Rr222105-kinematics-of-machinery

Set No. 1

Code No: RR222105

II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008 KINEMATICS OF MACHINERY (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Distinguish clearly between a ‘structure’ and a ‘Machine’. (b) Explain various inversions of single and double slider crank chains.

[4+12]

2. What do you mean by a Pantograph? With a neat sketch explain the principal and working of the pantograph. What are its uses? [16] 3. In the mechanism shown in Figure 3 below O and Q are fixed centres. If the crank OC revolves at a uniform speed of 120rpm, find the acceleration of the links CP, PA and AQ. [16]

Figure 3 4. A control mechanism is shown in Figure 4. If the angular velocity and the angular acceleration of the link O2 AB,i.e. link 2 is 15 rad/sec, and 100 rad/sec2 respectively, both in the counter clockwise sense, draw the velocity and acceleration polygons and determine acceleration of the slider link 4 or point C. The various dimensions of the mechanism are: O2 B = 225 MM, O2 A = 450 MM AB = 292 mm, BC = 375 mm

1 of 3

[16]

Set No. 1

Code No: RR222105

Figure 4 5. For two shafts connected by a Hooke’s joint show that if shaft 1 has uniform angular velocity ω1 , the angular acceleration of shaft 2 is given by: ω 2 cos α. sin2 α. sin2 θ ∂ω2 = 1 1−sin2 α. cos2 θ 1 ∂t ( 1) where θ1 is the angle of rotation of shaft 1 from the position where its forked end in the plane containing the shaft, and α is the angle of deviation of the drive.[16] 6. A flat ended valve tappet is operated by a symmetrical cam with circular arcs for flank and nose profiles. The total angle of action is 1500 base circle diameter 125 mm and the lift 25 mm. During the lift, the period of acceleration is half that of the retardation. Speed of cam shaft is 1250 r.p.m. The straight line path of the tapper passes through the cam axis. Find (a) Radii of the nose and flank, and (b) Maximum acceleration and retardation during the lift.

[16]

7. (a) What are the common curves used for tooth profile? What is an involute stub tooth? (b) Two gear wheels of 100 mm and 150 mm pitch diameters have involute teeth of 8 mm module pitch and an angle of obliquity of 170 . The addenda are 8 mm each. Determine i. the length of the path of contact, ii. the number of pairs of teeth in contact and iii. the angle turned through by the smaller wheel while any one pair of teeth is in contact. [6+10] 8. An arm R is fixed at the end of the shaft X and a compound pinion B and C is free to rotate in bearings at the end of this arm. B gears with a wheel A which is to rotate on X at 200 rpm and C gears with the wheel D fixe to a shaft Y which is coaxial with X. Wheel A has 72 teeth and B has 12 teeth. Find suitable numbers of teeth for wheels C and D so that the shaft Y shall rotate at 1070 rpm approximately, in the opposite direction to X which rotates at 1000 rpm. If the shaft X receives 10 HP determine the orque delivered by the shaft Y. [16] 2 of 3

Set No. 1

Code No: RR222105 ⋆⋆⋆⋆⋆

3 of 3

Set No. 2

Code No: RR222105

II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008 KINEMATICS OF MACHINERY (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Define motion and state its types. Distinguish between completely constrained, partially constrained and incompletely constrained motions. Where do you find their applications? (b) What is meant by degrees of freedom of a mechanism?

[12+4]

2. What do you mean by a Pantograph? With a neat sketch explain the principal and working of the pantograph. What are its uses? [16] 3. The crank AO of the mechanism shown in Figure 3below rotates at a uniform speed of 90rpm in clockwise direction. The length of various links are OA = 2.5cm, AB = BC = BQ = 10cm, QC is vertical and ‘O’ is 12.5cm to the left and 10cm below ‘Q’. For the configuration shown determine linear acceleration of slider C and angular acceleration of links AB, BQ and BC. [16]

Figure 3 4. In the circuit bracket mechanisms represented in Figure 4 the point P moves in a vertical straight line. In the configuration O4 B is vertical .If the angular velocity

1 of 3

Set No. 2

Code No: RR222105

and angular acceleration of link Q4 A is 45 rad/sec and 300 rad/sec2 respectively, both in clockwise sense, Determine the velocity and acceleration of point P. [16]

Figure 4 5. A Hook’s joint is used to connect two shafts whose axes are inclined at 200 . The driving shaft rotates uniformly at 6000 rpm. What are the extreme angular velocities of the driven shaft? Find the maximum value of retardation or acceleration and state the angle where both will occur. [16] 6. (a) Explain a radial cam mechanism and describe the types of cams with sketches. (b) Sketch the different types of cam followers. (c) Explain angle of Ascent, dwell and angle of descent.

[5+5+6]

7. (a) Define and explain the term (with the help of a neat sketch) path of approach, path of recess and path of contact between two mating gears. (b) Two mating involute spur gears have 28 and 45 teeth and a standard addendum of one module. Find the length of path of contact and length of arc of contact in terms of module when pressure angle is 200 . [6+10] 8. In an epicyclic gear train, as shown in Figure 8 the wheel C Is keyed to the Shaft B and wheel F is keyed to shaft A. The wheels D and E rotate together on a pin fixed to the arm G. The number of teeth on wheels C, D, E and F are 35,65,32 and 68 respectively. If the shaft A rotates at 60 r.p.m. and the shaft B rotates at 28 r.p.m. in the opposite direction, find the speed and direction of rotation of arm G. [16]

2 of 3

Set No. 2

Code No: RR222105

Figure 8 ⋆⋆⋆⋆⋆

3 of 3

Set No. 3

Code No: RR222105

II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008 KINEMATICS OF MACHINERY (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Find out the degrees of freedom of the gear system shown in the following Figure 1. (b) The distancce between two parallel shafts is 15 mm and they are connected by an Oldham’s coupling. The driving shaft revolves at 150 r.p.m.What will be the maximum speed of sliding of the tongue of the intermediate piece along its groove? (c) What are resistant bodies? Is it necessary that the resistant bodies be rigid? Give reasons for your answer. [4+8+4]

Figure 1 2. Describe any approximate straight-line motion mechanism with necessary equations. [16] 3. An inversion of a slide crank mechanism shown in Figure 3. For angular velocity of 300rpm. For the crank O2 Q in the counter – clockwise sense, determine: (a) Angular velocity of link 4 (b) Velocity and acceleration of point P

1 of 3

Set No. 3

Code No: RR222105

The main dimensions of the linkage are: O2 Q = 6cm and O4 P = 30cm.

[16]

Figure 3 4. In a link arrangement shown in Figure 4 O1 and O2 are fixed points. O2 A rotates at a speed of 10 radians per second in the direction shown by the arrowhead. A moves in a slot in O2 B. D is a fixed spindle about which the bell crank lever oscillates. Find the speed of E. Given CF1 = EF2 = 12.5 cm and F2 is vertically above F1 , O1 A = 5 cm, O1 O2 = 7.5 cm, O2 B = 15 cm, DF1 = 10 CM, DF2 = 7.5 cm. [16]

Figure 4 5. The driving shaft of a Hooke’s joint has a uniform angular speed of 300 r.p.m. Determine the maximum permissible angle between the axes of the shaft to permit a maximum variation in speed of the driven shaft by 6% of the mean speed. [16] 6. A flat ended valve tappet is operated by a symmetrical cam with circular arcs for flank and nose profiles. The total angle of action is 1500 base circle diameter 125 2 of 3

Set No. 3

Code No: RR222105

mm and the lift 25 mm. During the lift, the period of acceleration is half that of the retardation. Speed of cam shaft is 1250 r.p.m. The straight line path of the tapper passes through the cam axis. Find (a) Radii of the nose and flank, and (b) Maximum acceleration and retardation during the lift.

[16]

7. Two gears in mesh have a module of 10 mm and pressure angle of 250 . The pinion has 20 teeth and the gear has 52 teeth. The addendum on both gears is equal to one module. Find (a) the number of pairs of teeth in contact. (b) The angles of action the pinion and the gear wheel and (c) the ratio of the sliding velocity to the rolling velocity at the pitch point and at the beginning of engagement and end of engagement. [16] 8. Figure 8 shows diagrammatically a compound epicycic gear train. Wheels A, D and E are free to rotate independently on spindle O, While B, C are compounded and rotate together on spindle P, on the end of arm OP. All the wheels have teeth of the same pitch, A has 12 teeth, B has 30 and C has 14 teeth cut externally. Find the number of teeth on wheels D and E which are cut internally. If the wheel A is driven clockwise at 1 rps, while D is driven counter clockwise at 5 rps, determine the magnitude and direction of the angular velocities of arm OP and wheel E. [16]

Figure 8 ⋆⋆⋆⋆⋆

3 of 3

Set No. 4

Code No: RR222105

II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008 KINEMATICS OF MACHINERY (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Find out the degrees of freedom of the gear system shown in the following Figure 1. (b) The distancce between two parallel shafts is 15 mm and they are connected by an Oldham’s coupling. The driving shaft revolves at 150 r.p.m.What will be the maximum speed of sliding of the tongue of the intermediate piece along its groove? (c) What are resistant bodies? Is it necessary that the resistant bodies be rigid? Give reasons for your answer. [4+8+4]

Figure 1 2. (a) What are straight line motion mechanisms? Name the different types of mechanisms used for straight line motion. (b) Sketch the Peaucellier straight line motion and prove that the tracing point ‘P’ describes a straight line path. [4+12] 3. (a) Define rubbing velocity at a in joint. What will be the rubbing velocity at pin joint when the two links move in the same and opposite directions? (b) A Petrol engine has a stroke of 36 cm and a connecting rod 90 cm. At certain instant, the crank makes an angle of 300 from the inner dead centre while 1 of 3

Set No. 4

Code No: RR222105

rotating at 240 r.p.m in clockwise direction and has an angular acceleration of 500 rad/ S2 . Determine the following: i. Velocity and acceleration of piston. ii. Angular velocity and angular acceleration of connecting rod. iii. Velocity and acceleration of the point on the connecting rod 40 cm from the centre of the big end bearing. [6+10] 4. Explain with sketches how the instantaneous centers of the following mechanisms are obtained. (a) Four bar chain (b) simple slider crank chains.

[8+8]

5. (a) Describe the working of Davis steering gear mechanism giving neat sketch. Derive the condition for correct steering of the above mechanism. (b) The Distance between the steering pivots of a Davis Steering gear is 1.3m. The wheel base is 2.75 metres. What will be the inclination of the track arms to the longitudinal axis of the vehicle if it is moving in a straight path. [8+8] 6. A cam operating a knife - edged follower has the following data: (a) Follower moves outwards through 40mm during 600 of cam rotation. (b) Follower dwells for the next 450 . (c) Follower returns of its original position during next 900 . (d) Follower dwells for the rest of the rotation. The displacement of the follower is to take place with simple harmonic motion during both the outward and return strokes. The least radius of the cam is 50mm. Draw the profile of the cam when the axis of the follower is offset 20mm towards right from the cam axis. If the cam rotates at 300 r.p.m., determine maximum velocity and acceleration of the follower during the outward stroke and the return stroke. [16] 7. (a) Explain the common materials used for gears? (b) A gear wheel having 20 teeth of involute form of module pitch 6 mm and an angle of obliquity of 200 , drives another wheel of the same dimensions. Calculate the length of the arc of contact if the addendum is one module. If the addendum was altered so that the arc of contact was the maximum possible, what would be the length of this arc and the addendum required for this? [4+12] 8. (a) What are the different types in an epicyclic gear trains. (b) A pinion A has 15 teeth and is rigidly fixed to a motor shaft. The wheel B has 20 teeth and gears with A and also with the fixed annular wheel D. The pinion C has 15 teeth and is fixed to the wheel B and gears with annular wheel E which is keyed to a machine shaft. B and C can rotate together on a pin 2 of 3

Set No. 4

Code No: RR222105

carried by an arm, which rotates about the shaft on which A is fixed. If the motor runs at 1000 rpm, find the speed of the machine. [16] ⋆⋆⋆⋆⋆

3 of 3