Set No. 1
Code No: R05310304
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III B.Tech I Semester Regular Examinations, November 2007 KINEMATICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Enumerate the inversions of a double slider-crank chain. Give examples.
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(b) The length of the fixed link of a crank and slotted lever mechanism is 300 mm and that of the crank 110 mm. Determine,
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i. the inclination of the slotted lever with the vertical in the extreme position. ii. the ratio of the time of cutting stroke to the time of return stroke and iii. the length of the stroke, if the length of the slotted lever is 500 mm and the line of stroke passes through the extreme positions of the free end of the lever. [6+10]
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2. A torque of 75 N-m is applied to the link OA at A of a Gross-Hopper mechanism shown in figure 2. The link OA makes an angle of 20 degrees with the horizontal. Find the magnitude of the vertical force exerted at B to overcome the resisting torque of 75 N-m. The lengths of the links are: OA=40 mm, AC= 60 mm and CB= 150 mm. If the link OA makes an angle of 10 and zero degrees with the horizontal, what will be the vertical force at B to overcome the torque of 75 N-m? [16]
Figure 2 3. (a) State and Explain Kennedy’s theorem as applicable to instantaneous center of rotation of three bodies.
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Set No. 1
Code No: R05310304
(b) In the mechanism shown in Figure 3. the crank OA makes 400rpm in the counter clockwise direction. Find
Figure 3
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i. angular velocity of the link BA and ii. velocity of the slider at A. The lengths of the links are OA= 60mm, OB= 220 mm and BC= 300mm. [6+10]
4. (a) Derive the fundamental equation for correct steering.
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(b) What are the relative merits and demerits of the Ackermann type of steering gear over that of Davis type?
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(c) Two shafts are to be connected by a Hooke’s joint. The driving shaft rotates at a uniform speed of 500rpm and the speed of the driven shaft must lie between 475 and 525 rpm. Determine the maximum permissible angle between the shafts. Also determine the maximum and minimum speeds of the driven shaft. [6+4+6] 5. (a) Derive an expression for displacement, velocity and acceleration of a tangent cam with roller follower. When roller is in contact with flank. (b) A tangent cam with straight working faces tangential to a base circle of 120mm diameter has a roller follower of 48mm diameter. The line of stroke of the roller follower passes through the axis of the cam. The nose circle radius of the cam is 12mm and the angle between the tangential faces of the cam 900 . If the speed of the cam is 180rpm, determine the acceleration of the follower when
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i. During the lift, the roller just leaves the straight flank. ii. The roller is at the outer end of its lift, i.e at the top of the nose.
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6. (a) What is standard system of gears? How does it ensure interchangeability of gears? (b) Two 200 involute spur gears have a module of 10mm. The addendum is one module. The larger gear has 50 teeth and the pinion 13 teeth. Does the interference occur? If it occurs, to what value should the pressure angle be changed to eliminate interference? [16]
7. A leather belt 150mm wide 6mm thick and weighing 6 N/m length connects two pulleys each 1m in diameter and on parallel shafts. The belt is found to slip when the moment of resistance is 600N.m and the speed is 500 rpm. If the coefficient of friction between the belt and the pulleys is 0.24, find the largest tension in the belt. [16] 2 of 3
Set No. 1
Code No: R05310304 8. (a) Explain about Epicyclic gear train.
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(b) In the epicyclic gear train shown in figure 8b, a gear C which has teeth cut internally and externally is free to rotate on an arm driven by shaft S1 . It meshes externally with the casting D and internally with the pinion B. The gears have the following number of teeth: TB = 24, TC = 32 and 40, TD = 48 Find the velocity ratio between i. S1 and S2 when D is fixed. ii. S1 and D when S2 is fixed.
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Figure 8b
Set No. 2
Code No: R05310304
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III B.Tech I Semester Regular Examinations, November 2007 KINEMATICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Enumerate the inversions of a double slider-crank chain. Give examples.
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(b) The length of the fixed link of a crank and slotted lever mechanism is 300 mm and that of the crank 110 mm. Determine,
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i. the inclination of the slotted lever with the vertical in the extreme position. ii. the ratio of the time of cutting stroke to the time of return stroke and iii. the length of the stroke, if the length of the slotted lever is 500 mm and the line of stroke passes through the extreme positions of the free end of the lever. [6+10] 2. (a) Name the mechanisms that generate straight lines.
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(b) Prove that the peaucellier mechanism generates a straight-line motion. [4+12] 3. A crank and rocker mechanism ABCD has the following dimensions: AB =0.75m, BC =1.25 m, CD =1 m, AD =1.5 m and CF = 500 mm. AD is the fixed link. F lies on BC produced. Crank AB has an angular velocity of 30 rad/s counter clock-wise and a deceleration of 200 rad/s2 at the instant angle DAB= 300 . Find (a) The instantaneous linear acceleration of C and F and
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(b) The instantaneous angular velocities and accelerations of links BC and CD. [16] 4. (a) Explain Davis steering gear with a neat sketch.
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(b) For a Davis steering gear, derive the expression for the angle of inclination of the track arms to longitudinal axis of the vehicle in terms of the distance between the pivots of the front axle and wheelbase. (c) In a Davis steering gear the distance between the pivots of the front axle is 90 cm and the wheelbase is 220 cm. When the vehicle is moving along a straight path, find the inclination of the track arms to the longitudinal axis of the vehicle. [4+8+4]
5. (a) Explain with the help of displacement, velocity and acceleration diagrams, a uniform acceleration and uniform retardation profile cam. (b) Draw the profile of a cam operating a roller reciprocating follower and with the following data: 1 of 2
Set No. 2
Code No: R05310304
Minimum radius of cam = 25mm, Lift = 30mm, roller diameter = 15mm. The cam lifts the follower for 1200 with SHM followed by a dwell period of 300 . Then the follower lowers down during 1500 of the cam rotation with uniform acceleration and deceleration followed by a dwell period. If the cam rotates at a uniform speed of 150 rpm, calculate the maximum velocity and acceleration of the follower during the descent period. [16]
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6. (a) Define addendum circle, dedendum circle, arc of contact of gears.
(b) Two gears in mesh have a module of 8mm and a pressure angle of 200 . The larger gear has 57 while the pinion has 23 teeth. If the addenda on pinion and gear wheels are equal to one module, find
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i. the number of pairs of teeth in contact ii. the angle of action of the pinion and the gear wheel iii. the ratio of the sliding to rolling velocity at A. the beginning of contact B. the pitch point C. the end of contact
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7. A leather belt 150mm wide 6mm thick and weighing 6 N/m length connects two pulleys each 1m in diameter and on parallel shafts. The belt is found to slip when the moment of resistance is 600N.m and the speed is 500 rpm. If the coefficient of friction between the belt and the pulleys is 0.24, find the largest tension in the belt. [16]
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8. In an epicyclic gear train of the sun and planet type shown in figure 8, the pitch circle diameter of annular wheel A is to be nearly equal to 216mm, and the module is 4mm. When the annular wheel is stationary, the spider which carries three plant gears P of equal size, has to make one revolution for every five revolutions of the driving spindle carrying S gear. Determine the number of teeth on all the wheels and also the exact pitch circle diameter of A. [16]
Figure 8 ⋆⋆⋆⋆⋆
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Set No. 3
Code No: R05310304
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III B.Tech I Semester Regular Examinations, November 2007 KINEMATICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆
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1. (a) What is the difference between quick return motion of crank and slotted lever type and that of whit worth type?
(b) Find the distance between the fixed centers of a Whitworth quick return motion mechanism if the length of driving link is 40mm, return stroke is 150mm and time ratio of cutting to return stroke is 2. [6+10] 2. (a) Name the mechanisms that generate straight lines.
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(b) Prove that the peaucellier mechanism generates a straight-line motion. [4+12]
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3. In the mechanism shown in Figure 3. The crank OA rotates at 50 rpm and the lengths of the links are OA= 125 mm, AC= 600 mm, QC= 150 mm, QD= 150 mm, CD= 130 mm, BD= 550 mm and OQ= 625 mm. When the angle AOQ= 45 degrees, determine, (a) The linear acceleration of the slider at B. [10+6]
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(b) The angular acceleration of the links AC, CQD and BD.
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4. Describe the working of a Hooke’s joint with a neat sketch. Also prove that the ratio of angular velocity of the driven shaft to that of the driving shaft with a α Hooke’s joint is 1−sincos 2 α cos2 θ , where θ is the angle turned by the driving shaft at any instant and α is the angle of inclination of driven shaft with driving shaft. [16] 5. (a) With the help of neat sketches explain the types of cams and followers. 1 of 2
Set No. 3
Code No: R05310304
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(b) Draw the profile of a cam operating a knife-edge follower having a lift of 30mm. The cam raises the follower with SHM for 1500 of the rotation followed by a period of dwell for 600 . The follower descends for the next 1000 rotation of the cam with uniform velocity, again followed by a dwell period. The cam rotates at a uniform velocity of 120rpm and has a least radius of 20mm. What will be the maximum velocity and acceleration of the follower during the lift and the return? [16] 6. (a) Explain ’law of gearing’.
7. (a) Discuss about selection of belt drive.
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(b) A pair of spur gears have 16 and 18 teeth, a module of 13mm, addendum of 13mm, and pressure angle of 14.50 . Show that the gears have interference. Determine the amount by which the addendum must be reduced to eliminate the interference. [16]
Neglecting belt thickness. Taking belt thickness as 5mm. Assuming for case (ii) a total slip of 4% and Assuming for case (ii) a slip of 2% on each pulley.
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i. ii. iii. iv.
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(b) A shaft runs at 80 rpm and drives another shaft at 150rpm through belt drive. The Diameter of the driving pulley is 600mm. Determine the diameter of the driven pulley in the following cases:
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8. An epicyclic gear train consists of three gears 1,2 and 3 as shown in figure 8. The internal gear 1 has 72 teeth and gear 3 has 32 teeth. The Gear 2 meshes with both gear 1 and gear 3 and is carried on an arm A which rotates about the centre O2 at 20 rpm. If the gear 1 is fixed, determine the speed of gears 2 and 3. [16]
Figure 8 ⋆⋆⋆⋆⋆
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Set No. 4
Code No: R05310304
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III B.Tech I Semester Regular Examinations, November 2007 KINEMATICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆
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1. (a) What is a Kinematic chain? What is the relation between the number of links and number of pairs in a kinematic chain? (b) Give diagrammatic sketches of the following mechanisms and state on which Kinematic chain each mechanism is based: Oscillating cylinder engine Oldham shaft coupling Pendulum pump Scotch yoke mechanism Watt’s indicator.
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i. ii. iii. iv. v.
[6+10]
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2. (a) Explain Scott Russell mechanism through a neat sketch. Show that it generates a straight-line motion. (b) What are the limitations of Scott Russell mechanism.
[12+4]
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3. The crank OP of a crank and slotted lever mechanism shown in figure 3. rotates at 200 rpm in the counter-clockwise direction. Various lengths of the links are OP = 90 mm, OA = 300 mm, AR = 480 mm and RS= 330mm. The slider moves along an axis perpendicular to AO and is 120 mm from O. Determine the velocity of the slider when the angle AOP is 135o and also the maximum velocity of the slider. [16]
Figure 3 4. (a) Sketch Ackermann steering gear and explain its advantages.
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Set No. 4
Code No: R05310304
(b) For an Ackermann steering gear, derive the expression for the angle of inclination of the track arms to longitudinal axis of the vehicle.
5. (a) With the help at neat sketches explain the types of cams.
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(c) The driving shaft of a Hooke’s joint rotates at a uniform speed of 300 rpm. If the total maximum variation in speed of the driven shaft is 8 percent of the mean speed, determine the greatest permissible angle between the axes of the shaft. Also find the maximum and minimum speeds of the driven shaft. [4+7+5]
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(b) A cam is to operate an offset roller follower. The least radius of the cam is 50mm, roller diameter is 30mm, and offset is 20mm. The cam is to rotate at 360rpm. The angel of ascent is 480 , angle of dwell is 420 , and angle of descent is 600 . The motion is to be SHM during ascent and uniform acceleration and deceleration during descent. Draw the cam profile. Also calculate the maximum velocity and acceleration during descent. [16] 6. (a) Sketch a pair of gears and represent meshing on it.
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(b) An internal spur gear having 200 teeth meshes with a pinion having 40 teeth and a module of 2.5mm. Determine:
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i. the velocity ratio if the pinion is the driver. ii. the centre distance, and iii. if the centre distance is increased by 3mm, find the resulting pressure angle. [16] 7. A machine which is to rotate at 400 rpm is run by an engine turning at 1500rpm, through a silent chain, having a pitch of 15mm. The number of teeth on a sprocket should be from 18 to 105. The linear velocity of chain drive is not to exceed 10m/s. Find the suitable number of teeth for both the sprockets. [16] 8. (a) Explain about automotive differential.
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(b) An epicyclic gear consists of a pinion, a wheel of 40 teeth and an annulus with 84 internal teeth concentric with the wheel. The pinion gear with the wheel and the annulus. The arm that carries the axis of the pinion rotates at 100rpm. If the annulus is fixed, find the speed of the wheel; if wheel is fixed, find the speed of the annulus. [16] ⋆⋆⋆⋆⋆
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