : (i) the power transmitted (ii) the torque on each of the two shafts. (16)

Or

(b) A car moving along a level road is having the following data : Wheel base of car = 2.85 m Height of CG from road surface = 600 mm Perpendicular distance of CG from rear axle = 1.2 m Speed = 60 km/h; // = 0.1; Find the minimum distance in which the car may be stopped when brakes are applied (i) to the rear wheels (ii) to all the four wheels. (16)



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B.E./B.Tech. DEGREE EXAMINATION, MAY/JUNE 2007.

Fourth Semester (Regulation 2004)




Time: Three hours Maximum: 100 marks



PART A — (10 x 2 = 20 marks)

1. Enumerate the difference between a Machine and a Structure. 2. List out the inversions of a double slider crank chain. 3. Define rubbing velocity. 4. Define Corioli's component of acceleration. 5. State the expressions for maximum velocity and acceleration of a follower moves with Cycloidal

motion 6. What is prime circle of a carn? What is the radial distance between the prime circle and base circle

for a carn with knife edge follower? 7. What is axial pitch of a helical gear? 8. List out the applications of epicyclic gear train. 9. What is the condition of maximum efficiency of a Screw jack? 10.What are the advantages of wire ropes over fabric ropes?

PART B — (5 x 16 = 80 marks)

11. (a) (i) Define transmission angle of a four bar linkage. What is the effect of transmission angle on mechanical advantage? (4)

(ii) Briefly explain various types of constrained motions. (4) (iii) Illustrate a crank and slotted lever mechanism as an inversion of single slider crank

chain. Deduce an expression for length of stroke in terms of link lengths. (8)

Or

(b) Analytically perform the displacement analysis of a four bar mechanism. 12. (a) The driving crank AD of the quick-return mechanism, as shown in Fig. 12. (a). revolves at a uniform speed of 200 r.p.m. Find the velocity and acceleration of the tool-box R, in the position shown, when the crank makes an angle of 60° with the vertical line of centers PA. What is the acceleration of sliding of the block at B along the slotted lever PQ?



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Fig. 12 (a) Or

(b) For the toggle mechanism as shown in Fig. 12 (b), the slider D is constrained to move along horizontal direction. The crank rotates at 180 rpm. The dimension of various links are as follows. OA = 180 mm ; CB = 240 mm; AB = 360 mm; BD = 540 mm. For the given configuration determine the velocity of the slider and angular velocity of links AB, BC and BD. Also determine the linear acceleration of the slider D.

Fig. 12 (b)

13. (a) A cam with a minimum radius of 25 mm, rotating in clockwise direction with a uniform speed of 100 rpm is to be designed to give the motion for a roller follower as follows. (i) To raise through 50 mm during 120° rotation of cam with SHM. (ii) Fully raised through next 30° (iii) To lower during next 60° with UAUR (iv) Dwell for the remaining period. Draw the profile of the cam when the line of stroke of the follower is offset by 15 mm from the axis of the camshaft.

Or

(b) Construct a tangent carn 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.



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14. (a)(i) An epicyclic gear train is shown in the Fig. 14 (a). How many revolutions does the arm makes, (1) when A makes one revolution in clockwise and D makes t a revolution in the opposite sense (2) when A makes one revolution in clockwise and D remams stationary. The number of teeth in gears A and D are 40 and 90 respectively. (10)

Fig 14 (a)

(ii) What is reverted gear train? Explain the arrangement of various gears in a reverted gear train and express the characteristic equations used to define their operation.(6)

Or

(b) (i) State and prove law of gearing (4). (ii) A pair of involute spur gears with 16° pressure angle and pitch of module 6 mm is in mesh. The number of teeth in pinion is 16 and its rotational speed is 240 rpm. The gear ratio is 1.75. In order to avoid the interference, determine (1) addenda on pinion and wheel (2) length of path of contact (3) maximum velocity of sliding on either side of pitch point. (12) 15. (a) (i) A square threaded bolt of root diameter 22.5 mm and pitch 5 mm is tightened by screwing a nut whose mean diameter of bearing surface is 50 mm. If the coefficient of friction between nut and bolt is 0.1 and nut and bearing surface is 0.16, determine the force required at the end of spanner 500 mm long when the load on the bolt is 10 kN. (8) (ii) A leather faced conical clutch has a cone angle of 30°. If the (J intensity of pressure between the contact surfaces is limited to 0.35 N/mm2 and the breadth of the conical surface is not to exceed 1/3rd of the mean radius. Determine the dimensions of the contact surfaces to transmit 22.5 KW at 2000 rpm. Assume uniform wear rate and J1 =0.15 .(8)

Or



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(b) (i) Derive the expression for Frictional torque on cone clutch based on uniform pressure theory (6) (ii) The brake whose dimensions are shown in figure 15 (b) has a co-efficient of friction of 0.3 and is to have a maximum pressure of 1000 kPa against the friction material. (1) Using an actuating force of 1750 N, determine the face width of the Shoes (both shoes have same width) and (2) What torque will the brake absorb?



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B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2006.

Fourth Semester



(Common to BE (Part-Time) Third Semester Regulation 2005)

(Regulation 2004)


Sketches to be drawn neatly.

Give brief procedure for graphical constructions.


PART A — (10 x 2 = 20 marks)

1. What is Kutzbach criterion for planar mechanism? 2. Sketch an exact straight line mechanism, with link proportions. 3. Explain normal component of acceleration. 4. State Corioli's law. 5. What are the classifications of cams based on contact surfaces? 6. State the basic requirements for high speed cams. 7. Define module of gears and its relation to circular pitch. 8. Explain briefly the use of differential in an automobile. 9. What are timing belts? 10. Explain briefly significance of friction in braking.

PART B — (5 x 16 = 80 marks)

11 .(a) (i)What is meant by interference in gears? What are the measures to eliminate the

same? (4) (ii) An epicyclic train has a pinion A having 15 teeth, centrally located and rigidly connected to shaft of driving motor. Another gear B having 20 teeth is gearing with A and also with annular fixed wheel D. Gear C is integral with B and meshes with another annular wheel E which is keyed to the shaft of driven unit. The arm rotates about driving shaft and carries compound gear B, C. Sketch the arrangement and determine speed of machine for a motor speed of 1000 rpm. Also determine torque on machine shaft for a motor torque of 100 N-m. (12)

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

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

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

Or



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(b)(i) Explain the inversions of single slider crank chains, with neat sketches(10) (ii) Explain mechanical advantage and transmission angle related to four-bar

mechanisms. (6)

13. (a) (i)Compare instantaneous center method and velocity polygon method for velocity analysis of mechanisms.(4) (ii) A four bar linkage has following dimensions : Crank AO2 = 150 mm ; Link AB = 450 mm; Link BO4 = 300 mm; Link 0204 = 200 mm; Link 0204 is fixed. Find the angular acceleration of links AB and B04 when the crank is rotating with a constant angular velocity of 200 rad/s counter clockwise and also positioned of 45° to horizontal.

Or (b) (i)State the properties of relative velocities of points on kinematic links. (4)

(ii) In a small stearn engine running at 600 rad/min counter clockwise length of crank is 80 mm and ratio of connecting rod length to crank radius is 3. For the position when crank makes 45° to horizontal determine acceleration of piston. Find also total acceleration of a point X on connecting rod 80 mm from crank pin. (12)

14. (a) Draw the profile of disc cam to give uniform acceleration and retardation out stroke of 25 mm to a knife edge follower during first half of revolution. Return of cam also takes place with uniform motion during remaining half of cam revolution. Assume minimum radius of cam as 25 mm.

Or (b) Draw the profile of a cam to give following motion to a reciprocating follower with a flat 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 initial position during 120° of cam rotation, (iv) Follower to dwell for remaining 90° of cam rotation. Minimum radius of cam = 25 mm. Out stroke and return stroke of the follower are simple harmonic.

15. (a) (i) Pitch of 50 mm dia threaded screw of a screw jack is 12.5 mm. Coefficient of friction between screw and nut is 0.10. Determine the torque to raise a load of 25 kN rotating with the screw. Also find the torque required to lower the load and efficiency of screw jack. (8)

(ii) 100 kW is to be transmitted by a rope drive through a 160 cm diameter 45° grooved pulley running at 200 rpm. Angle of overlap is 140° and coefficient of friction between pulley and rope is 0.25. Mass of rope is 0.7 Kg/m and it can withstand a tension of 800 N. Considering centrifugal tension, find the following : (1) Number of ropes required (2) Initial tension in the rope. (8)

Or (b) (i) Explain the following :

(1) Crowning of pulleys (2) Self-locking of brakes (3) Uses of brakes in automobiles.

(ii) A 10 kW engine develops a maximum torque of 100 N-m and is driving a car having a single plate clutch of two active surfaces. Axial pressure is not to exceed 0.85 bar. External diameter of friction plate is 1.25 times internal diameter. Assume uniform wear and co-efficient of friction = 0.3. Determine dimension of friction plate and axial force exerted by the springs. (8)



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BE./B.Tech. DEGREE EXAMINATJON, MAY/JUNE 2006

Fourth Semester



(Regulation 2004)

(Common to RE (Part-Time) Third Semester)


Instructions: • Answer ALL questions.

Sketches should be drawn neatly. • Give brief procedure for graphical constructions. • Answers 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 jn the equations will

carry zero marks. • A3 size drawing sheet will be supplied on request. Use both sides

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


PART A — (10 x 2 = 20marks) 1. 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 a two pin socket.

2. State the differences between a crank-rocker mechanism and a drag-link mechanism.

3. A four-bar mechanism has coupler pin centres at A and B, and fixed pivot centres at Ao and Bo. Write the two vector equations involving the output velocity vector of B.

4. How will you determine the total acceleration {)f a point on a link, when the normal component of acceleration and the tangential component of acceleration are known?

5. State atleast , one advantage and one disadvantage of flat faced follower over roller follower in a cam mechanism.

6. What is undercutting and its effect on a camn-roller follower system? 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. In a screw jack, the coefficient of friction between screw and nut is 0.1 and the

helix angle of the screw thread is 3.5°. Find the efficiency of the screw jack. 10. A force of 80 N is applied to the brake of a bicycle rear wheel and the distance

covered by the bicycle before coming to rest is 12.5 meters. If the co-efficient friction is 0.6, find the work done against the friction.



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PART B — (fi x 16 = 80 marks)

11. (i) Distinguish, with suitable free hand sketches, the following : (1) A spherical pair and a planar pair. (2) Dead centre positions and toggle positions of a four-bar mechanism.(5)

(ii) Prove, with neat sketches, that an elliptical trammel can be used to trace

many elipses and one circle. (5) (iii) Link lengths of a four-bar mechanism are mentioned below :

Fixed link = 72 mm Input link = 32 mm Coupler = 50 mm Output link = 60 mm Determine, graphically, the rocker swing angle of the output and find whether this mechanism is a quick return mechanism or not ; if the left input link rotates clockwise and the right output link completes forward stroke from left extreme position to right extreme position. (6)

12. (a) In the posit ion of the four-bar mechanism shown in FigQ 12 (a), determine using graphical method

(i) The absolute linear velocity of coupler point C, the angular velocities of the coupler link and the output link. (6)

(ii) The absolute linear acceleration of point B, the angular accelerations of the coupler link and the output link. (9)

(iii)What is your inference from the sense of angular velocity of the output link and its sense of angular acceleration? (1)

For the construct ion o f ve locit y po lygon, use a velocit y sca le o f 1 mm = 2 mm/sec and fo r acce ler at io n po lygo n use a sca le o f 1 mm = 15 mm/sec2.

Fig. Q 12. (a)

Or



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(b) (i) In a four-bar mechanism ABCD, the fixed link AD is 110 mm, input

link AB is 75 mm, coupler BC is 100 mm and the follower CD is 90 mm. Ident ify the mechanism as crank-rocker (or) double crank (or) double rocker. Determine, also, analyt ically the maximum transmission angle for this mechanism. (5)

( ii) Der ive express io ns fo r t he relat ionship between the angu lar velocit ies

of links in terms of known link lengths, angular positions of links and angular ve locity o f the input link, for a four-bar linkage. (7)

(iii) On rotat ing link with a speed of 15 rpm, a slider is moving with a linear

velocity, u. The linear velocity vector is acting in north-east d irect io n and the Cor io l is acce ler at ion vecto r o f magnitude 125.67 mm/sec2 acts in South-east direction. Sketch the vectors, and determine the sense of rotat ion o f t he rotat ing link, and the magnitude of linear velocity vector, u. (4)

13. (a) In the assembly line of a factory, to shift components from the lower conveyor to upper conveyor, a cam with in-line roller follower is needed. The requirements are : Follower to move the component upward from the lower conveyor with simple harmonic mot ion through 40 mm in 10 seconds, to remain in the topmost position for 3 seconds during which another mechanism pushes the component to the upper conveyor, then return to the lower conveyor line in the next 6 seconds with uniform acceleration and retardation, to remain in the same level for 5 seconds to receive the component and then to repeat the cycle. Minimum radius of the cam profile is 45 mm and the radius of the roller is 10 mm. Draw

(i) The displacement diagram with 360° cam rotation angle is represented by 180 mm length in X-axis, and (6) (ii) The cam profile with roller follower indicat ing important

nomenclatures and data. (10)

Or

(b) (i) Define, with a neat sketch, the pressure angle of a cam-knife edge follower system. (2) (ii) Draw free hand sketches of displacement, velocity acceleration and jerk of simple harmonic full rise motion for a cam and write the equations for displacement and its derivatives at any angle, θ, in terms of the lift of the follower, S, and the total cam rotation angle for rise, β . (5)

(iii) A tangent cam with a base circle diameter of 50 mm operates a in-line roller follower of 20 mm diameter. The angle between the tangent ial faces of the cam is 60° and the lift of the follower is 15 mm. Sketch, neatly, the cam and follower indicat ing the important parameters, and find the main dimensions of the cam. (9)



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14. (a) (i) State the advantages of worm gear drive over other gear drives. (2)

(ii) Two 20° pressure angle gears have a module of 4 mm. The number of teeth on pinion is 24 and it rotates at 600 rpm. Number of teeth on gear is 40. Addendum equals module for both pinion and gear. Determine the velocity of sliding at the final point of contact. (5) .

(iii) Derive the expression to determine the length of path of contact of meshing gear teeth. (6)

(iv) In a rack and pinion gear with 22.5° pressure angle, the number of teeth on the pinion is 14. If, addendum equals module, determine the possibility of interference. (3) Or

(b) ( i) A non-reverted compound gear train with spur gears has to be designed for a speed ratio of 300. The stock gears available have number of teeth from 15 to 75 in steps of five as 15, 20, 25,…, 70, 75. Minimum speed ratio of a gear pair should not be less than 3 and the gear ratios should be integers. Design the gear train, determine the number of teeth on each gear and sketch the arrangement. (5)

(ii) In an epicyclic gear train, the members are fixed sun gear, S, with 50 teeth, planet gear, P, with 20 teeth and the arm, A, which carries t h e p l a n e t . T he a r m r o t a t e s a bo u t t he s u n g e a r a x i s a t 50 rpm in clockwise rotation, sketch the 2.rrangement and determine the speed of the planet gear and its direction of rotation.(5)

(iii) Draw, a bevel gear automotive differential, and explain its principle

of working.(6)

15. (a) An open belt running over two pulleys of 1.5 m and 1.0 m diameters connects two parallel shafts 4.80 m apart. The initial tension in the belt is 3000 N. The smaller pulley is rotating at 600 rpm. The mass of belt is 0.6703 kg/m length. The coefficient of friction between the belt and pulleys is 0.3. Find (i) The exact length of the belt required, and (4) (ii) The power transmitted taking centrifugal tension into account. (12)

Or

(b) (i) A body of weight 450 N is pulled up along an inclined plane with 30° inclination to the horizontal at a steady speed. If the co-efficient of friction between the body and the plane is 0.25 and force is applied parallel to the inclined plane, find the force required. Find, also, the work done on the body, if the distance travelled by the body is 10 m along the plane. (6)

ii) The external and internal radii of a friction plate of a single clutch are 120 mm and 60 mm respectively. The friction surfaces are held together with a total axial thrust of 1500 N. for, uniform wear, find the maximum, minimum and average pressure n the contact surface. (10)



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

Fourth. Semester Aeronautical Engineering

AE 1253/AT 1252/PR 1252 — MECHANICS OF MACHINES (Common to Automobile

Engineering and Production Engineering)

(Regulation 2004)

Time : Threehours Maximum : 100 marks


PART A — (10 x 2 = 20 marks)

1. State the difference between a planar mechanism and spatial mechanism. 2. Determine the number of degrees of freedom of the mechanism shown below :

3. Define limiting angle of friction and angle of repose. 4. Why is the pulley face given a convex curvature and is never kept flat? 5. List a comparison between involute and cycloidal tooth profile for the following

characteristics; pressure angle, ease to manufacture, centre distance and interference. 6. What Is meant by a reverted gear train and state atleast 2 applications of the same? 7. What is the difference between a discrete and a continuous system? Is it possible to solve

any. vibration problem as a discrete one? 8. Define static balancing and dynamic balancing. State the necessary condition to achieve

them. 9. What is meant by whirling speed? 10. Explain why only a part of the unbalanced force due to reciprocating masses is balanced

by revolving mass.

PART B — (5 x 16 = 80 marks)

11 (a) (i) What is meant by kinematic inversion and state the applications of the various inversions of a four bar kinematic chain. (6) (ii) The figure below shows a rock crushing mechanism. Determine the rotational velocity of the crushing ram, in the shown configuration, as the 60 mm cranks rotates at 120 rpm, clockwise. (10)



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Or

(b) In a slider crank mechanism the crank radius is 10 cm and the connecting rod 40 cm long. The crank rotates in anticlockwise direction at a constant speed of 600 rpm. Find the acceleration of the slider and angular acceleration of connecting rod at an instant when the crank is past the inner dead centre by 45 degrees. 12. (a) A single plate clutch, with both sides effective, has inner and outer diameters of friction surface to be 260 mm and 350 mm respectively. The maximum intensity of pressure is not to exceed 0.15 MPa. The coefficient of Motion is 0.3. Determine the power transmitted by the clutch at speed of 2400 rpm for (i) uniform wear, and for (ii) uniform pressure

Or

(b) An open belt drive is used to connect two parallel shafts 4 m apart. The diameter of bigger pulley is 1.5 m and that of the smaller pulley is 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, power lost in friction and efficiency of the drive. 13. (a) Two 20 degree involute gears in mesh have a gear ratio of 2 and 20 teeth on the pinion. The module is 5 nun and the pitch line speed is 1.5. m/s. Assuming addendum to be equal to one module, find the angle turned through by pinion when one pair of teeth is in mesh and maximum velocity of sliding.

Or

(b) In a gear train, shown below, the gear B is connected to the input shaft. The arm A carrying the compound wheels D and E, turns freely on the output shaft. If the input speed is 1200 rpm anti clockwise, when seen from the right, determine the speed of the output shaft under the following conditions (i) when the gear C is fixed, and (ii) when gear C rotates at 10 rpm counter clockwise direction.



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14. (a) A twin cylinder uncoupled locomotive has its cylinders 60 cm apart and balanced masses are 60° apart, the planes being symmetrically placed about the centre line. For each cylinder, the revolving masses are' 300 kg at crank pin radius of 32 cm and reciprocating parts 285 kg. All the revolving and 2/3rd of the reciprocating masses are balanced. The driving wheels are 1.8 m. diameter. When the engine runs at 60 KMPH, find (i) the swaying couple, (ii) the variation in tractive effort and (iii) the hammer blow. The distance between centre line of wheels is 1.5 m.

Or

(b) A shaft carries four rotating masses as shown in the figure. The balancing masses are to be placed in planes L and M, If the balancing masses revolve at a radius of 100 Him, find their magnitude and angular positions.

15. (a) A vibrating system is denned by the following parameters : m = 2 kg, k = 100 N/m C = 3 N-sec/m Determine (i) the damping factor, (ii) the natural frequency of damped vibration (iii) Logarithmic decrement (iv) the ratio of two consecutive amplitudes and (v) the number of cycles after which the original amplitude is reduced to 10 percent.

Or

(b) Two equal masses of weight 400 kg each and radius of gyration 40 cm axe keyed to the opposite ends of a shaft 60 cm long. The shaft is 7.5 cm diameter for the first 25 cm of its length, 12.5 cm diameter for the nest 10 cm and 8.5 cm diameter for the remaining of its length. Find the frequency of free torsional vibrations of the system and the position of node.



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B.E/B.Tech, DEGREE EXAMINATION, NOVEMBER/DECEMBER 2008.

Fourth Semester

Aeronautical Engineering

AE 1253/AT 1252/ PR 1252 — MECHANICS OF MACHINES

(Common to Automobile Engineering and Production Engineering)

(Regulation 2004)



PART A — (10 x 2 = 20 marks) 1. What are the important kinematic chains with four kinematic pair? 2. What is the importance of finding accelerations of various points in a

mechanism? Name the two different methods of finding acceleration in a mechanism. 3. Prove that the angle of friction is equal to the angle of the inclined plane, when a solid

body of weight W placed on the inclined plane, is about to slide down. 4. Differentiate between:

(a) Pivot and collar bearing (b) Theory of uniform pressure and theory of uniform wear.

5. Explain the terms : (a) module (b) pressure angle.

6. What do you mean by 'interference between two mating gears? 7. What do you mean by static balancing and dynamic balancing? What are the necessary

conditions to achieve them? 8. Define and explain the term 'Balancing of Rotating Masses'. What is the effect of

unbalancing of rotating parts in a high speed engine? 9. Prove that the natural angular velocity (or circular frequency) of a body having free

longitudinal vibration is given by

ω =

Where ωn = Circular frequency or natural angular velocity, s = Stiffness of the spring to which the body of mass m is attached and m = Mass of vibrating body

10. What do you understand by "Torsionally equivalent shaft'?

PAKT B — (5 x 16 = 80 marks)

11. (a) (i) Explain in details the double-slider crank mechanism. Name all the inversions of double-slider crank mechanism. (ii) With a neat sketch explain the inversion of double-slider crank mechanism which is used in elliptical trammel.

Or (b) In the steam engine mechanism, shown in figure 1 the crank AB rotates at 200 r.p.m. Find the velocities of C, D, E, F and P. Also find the acceleration of the slider at C. The dimensions of the various links are: AB = 12cm, BC = 48 cm, CD = 18 cm, DE = 36cm and EF = 12 cm and FP = 36 cm.



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12. (a) The external and internal radii of a friction clutch of disc type are 90 mm and 50 mm respectively. Both sides of the friction clutch are effective and co-efficient of friction is equal to 0.25. The friction clutch is used to rotate a machine from a shaft which is rotating at a constant speed of 240 r.p.m. The moment of inertia of the rotating parts of the machine is 5.5 kg m2. The intensity of pressure is not to exceed 0.8 x 105N/m2. Assuming uniform wear, determine the time required for the machine to attain the full speed when the clutch is suddenly applied. Also determine the energy lost in slipping of the clutch.

Or

(b) An open belt connects two flat pulleys, the smaller pulley being of 400 mm in diameter. The angle of lap on the smaller pulley is 160° and co-efficient of friction between belt and pulley is 0.25. Which of the following alternatives would be more effective in increasing the power that could be transmitted: (i) increasing the initial tension by 10%. (ii) increasing the co-efficient of friction by 10% by the application of suitable dressing to the belt? 13. (a) Two mating involute spur gears of 20° pressure angle have a gear ratio of 2. The number of teeth on the pinion is 20 and its speed is 250 r.p.m. The modular pitch of the teeth is 12 mm. If the addendum on each wheel is such that the path of approach and the path of recess on each side are half the maximum possible length each, find : (i) the addendum for pinion and gear wheel; (ii) the length of arc of contact; (iii) the maximum velocity of sliding during approach and recess, Assume pinion to be the driver

Or



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(b) Figure 2 shows an epicyclic gear train. Pinion A has 15 teeth and is rigidly fixed to the motor shaft. The wheel B has 20 teeth and gears with A and also with the annular fixed wheel D. Pinion C has 15 teeth and is integral with B (B, G being a compound gear wheel). Gear C meshes with annular wheel E, which is keyed to the machine shaft. The arm rotates about the same shaft on which A is fixed and carries the compound wheel B, C. If the motor runs at 1000 r.p.m., find the speed of the machine shaft. Find the torque exerted on the machine shaft if the motor develops a torque of 100 Nm .

14. (a) Figure 3 shows a long shaft carries three pulleys, two at its ends and the third at midpoint. The two end pulleys have masses 48 kg and 20 kg and their centre of gravities are 1.5cm and 1.25 cm respectively from the axis of the shaft, the middle pulley has mass 56 kg and its C.G. is 1.5 cm from the shaft axis. The pulleys are so keyed to the shaft that the assembly is in static balance. The shaft rotates at 300 r.p.m. in two bearings 180 cm apart with equal overhungs on either sides. Determine relative angular position of the pulleys.

(b) A four-cylinder vertical engine is in complete primary balance. The length of the cranks are 150 mm. The planes of rotation of the first, second and fourth cranks are 400 mm, 200 mm and 200 mm respectively from the third crank and their reciprocating masses are 50 kg, 60 kg and 50 kg respectively. Find (i) the mass of the reciprocating parts for the third cylinder and (ii) the relative angular positions of the cranks.



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15. (a) Figure 4 show a flywheel of mass 750 kg mounted on a vertical shaft of diameter 50 mm.

The both ends of the shaft are fixed. The length La, of the shaft is 1350 mm whereas the length L2 is 900 mm. If E = 200 GN/m2, then find the natural frequencies of the longitudinal and transverse vibrations. Neglect the weight of the shaft.

Or

(b) A reciprocating l.C. engine is coupled to a centrifugal pump through a pair of gears. The shaft from the flywheel of the engine to the gear wheel has a 45 mm diameter and is 1 m long. The shaft from the pinion to the pump has a 30mm diameter and is 810mm long. Pump speed is four times the engine speed. The moment of inertia of flywheel, gear wheel, pinion and pump are 400 kg m2, 8 kg m2, 2 kg m2 and 10 kg m2 respectively. If the modulus of rigidity of shaft material is 80 GN/m2, find the natural frequency of torsional vibrations of the systems.


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