Set No. 1
Code No: R05310304 R05310304
III B.Tec B.Tech h I Semest Semester er Regula Regularr Examin Examinati ations ons,, Nov Novem ember ber 2007 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) En Enumer umerate ate the invers inversions ions of a double sliderslider-cran crank k chain. chain. Give Give examples. examples. (b) The length of the fixed link of a crank and slotted lever mechanism mechanism is 300 mm and that of the crank 110 mm. Determine, 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 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 torqu torquee of 75 N-m. N-m. Th Thee lengt lengths hs of the links links are: are: OA=4 OA=400 mm, mm, AC= 60 mm and CB= CB= 150 150 mm. mm. If the link OA makes makes an angl anglee of 10 and and zero zero degrees degrees with 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 State and Explai Explain n Kennedy’s Kennedy’s theorem theorem as applicabl applicablee to instan instantane taneous ous center center of rotation of three bodies.
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Set No. 1
Code No: R05310304 R05310304
(b) In the mech mechan anis ism m show shown n in Figure Figure 3. the crank crank OA makes makes 400rpm 400rpm in the counter clockwise direction. Find 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]
Figure 3 4. (a) Derive Derive the the fundamen fundamental tal equati equation on for correct correct steeri steering. ng. (b) What are the relative merits and demerits demerits of the Ackermann Ackermann type of steering gear over that of Davis type? (c) Two shafts shafts are to be connected by a Hooke’s Hooke’s joint. The driving driving shaft rotates at a uniform speed of 500rpm and the speed of the driven shaft must lie between 475 and 525 rpm. Determi Determine ne the maximu maximum m permissi permissible ble angle between between the shafts. Also determine determine the maximum maximum and minimum speeds of the driven driven shaft. [6+4+6] 5. (a) Derive Derive an expressi expression on for displacem displacemen ent, t, velocit velocity y and acceleratio acceleration n of a tangent tangent cam with roller follower. When roller is in contact with flank. (b) A tangent cam with straight straight working faces tangential tangential to a base circle of 120mm diameter diameter has a roller follower 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 th the speed of the cam is 180rpm, determine the acceleration of the follower when i. During the lift, the roller just leaves the straight flank. ii. ii. Th Thee roller roller is is at the the outer outer end end of its its lif lift, t, i.e i.e at at the top top of of the nos nose. e.
[16] [16]
6. (a) What is standa standard rd system system of gears? gears? How How does it ensure interc interchang hangeabi eabilit lity y of gears? (b) Two 200 invo involut lutee spur gears gears have have a module module of 10mm. The addendum addendum is one modul module. e. Th Thee larg larger er gear gear has has 50 teeth teeth and the pinio pinion n 13 teeth teeth.. Does Does the the interf interferen erence ce occur o ccur?? If it occurs, occurs, to wha whatt value should should the pressure pressure angle 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 moment of resistance resistance is 600N.m 600N.m and the speed is 500 rpm. If the coefficient 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 R05310304 8. (a) Explai Explain n about about Epicy Epicycli clicc gear gear train. train.
(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 S 1 . It meshes externally with the casting D and internally with the pinion B. The gears have the following number of teeth: T B = 24, T C C = 32 and 40, T D = 48 Find the velocity ratio between i. S 1 and S 2 when D is fixed. ii. S 1 and D when S 2 is fixed.
[16]
Figure 8b ⋆⋆⋆⋆⋆
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Set No. 2
Code No: R05310304 R05310304
III B.Tec B.Tech h I Semest Semester er Regula Regularr Examin Examinati ations ons,, Nov Novem ember ber 2007 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) En Enumer umerate ate the invers inversions ions of a double sliderslider-cran crank k chain. chain. Give Give examples. examples. (b) The length of the fixed link of a crank and slotted lever mechanism mechanism is 300 mm and that of the crank 110 mm. Determine, 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 Name the mechani mechanisms sms that that generate generate straig straight ht lines. lines. (b) Prove Prove that the peaucell p eaucellier ier mechanism mechanism generates a straight-line straight-line motion. 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 instantaneous linear linear acceleration acceleration of C and F and (b) The instantaneous instantaneous angular velocities velocities and accelerations of links BC and CD. [16] 4. (a) Explai Explain n Davis Davis steer steering ing gear gear with with a neat sketc sketch. h. (b) For a Da Davis vis steering steering gear, gear, derive derive the express expression ion for the angle of inclin inclinati ation on 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 steering gear the distance between the pivots 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) Explai Explain n with the help of displacem displacemen ent, t, velocit velocity y and accelerati acceleration on diagrams diagrams,, a uniform acceleration and uniform retardation profile cam. (b) Draw Draw the profile profile of a cam operating operating a roller roller reciproca reciprocatin tingg follow follower er and with the following data: 1 of 2
Set No. 2
Code No: R05310304 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 p eriod. [16] 6. (a) Define Define addendum addendum circle circle,, dedendum dedendum circle circle,, arc of contact contact of gears. 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 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 beginning of contact contact B. the pitch pitch point C. the end of contact
[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 moment of resistance resistance is 600N.m 600N.m and the speed is 500 rpm. If the coefficient coefficient of friction between the belt and the pulleys is 0.24, find the largest tension in the belt. [16] 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 drivin drivingg spindl spindlee carryin carryingg S gear. gear. Determi Determine ne the nu numbe mberr 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 R05310304
III B.Tec B.Tech h I Semest Semester er Regula Regularr Examin Examinati ations ons,, Nov Novem ember ber 2007 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) What is the differe difference nce between between quick quick return return motion motion of crank and slotte slotted d lever lever type and that of whit worth type? (b) Find the distance between between the fixed centers of a Whitworth 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 Name the mechani mechanisms sms that that generate generate straig straight ht lines. lines. (b) Prove Prove that the peaucell p eaucellier ier mechanism mechanism generates a straight-line straight-line motion. motion. [4+12] 3. In the mechan mechanis ism m shown shown in Figu Figure re 3. Th Thee crank crank OA rotates 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, determine, (a) The linear linear accelerati acceleration on of the slider slider at B. (b) (b) The ang ngu ular accel celerati ration on of the the links nks AC, CQD and BD.
[10+6 0+6]
Figure 3 4. Descri Describe be the working working of a Hooke’s Hooke’s joint joint with with a neat sketc sketch. h. Also Also prove prove that the ratio of angular velocity of the driven shaft to that of the driving shaft with a Hooke’s joint is 1−sincosα αcos 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] 2
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5. (a) With With the help of neat sketc sketches hes explai explain n the types of cams cams and follow followers ers.. 1 of 2
Set No. 3
Code No: R05310304 R05310304
(b) Draw the profile profile of a cam operating op erating a knife-edge knife-edge follower follower having having a lift of 30mm. 0 The cam raises the follower with SHM for 150 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 uniform velocit velocity y of 120rpm 120rpm and has a least least radius radius of 20mm. 20mm. What will will be the maximum velocity and acceleration of the follower during the lift and the return? [16] 6. (a) Explai Explain n ’la ’law w of of geari gearing’ ng’.. (b) A pair of spur gears have 16 and 18 teeth, a module of 13mm, addendum of 13mm, and pressure angle of 14.50. Sho Show w that the gears gears have have interf interferen erence. ce. Determine the amount by which the addendum must be reduced to eliminate the interference. [16] 7. (a) Discuss Discuss about selecti selection on of belt driv drive. e. (b) A shaft runs at 80 rpm and drives another another shaft at 150rpm through belt drive. drive. The Diameter of the driving pulley is 600mm. Determine the diameter of the driven pulley in the following cases: i. Neglecting belt thickness. ii. Taking belt thickness as 5mm. iii. Assuming for case (ii) a total slip of 4% and iv. Assuming for case (ii) a slip of 2% on each pulley.
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8. An epicyclic gear train consists of three gears 1,2 and 3 as shown in figure 8. The intern internal al gear 1 has 72 teeth and gear 3 has 32 teeth. The Gear 2 meshes with with both gear 1 and gear 3 and is carried on an arm A which rotates about the centre O2 at 20 rpm rpm. If If the the gear ear 1 is fixe fixed, dete determ rmiine the the speed peed of gear gearss 2 and 3. [16] 16]
Figure 8 ⋆⋆⋆⋆⋆
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Set No. 4
Code No: R05310304 R05310304
III B.Tec B.Tech h I Semest Semester er Regula Regularr Examin Examinati ations ons,, Nov Novem ember ber 2007 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) What is is a Kinemati Kinematicc chain? chain? What is is the relatio relation n between between the the number number of links links and number of pairs in a kinematic chain? (b) Give Give diagrammatic diagrammatic sketches sketches of the following following mechanisms and state on which Kinematic chain each mechanism is based: i. Oscillating cylinder engine ii. Oldham shaft coupling iii. Pendulum pump iv. Scotch Scotch yoke mechanism mechanism v. Watt’s indicator.
[6+10]
2. (a) Explai Explain n Scott Russel Russelll mechani mechanism sm through through a neat sketc sketch. h. Sho Show w that it genergenerates a straight-line motion. (b) What are the limitations of Scott Russell mechanism.
[12+4]
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 135 and also the maximum velocity of the slider. [16] o
Figure 3 4. (a) Sketch Sketch Ackerm Ackermann ann steering steering gear and explain explain its advantag advantages. es.
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Set No. 4
Code No: R05310304 R05310304
(b) For an Acke Ackerman rmann n steering steering gear, derive derive the expressio expression n for the angle angle of incliinclination of the track arms to longitudinal axis of the vehicle. (c) The driving driving shaft shaft of a Hooke’s Hooke’s joint joint rotates rotates at a uniform uniform speed 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] 5. (a) With With the help help at neat ske sketch tches es explai explain n the types types of cams. cams. (b) A cam is to operate operate an offset roller roller follow follower. er. The least least radius 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 42 0 , 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 Also calcula calculate te the maxi maximu mum m veloci velocity ty and and acceler acceleratio ation n during during descen descent. t. [16] [16] 6. (a) Sketc Sketch h a pair of gears gears and and represen representt meshing meshing on it. it. (b) An internal internal spur gear having having 200 teeth teeth meshes meshes with a pinion pinion having having 40 teeth teeth and a module of 2.5mm. Determine: i. the velocit velocity y ratio if the pinion pinion is the drive driver. r. 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 numb er of teeth for both the sprockets. [16] 8. (a) Explai Explain n about autom automotiv otivee differen differentia tial. l. (b) An epicyclic gear consists of a pinion, a wheel of 40 teeth and an annulus with with 84 internal internal teeth concentr concentric ic with the wheel. wheel. The pinion pinion gear with 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 sp eed of the annulus. [16] ⋆ ⋆ ⋆ ⋆ ⋆
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