Kinematics Of Machinery May2006 Rr222105

Set No. 1

Code No: RR222105

II B.Tech II Semester Regular Examinations, Apr/May 2006 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.

Figure 1: [4+8+4] 2. Describe any mathematically true straight-line motion mechanism with necessary equation. [16] 3. For the stream engine mechanism shown in Figure 2 determine the sliding acceleration of slides F and the angular acceleration of link, CE, for a crank speed of 143rpm for the given configuration. Dimensions of various links are OA = 30cm, AB = 120cm, BC = 45cm, CE = 120cm and EF = 120cm. [16] 1 of 3

Set No. 1

Code No: RR222105

Figure 2: 4. In a Whitworth quick return motion, a crank AB rotates about the fixed center A. The end B operates a slider reciprocating in a slotted link, rotating about a fixed center D, 5 cm vertically above A. The crank AB which is 10 cm long, rotates in a clockwise direction at speed of 100 rpm. Find the angular acceleration of a slotted link for the configuration in which AB has turned through an angle of 45 degrees past its lowest position. [16] 5. Design a pantograph for an indicator to obtain the indicator diagram of an engine. The distance from the tracing point of the indicator is 120 mm. The indicator diagram should represent five times the gas pressure inside the cylinder of an engine. [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. 7. (a) Define the following terms: i. Pitch circle diameter ii. Circular pitch iii. Diametral pitch 2 of 3

[16]

Set No. 1

Code No: RR222105 iv. Module v. Pressure angle vi. Pressure line

(b) A pair of gears have 16 and 22 teeth, module pitch is 12.5 mm, addendum 12.5 mm, dedendum 14.25 mm and pressure 200 . The pinion drives in anti-clock wise direction. Determine i. ii. iii. iv.

Pitch circle radii Base circle radii the circular pitch Angle of approach and recess

[6+10]

8. In an epicyclic gear of the sun and planet type the pitch circle diameter of the internally toothed ring is 200mm and the module, 5mm. When the ring is stationary the spider, which carries three planet wheels of equal size, is to make one revolution for every five of the driving spindle carrying the sun wheel. Determine suitable numbers of teeth for all the wheels.Shows that if the planet wheels are at equal angular intervals it is a condition for assembly that the sum of the number of teeth in the sun wheel and annulus must be divisible by three. (Figure 3) [16]

Figure 3:

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Set No. 2

Code No: RR222105

II B.Tech II Semester Regular Examinations, Apr/May 2006 KINEMATICS OF MACHINERY (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. What is a quadric cycle chain? Explain all the inversions of it and applications. [16] 2. A grass hopper straight line mechanisms gets its motion from a crank OA. The end A of the crank in joined to a long rod PQ such that Q A is 6cm. The end Q is further joined to along vertical link O1 Q, 24 Cm long moving with centre O1 . The length of rod PQ is also 24 Cm and its end P describes an approximate vertical straight line. Determine the radius of crank OA. Find also 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. An inversion of a slide crank mechanism shown in Figure 1. 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 The main dimensions of the linkage are: O2 Q = 6cm and O4 P = 30cm.

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[16]

Set No. 2

Code No: RR222105

Figure 1: 4. Prove Klein’s construction for determining acceleration of a slider in a slider crank mechanism. Hence show that acceleration of the position of an engine at inner and outer dead  positions is given  by   center fp = ω 2 r 1 + n1 and fp = ω 2 r 1 − n1 respectively Where fp = acceleration of piston ω = angular velocity of crank r = crank radius L = length of connecting rod, and n = Lr [16] 5. (a) Sketch a pantograph, explain its working and show that it can be used to reproduce to an enlarged scale a given figure. (b) The angle between the axes of two shafts joined by Hooke’s joint is 250 . The driving shaft rotates at a uniform speed of 180 r.p.m, The driven shaft carries a study load of 7.5 k.w. Calculate the mass of the fly wheel of the driven shaft if its radius of gyration is 150 mm and the out put torque of the driven shaft does not vary by more than 15% of the input shaft. [6+10] 6. The following data relate to a cam operating an oscillating roller follower minimum diameter of the cam 44 m.m. Diameter of the Roller 10 m.m. Length of the follower arm 40 m.m. Distance of fulcrum centre from cam centre 50 m.m. Angle of Ascent : 750 Angle of Descent : 1050 Angle of dwell for the follower in the highest position 600 . Angle of oscillation of follower 280 Draw the profile of the cam if the ascent and descent take place with 5 H.M. [16] 2 of 3

Set No. 2

Code No: RR222105

7. (a) Derive an expression for the velocity of sliding between a pair of involute teeth. (b) A pinion with 20 teeth is in mesh with a gear of 60 teeth. The pressure angle is 200 and addendum is 7 mm. Determine i. the number of pairs of teeth in contact and the angle turned by the pinion and the gear wheel when one pair of teeth is in contact. ii. Sliding velocity at the beginning of engagement, at the pitch point and at the termination of the engagement. [8+8] 8. (a) Explain the difference between a compound gear train and an epicyclic gear train. (b) In an epicyclic gear train, as shown in Figure 2, the number of teeth on wheels A,B and C are 48, 24 and 50 respectively. If the arm rotates at 400 r.p.m., clockwise, find: i. Speed of wheel C when A is fixed and ii. Speed of wheel a when C is fixed.

Figure 2:

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[4+12]

Set No. 3

Code No: RR222105

II B.Tech II Semester Regular Examinations, Apr/May 2006 KINEMATICS OF MACHINERY (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) State the difference between the closed and unclosed pairs giving examples in each case. (b) What is a Kinematic chain? How is it formed from the links?

[10+6]

2. Describe any approximate straight-line motion mechanism with necessary equations. [16] 3. In a quick return mechanism, as shown is Figure 1, the driving crank OA is 60 mm long and rotates at a uniform speed of 200r.p.m in clockwise direction. For the positions shown, find (a) velocity of the ram R (b) acceleration of the ram R; and (c) acceleration of the sliding block A along with the slotted bar CD.

1 of 3

[16]

Set No. 3

Code No: RR222105

Figure 1: 4. Prove Klein’s construction for determining acceleration of a slider in a slider crank mechanism. Hence show that acceleration of the position of an engine at inner and outer dead  positions is given  by1   center 1 2 2 fp = ω r 1 + n and fp = ω r 1 − n respectively Where fp = acceleration of piston ω = angular velocity of crank r = crank radius L = length of connecting rod, and n = Lr [16] 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. Draw the profile of a cam operating a knife edged follower from the following data. (a) It lifts the follower through 3.75 cm during its 600 rotation with S.H.M. (b) The follower remains at rest for next 400 rotation of the cam. (c) The follower then descents to its original position during 900 rotation of the cam with S.H.M. 2 of 3

Set No. 3

Code No: RR222105

(d) The follower remains at rest for the rest of the revolution. The least radius of the cam is 5 cm. If the cam rotates at 300 RPM. Find the maximum velocity and acceleration of the follower during ascent and descent. The axis of the follower passes through the axis of the cam shaft. [16] 7. Two mating involute spur gears of 200 pressure angle have a gear ratio of 2. The number of teeth on the pinion is 20 and its speed is 250 rpm. The module 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 (a) the addendum for pinion and gear wheel (b) the length of arc of contact (c) the maximum velocity of sliding during approach and recess. Assume pinion to be driver.

[16]

8. An epicyclic gear consists of bevel wheels as shown in Figure 2. The driving pinion A has 20 teeth and meshes with the wheel B which has 25 teeth. The wheels B and C are fixed together and turn freely on the Shaft F. The shaft F can rotate freely about the main axis XX. The wheel C has 50 teeth and meshes with wheels D and E, each of which has 60 teeth. Find the speed and direction of E when A rotates at 200 r.p.m. if 1. D is fixed and 2. D rotates at 100 r.p.m. in the same direction as A.In both the cases, find the ratio of the torques transmitted by the shafts of the wheels A and E, the friction being neglected. [16]

Figure 2:

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Set No. 4

Code No: RR222105

II B.Tech II Semester Regular Examinations, Apr/May 2006 KINEMATICS OF MACHINERY (Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Sketch an Oldham’s coupling and describe its operation. Prove that the velocity ratio transmitted by the coupling is unity at any instant either by considering the original Kinematic chain from which it is derived or any other inversion of the original Kinematic chain. (b) Describe elliptical trammels. How does it enable you to describe a true ellipse? [8+8] 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. A quick return mechanism is shown in Figure 1 below. Link 2 rotates uniformly at 20rad/sec. Draw the acceleration polygon. Find the absolute acceleration of point B. [16]

Figure 1: 4. Prove Klein’s construction for determining acceleration of a slider in a slider crank mechanism. Hence show that acceleration of the position of an engine at inner and 1 of 2

Set No. 4

Code No: RR222105 outer dead  positions is given  by1   center 1 2 2 fp = ω r 1 + n and fp = ω r 1 − n respectively Where fp = acceleration of piston ω = angular velocity of crank r = crank radius L = length of connecting rod, and n = Lr

[16]

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. Draw full size profile of a cam which will lift a 2.5 cm diameter knife edged follower through 4 cm. The centre line of the follower passes through the centre of rotation of the cam. Ascent of follower takes place with S.H.M. in 0.1 second, followed by a period of rest of 0.025 sec. The follower then descends with uniform acceleration and retardation in 0.075 second. The cam rotates at a uniform speed of 120 r.p.m. and the least radius of the cam is 10 cm. Also plot velocity and acceleration diagrams of the follower during one revolution of the cam and mark important values thereon. [16] 7. (a) Derive the formula for the length of the path of contact for two meshing spur gear having involute profile. (b) Find graphically, the length of the path of contact when pinion with 18 teeth meshes with an internally toothed wheel with 72 teeth, when the pressure angle is 200 , module pitch is 4 mm and the addenda of pinion and wheel are 8.7 mm and 3.7 mm respectively. [8+8] 8. (a) Explain the difference between, simple, compound and Epicyclic gear trans trains. (b) A compound train consists of six gears The number of teeth on the gears are as follows: 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 the gears D and E are on anopther shaft. The gear A drives gear B, gear C drives gear D and gear E drives gear F. If the gear A transmits 1.5 kW at 100 r.p.m and the gear train has an efficiency of 80 per cent, find the torque on gear F. [6+10] ⋆⋆⋆⋆⋆

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