1. (a) Discuss various types of Kinematic links with examples. (b) Explain different types of constrained motions with examples.

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1 Code No: RR Set No. 1 III B.Tech I Semester Supplementary Examinations, February 2007 KINEMATICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics and Production Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Discuss various types of Kinematic links with examples. (b) Explain different types of constrained motions with examples. [8+8] 2. Explain the Scot-Russel mechanism and show that it generates straight-line motion. [16] 3. In the mechanism, as shown in Figure 1, the crank OA rotates at 20 r.p.m anticlockwise and gives motion to the sliding blocks B and D. The dimensions of the various links are OA = 300 mm; AB = 1200 mm; BC = 450 mm; and CD = 450 mm. For the given configuration, determine: (a) Velocities of sliding at B and D (b) Angular velocity of CD (c) Linear acceleration of D and (d) Angular acceleration of CD. [16] 1 of 3

2 Code No: RR Set No. 1 Figure 1: 4. An engine mechanism ABC has a crank AB of length 4 cm rotating about A. The connecting rod BC is 12 cm long and the piston C has a mass of 100 gm. C moves along the line AC. Draw the velocity diagram and the acceleration diagram for a uniform crank speed of 150 rad/sec in clockwise direction when the angle BAC is What is torque required at the crank to accelerate the piston C at this position? [16] 5. Two shaft P & Q connected together by Hooke s joint have their axes inclined at The shaft P revolves at uniform speed of 1500 r.p.m and the shaft Q carries a fly wheel of weight 150 N, radius of gyration 100 mm. Find the maximum torque in shaft Q, if it is assumed that the shafts are torsionally rigid. [16] 6. A cam operating a knife - edged follower has the following data: (a) Follower moves outwards through 40mm during 60 0 of cam rotation. (b) Follower dwells for the next (c) Follower returns of its original position during next (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 atleast eight properties of involute toothed gear in mesh. 2 of 3

3 Code No: RR Set No. 1 (b) If the angle of obliquity of a pair of gear wheels is 20 0, and the arc of approach or recess not less than the pitch, what will be the least number of teeth on the pinion. [6+10] 8. An epicyclic bevel gear train, as shown in Figure 2 has fixed gear B meshing with pinion C. The gear E on the driven shaft meshes with the pinion D. The pinions C and D are keyed to a shaft, which revolves in bearings on the arm A. The arm A is keyed to the driving shaft. The number of teeth are: TB = 75, Tc = 20, TD = 18 and TE = 70. Find the speed of the driven shaft, if 1. The driving shaft make 1000 r.p.m. and 2. The gear B turns in the same sense as the driving shaft at 400 r.p.m. the driving shaft still making 1000 r.p.m. [16] Figure 2: 3 of 3

4 Code No: RR Set No. 2 III B.Tech I Semester Supplementary Examinations, February 2007 KINEMATICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics and Production Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Sketch slider crank chain and its various inversions, stating actual machines in which these are used in practice. [16] 2. Explain the following mechanisms: (a) Grasshopper mechanism (b) Tchebicheff s mechanism (c) Robert s mechanism. [5+6+5] 3. In the slider crank mechanism shown in Figure 1 block P reciprocates along the fixed line AB and the crank has a uniform speed of 230rpm. Determine for the given configuration, the velocity and acceleration of the block P and the point D. [16] Figure 1: 4. In the Atkinson engine mechanism shown in Figure 2 the velocity and acceleration of the slider at D are given as 40 cm/ sec and 450 cm/sec 2. Determine ω 2,α 2, ω 3,and α 3. Take O 2 A = 4.5 cm, AB = 12 cm, O 4 B= 6 cm, BC = 2cm AC = 13 cm, CD = 14 cm. [16] 1 of 3

5 Code No: RR Set No. 2 Figure 2: 5. The angle between the axes of two horizontal shafts to be connected by Hook s joint is The speed of driving shaft is 150rpm. The driven shaft carries a flywheel weighing 10 Kg and having a radius of gyration of 10 Cm. If the forked end of the driving shaft rotates 30 0 from horizontal plane, find the torque required to drive the shaft to overcome the inertia of the flywheel. [16] 6. A radial translating flat - face follower has a lift of 3 cm. The rise takes place with SHM for of cam rotation, followed by dwell of 30 0 and simple harmonic return for followed by another dwell. The base circle radius of the cam is 3 cm. Obtain the cam profile and the minimum length of the follower face with a clearance of 0.3 cm at both the ends. Assume anticlockwise rotation of the cam. What are the maximum velocity and accelerations values during the follower rise when cam rotates at 50 r.p.m. [16] 7. (a) Name the curves, which satisfy the condition for, correct gearing and compare them giving atleast six points. (b) A gear wheel having 20 teeth of involute form of module pitch 6 mm with an angle of obliquity of 20 0, drives another wheel of the same dimensions. Calculate i. the length of the arc of contact if the addendum is one module. ii. 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 condition. [8+8] 2 of 3

6 Code No: RR Set No In the epicyclic train shown in Figure 3 the shaft A transmits 7.5kW to the shaft B. If the shaft A rotates at 700 r.p.m., find the torque transmitted by the pinions E and H respectively. The wheels G and H have 30 teeth; D and E have 52 teeth each. Wheel F is fixed. [16] Figure 3: 3 of 3

7 Code No: RR Set No. 3 III B.Tech I Semester Supplementary Examinations, February 2007 KINEMATICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics and Production Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Explain giving examples the following terms: i. Kinematic link ii. Kinematic pair iii. Kinematic chain iv. Mechanism v. Machine vi. Inversion (b) Define and classify lower pairs and higher pairs with examples. [9+7] 2. (a) What is the purpose of a Pantograph? Explain it s working with a sketch. (b) Provide the mathematical proof for working of pantograph. [8+8] 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. [16] 1 of 3

8 Code No: RR Set No. 3 Figure 1: 4. The crank OA drives the rod AB as shown in Figure 2. A lever CD is pin-jointed to the rod at C and to a block D which moves in the fixed guides; there is a similar arrangement for the rod EF. The speed of block F is 0.72 m/sec for the configuration shown in the figure. Find the speed of crank OA in rpm. In figure the dimensions are given as hereunder OA = 18cm, AB = 72cm, AC = 40cm, CD = 36 cm, CE = 24 cm, EF = 30 cm. [16] 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 flat ended valve tappet is operated by a symmetrical cam with circular arcs for flank and nose profiles. The total angle of action is 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) Define the following: Involute, Cycloid, Epicycloid and Hypocycloid. 2 of 3

9 Code No: RR Set No. 3 Figure 2: (b) Two mating involute spur gears with module pitch of 8 mm have 23 and 57 teeth of 20 0 pressure angle. The addenda on pinion and gear are equal to one module. Find: i. number of pairs of teeth in contact, ii. angle turned through by pinion and gear wheels, and iii. ratio of sliding velocity to rolling velocity at the beginning of the contact, at the pitch point and at the end of contact. [6+10] 8. An epicyclic gear train, as shown in Figure 3 is composed of a fixed annular wheel A having 150 teeth. The wheel A is meshing with wheel B which drives wheel D through an idle wheel C,D being concentric with A. The wheels B and C are carried on an arm which revolves clockwise at 100 rp.m. about the axis of A and D. If the wheels B and D have 25 teeth and 40 teeth respectively, find the number of teeth and C and the speed and sense of rotation of C. [16] Figure 3: 3 of 3

10 Code No: RR Set No. 4 III B.Tech I Semester Supplementary Examinations, February 2007 KINEMATICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics and Production Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Show that the locus of the mid-point of the link connecting to the two slides in an elliptical trammel is a circle. (b) Define frame of a machine? Which link of the machine is known as frame? [10+6] 2. Two points P and Q, 4 cm apart are to be connected by a pantograph. The motion of P to the motion of P Q is 13 : 7. Fine the distance of Q from the fixed point O of the pantograph such that the point P moves at least 12.7 cm in either direction of live O Q P when it is horizontal. Find also the main dimensions of the pantograph. [16] 3. Explain how the velocity and acceleration in the following mechanisms are calculated by relative velocity method: (a) Four bar chain (b) Single slider crank chain. [8+8] 4. (a) Define the term instantaneous centre of rotation. (b) Sketch a quick return motion of the crank and slotted lever type and explain the procedure of drawing the velocity and acceleration diagram, for any given configuration of the mechanism by instantaneous centre method. [4+12] 5. (a) Derive an expression for the ratio of the shaft velocities for Hooke s joint and draw the polar diagram depicting the salient features of driven shaft speed. (b) Two shafts with an included angle of connected by a Hooke s Joint. The driving shaft runs at a uniform speed of 1500 R.P.M. The driven shaft carries a fly wheel of mass 12kg and 100 m.m radius of gyration. Find the maximum angular acceleration of the driven shaft and the maximum torque required. [10+6] 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 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 1 of 2

11 Code No: RR Set No. 4 (b) Maximum acceleration and retardation during the lift. [16] 7. (a) State and prove the law of gearing for constant velocity ratio and show how the involute profile satisfies the condition? (b) A pair of spur wheels with involute teeth is to give a gear ratio 3:1. The arc of approach is not being less than the circular pitch and the smaller wheel is the driver. Pressure angle is What is the least number of teeth that can be used on each wheel and find the addendum of the wheel in terms of the circular pitch? [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 1, 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. [4+12] Figure 1: 2 of 2

St.MARTIN S ENGINEERING COLLEGE Dhulapally, Secunderabad

St.MARTIN S ENGINEERING COLLEGE Dhulapally, Secunderabad-500 014 Subject: Kinematics of Machines Class : MECH-II Group A (Short Answer Questions) UNIT-I 1 Define link, kinematic pair. 2 Define mechanism