Rr312403 Kinematics of Machinery

8/14/2019 Rr312403 Kinematics of Machinery

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Code No: RR312403 Set No.1

III B.Tech. I Semester Supplementary Examinations, February -2007KINEMATICS OF MACHINERY

(Automobile Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

1. (a) What is meant by inversion of a mechanism? Describe with the help of suitablesketches the inversions of a single slider crank chain.

(b) In a Whitworth quick return motion mechanism, as shown in figure 1, the

distance between the fixed centres is 50mm and the length of the drivingcrank is 75mm. The length of the slotted lever is 150mm and the length ofconnecting rod is 135mm. Find the ratio of the time of cutting stroke to thetime of return stroke and also the effective stroke. [16]

Figure 1:

2. (a) With the help of neat sketch, explain peaucellier straight line mechanism andprove that tracing point describes a straight line path.

(b) Two points P and Q, 4cm apart are to be conneced by a pantograph. The

motion of P to the motion of Q is 13:7. Find the distance of Q from thefixed point O of the pantograph such that the point of P moves at least 12.7cm in either direction of line OQP when it is horizontal. Find also the maindimensions of the pantograph. [16]

3. In the mechanism, as shown in figure 2, the crank OA rotates at 20 rpm anticlock-wise and gives motion to the sliding blocks B and D. The dimensions of the variouslinks are OA=300mm, AB=1200mm; BC=450mm; CD=450mm.

For the given configuration, determine:

(a) velocities of sliding at B and D(b) angular velocity of CD

(c) linear acceleration of D and

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Figure 2:

(d) angular acceleration of CD [16]

4. (a) Sketch the Davis gear show that it satisfies the condition for correct steering.In spite of this, explain why, in actual practice, Ackermann steering gear,which doesnt satisfy the above condition in all positions is preferred to theformer?

(b) A Hookes joint connects a shaft running at a uniform speed of 900 rpm to asecond shaft. The angle between thier axes being 200. Find the velocity andacceleration of the driven shaft at the instant when the fork of the drivingshaft has turned through an angle of 150 from the plane of containing theshaft axes. [16]

5. Draw a cam profile to drive an oscillating roller follower to the specifications givenbelow:

(a) follower to move outwards through an angular displacement of 200 during the

first 120

0

rotation of cam.(b) follower to return to its initial position of during next 1200 rotation of cam.

(c) follower to dwell during the next 1200 of cam rotation

The distance between pivot centre and roller centre : 120mm

distance between pivot centre and cam axis = 130mm.

minimum radius of cam: 40mm;

radius of roller : 10mm

Inward and outwards strokes takes place with SHM. [16]

6. (a) Derive an expression for minimum number of teeth on the gear wheel in orderto avoid the interference.

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(b) Two gear wheels mesh externally are used to give a velocity ratio of 3:1.The teeth are of involute form; module=6mm, addendum= one module andpressure angle=200. The pinion rotates at 250 rpm. Find:

i. the no. of teeth on pinion to avoid interference on it and correspondingnumber on the gear wheel

ii. the number of pairs in contact

iii. the maximum velocity of sliding. [16]

7. (a) What is meant by slip? Derive the expression for velocity ratio in a compoundbelt drive by considering slip at all the pulleys.

(b) In an open flat belt drive, the diameters of driver and follower pulleys are

0.3m and 0.45m respectively. The width of the belt is 120mm, and the centredistance of the drive is 2m. The maximum tension in the belt is limited to 15N/mm width. The coe. of friction is 0.35. If the driver pulley rotates at 120rpm, determine the maximum power that can be transmitted by the drive.Take the density of belt material as 1000 kg/m3.

[16]

8. (a) State how you will determine the torques and the tooth loads on epicyclic geartrain.

(b) A compound epicyclic gear train is shown in the figure3. The gear A, D and E

are free to rotate on the axis P. The compound gear B and C rotate togetheron the axis Q at the end of arm F. All the gears have equal module. The no.of teeth on the gears A, B and C are 18, 45 and 21 respectively. The gears Dand E are annular gears. The gear A rotates at 120 rpm CCW and the gearD rotates at 450 rpm CW. Find the speed and direction of the arm and thegear E. [16]

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Figure 3:

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1. (a) In a quick-return motion mechanism of crank and slotted lever type, the ratioof maximum velocities is 2. If the length of stroke is 25cm, find

i. the length of slotted lever

ii. the ratio of times of cutting and retrun strokesiii. the maximum cutting velocity per second if the crank rotates at 30 rpm.

(b) Extend Grublers criterion for planar mechanism to obtain the degree of free-dom of a space mechanism as

F= 6(L-1)-5g-4C-4S

where g=Total no. of sliding pairs

C= Total no. of cylindrical pairs

S=Total no. of spherical pairs

L=Total no. of links [16]

2. (a) Under what conditions Scott-Russel mechanism traces out a straight line andan ellipse? State the limitations of Scott Russel mechanism.

(b) A Grass-Hopper straight line mechanism get its motion from a crank OA. Theend A of the crank is joined to a long rod PQ such that QA is 6cm. Theend Q is further joined to a long vertical link O1Q 24cm long moving withcentre O1. The length of rod PQ is also 24cm and its end P describes anapproximate vertical straight line. Determine the radius of crank OA. Findalso the maximum deviation of P from the vertical straight line in a travel of

6 cm on each side of its mean position. [16]

3. A double slider-crank mechanism is shown in figure 4 Crank2 rotates at constantangular velocity w2=10 rad/sec. Determine the velocity and acceleration of eachslider.

O2A=100mm, AB=200mm, AC=200mm

4. (a) State precisely what an automobile steering is expected to achieve. Establishthe relationship among the parameters of the mechanism necessary for thispurpose.

(b) The driving shaft of a Hookes joint runs at a uniform speed of 240 rpm andthe angle between the shaft is 200. The driven shaft with attached masseshas a mass of 55kg at a radius of gyration of 150mm.

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Figure 4:

i. If a steady torque of 200 N-m resists rotation of the driven shaft, find thetorque required at the driving shaft when = 450

ii. At what value of will the toal fluctuation of the driven shaft be limitedto 24 rpm? [16]

5. Derive expressions for displacement, velocity and acceleration for flat-faced followerof a circular cam when

(a) the contact is on circular flank, and

(b) the contact is on circulat nose

Illustrate by graphs how displacement, velocity and acceleration vary from instantto instant during ascent and descent. [16]

6. The following data relate to pair of 200 involute gears in mesh:

Module: 6mm; No. of teeth on pinion:17; No. of teeth

on gear:49; Addendum on pinion and gear wheel:1 module. Find:

(a) the no. of pairs of teeth in contact

(b) the angle turned through by the pinion and the gear wheel when one pair ofteeth is in contact and

(c) the ratio of sliding to rolling motion when the tip of a tooth on the largerwheel

i. is just making contact

ii. is just leaving contact, with its mating tooth

iii. is at the pitch point [16]

7. (a) Define creep with respect to belt drives and derive the expression for velocityratio in belt drive, in presence of creep.

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(b) An open belt drive is used to connect two parallel shafts 4m apart. Thediameter of bigger pulley is 1.5m and that of smaller pulley is 0.5m. The massof belt is 1 kg/m length. the maximum tension is not to exceed 1500N. Thecoe. of friction is 0.25. The bigger pulley, which is the driver, runs at 250rpm. Due to slip, the speed of driven pulley is 725 rpm. Calculate the powertransmitted, Power lost in friction and efficiency of the drive. [16]

8. (a) What is an epicyclic Gear Train? In what manner does it differ from a simpleor compound Gear train?

(b) A compound train consists of six gears. The no. of teeth on the gears are asfollows:

Gear: A B C D E F

No. of teeth: 60 40 50 25 30 24

The gears B and C are on one shaft while gears D and E are on another shaft.The gear A drives gear B, gear C drives gear D and E drives gear F. If thegear A transmits 1.5kw at 100 rpm and the gear train has an efficiency of 80%,find the torque on gear F. [16]

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1. (a) Explain different kinds of kinematic pairs giving examples for each one ofthem.

(b) Find the equivalent mechanisms with turning pairs for the mechanisms shown

in figure 5.

Figure 5:

2. (a) Figure 6 shows an arrangement for a pantograph. What are the conditions to

be satisfied for reducing diagram and give the scale of reduction. What arethe limitations of this mechanism for the given dimensions.

(b) Explain with the help of neat sketch any one approximate straight line mech-anism and discuss its limitations. [16]

3. In the mechanism shown in figure 7 the link O1A rotates at 24 rad/s. Find thevelocity and acceleration of point B, O1A=75mm; AB=200mm, O2B=200mm [16]

4. (a) For two shafts connected by a Hookes joint show that if shaft 1 has uniformangular velocity w1, the angular acceleration of shaft 2 is given byw2

t =w21cos sin2 sin 2

(1sin2 cos2 )2

where is angle of rotation of shaft 1 from the position where its forked endin the plane containing shaft, and is the angle of deviation of the drive.

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Figure 6:

Figure 7:

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(b) Two shafts are to be connected by a Hookes joint. The driving shaft is rotatedat a uniform speed of 500 rpm and the speed of the driven shaft must be 475and 525 rpm. Determine the maximum permissible angle between the shafts.

[16]

5. A cam, with minimum radius of 25mm, rotating clockwise at a uniform speed is tobe designed to give a roller follower, at the end of a valve rod, motion describedbelow:

(a) to raise the valve through 50mm during 1200 rotation of the cam

(b) to keep the valve fully raised during next 300

(c) to lower the valve during next 600 and

(d) to keep the valve closed during rest of the revolution

The daimeter of the roller is 20mm and the diameter of the cam shaft is 25mm.Draw the profile of the cam when the line of stroke of the valve rod passes throughthe axis of the cam shaft. [16]

6. (a) Derive the expressions for path of contact and arc of contact for involute gears,when the points at which engagement commences and terminates are withinthe points of tangency.

(b) The following data relate to two involute spur gears on mesh:

Pressure angle= 160

Gear ratio = 1.75No. of teeth on pinion=61Pinion speed = 240 rpmmodule = 6mm

In order that the interference does not take place find

i. the maximum working depth

ii. the length of path of contact

iii. the maximum velocity of sliding on either side of pitch point. [16]

7. In an open flat belt drive; the pulley diameters are 300mm and 450mm and thecorresponding angles of lap are 1600 and 2000. The smaller pulley runs at 240 rpm.The coefficient of friction between the pulleys and the belt is 0.3. It is found thatthe belt is on the point of slipping when 5 kW power is transmitted. To increasethe power transmitted; three alternatives are suggested viz;

(a) incrreasing the initial tension by 10%

(b) increasing the coefficient of friction by 10%

(c) decreasing the initial tension by 10%Which of the above three methods would be more effective? [16]

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8. (a) Prove that irrespective of whichever wheel is fixed, velocity ratio obtainedfrom a sun and planet gear is less than unity.

(b) An epicyclic geartrain, as shown in figure 8 is composed of a fixed annularwheel A having 150 teeth. The wheel A is meshing with wheel B which driveswheel D through an idle wheel C,D being concentric with A. The wheels Band C are carried on an arm which revolves clockwise at 100 rpm about theaxis of A and D. If the wheels B and D have 25 teeth and 40 teeth respectively,find the number of teeth on C and the speed and sense of rotation of C. [16]

Figure 8:

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1. (a) What is meant by inversion of a mechanism? Describe with the help of suitablesketches the inversions of a Quadric cycle chain.

(b) Determine the mobility of the mechanisms in figure 9. [16]

Figure 9:

2. (a) With the help of a neat sketch explain a pantograph and its principle of work-ing.

(b) With the help of a neat sketch explain Hart-straight line motion mechanismand prove that tracing point describes a straight line path. [16]

3. Determine the acceleration of slider C when crank 2 is rotating at 600 rpm clockwisewith a retarding angular acceleration of 40 rad/sec2. (figure 10) [16]

4. (a) Derive an expression for the ratio of shafts velocities for Hookes joint and

draw the polar diagram depicting the salient features of driven shaft speed.(b) Angle between axes of two shafts connected by a hookes joint is 180. Deter-

mine the angle turned through by the driving shaft

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Figure 10:

i. when velocity ratio is maximum, minimum and unity and

ii. when acceleration of driven shaft is maximum [16]

5. A cam has straight working faces (tangent) which are tangential to a base circleof diameter 90mm. The follower is a roller of diameter 40mm and the centre ofroller moves along a straight line passing through the centre line of the cam shaft.The angle between the tangential faces of the cam is 900 and the faces joined by anose circle of 10mm radius. The speed of rotation of the cam is 120rpm. Find theacceleration of the roller centre.

(a) when during the lift, the roller is just about to leave the straight flank and

(b) when the roller is at the outer end of its lift [16]

6. (a) Derive an expression for the lengths of arc of contact for two involute profilegears in mesh.

(b) Two mating involute gears of 200 pressure angle have a gear ratio of 2. The no.of teeth on the pinion is 20 and its speed is 300 rpm. The module is 12mm.The addendum on each wheel is such that the path of approach and path ofrecess on each side are half the maximum possible length each. Determine:

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 [16]

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7. Determine the width of the flat belt required, to transmit power from an electricmotor to an air compressor with the following data:Power=15kWCentre distance between pulleys = 1.5mDiameter of motor pulley = 250 mmSpeed of motor pulley = 720 rpmSpeed of compressor pulley = 180 rpmPermissible tensile stress in the belt material = 1.8 MPabelt slip = 2%coefficient of friction between the belt and pulleys = 0.3mass density of the belt material = 1000 kg/m3

thickness of the belt = 10mm. [16]

8. (a) Describe a differential with the help of a sketch. Prove that the two rearwheels will rotate at different speeds with its help when rounding a curve.

(b) In an epicyclic gear train, as shown in figure 11 the number of teeth on wheelsA, B and C are 50, 25 and 52 respectively. If the arm rotates at 420 rpm CW,find

i. speed of wheel C when A is fixed, and

ii. speed of wheel A when C is fixed [16]

Figure 11:

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Rr312403 Kinematics of Machinery

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