# Kinematics of Machinery 3rd AM10 ME2203

B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010
Third Semester
Mechanical Engineering
ME2203 - KINEMATICS OF MACHINERY
(Regulation 2008)

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PART A — (10 × 2 = 20 Marks)

1. Define Degree of Freedom and give the DOF for a cam with roller follower.
2. List out the applications of Straight line motion mechanisms.
3. A slider sliding at 100 mm/sec on a link, which is rotating at 60 rpm is subjected to Coriolis acceleration. Find its magnitude.
4. Define rubbing velocity.
5. Name any two types of cams with specified contours. -
6. What are the different types of motion with which a follower can move?
7. What is axial pitch of a helical gear?
8. What is the role of “Idlers” in gear trains?
9. Define virtual coefficient of friction.
10. State the condition for maximum power transmission in a belt drive and deduce the expression for corresponding belt velocity.

PART B — (5 × 16 = 80 Marks)

11. (a) Perform the kinematic analysis of the following Exact Straight Line motion mechanisms. (2 × 8 = 16)
(i) Peaucellier Mechanism.
(ii) Hart’s Mechanism.
Or
(b) (i) Sketch and explain any three inversions of a double slider crank chain. (9)
(ii) Illustrate a crank and slotted lever mechanism as an inversion of single slider crank chain. Deduce an expression for length of stroke in terms of link lengths. (7)

12. (a) The mechanism of a warping machine is shown in the figure given below. Various dimensions are as follows. O A 100mm; AC 700mm; 1 = = BC = 200mm ;BD 150mm; O D 200mm; O E 400mm; 2 2 = = = O C 200mm 3 = .
The crank O A 1 rotates at a uniform speed of 100 rad/sec. Determine the
(i) Linear velocity of the point E on the bell crank lever
(ii) Angular velocity of link AC and BD.
Or
(b) Derive the expression for determining the angular position of the coupler link and the output link of a four bar mechanism.

13. (a) It is required to set out the profile of a cam to give the following motion to the reciprocating follower with a flat mushroom contact face:
(i) Follower to have a stroke of 20 mm during 120° of cam rotation
(ii) Follower to dwell for 30° of cam rotation
(iii) Follower to return to its position during 120° of cam rotation
(iv) Follower to dwell for the remaining period.
The minimum radius of the cam is 25 mm. The outstroke of the follower is performed with simple harmonic motion and the return stroke with equal uniform acceleration and retardation.
Or
(b) Construct a tangent cam and mention the important terminologies on it.
Also derive the expression for displacement, velocity and acceleration of a reciprocating roller follower when the roller has contact with the nose.

14. (a) (i) State and prove “Law of gearing”, and thus derive the expression for “Velocity of sliding”. (10)
(ii) Prove that the maximum length of arc of contact between a pair of gear tooth to avoid interference is (r + R)tanf . (6)
Or
(b) (i) Diagrammatically show the following with reference to a spur gear tooth:
Face width, Pitch circle, Clearance, Tooth thickness, Addendum and Dedendum. (6 × 1 = 6)
(ii) An epicyclic gear train is shown in the following figure. How many revolutions does the arm makes when (1) A makes one revolution in clockwise and D makes 1/2 a revolution in the opposite sense and
(2) A makes one revolution in clockwise and D remains stationary?
The number of teeth in gears A and D are 40 and 90 respectively.(10)

15. (a) (i) Prove that the torque transmitted by a cone clutch, when the intensity of pressure is uniform is given by, with usual notations. (8)

(ii) An effort of 200 N is required to just move a certain body up an
inclined plane of an angle 15°, the force is acting parallel to the
plane. If the angle of inclination of the plane is made 20°, the effort
required parallel to the plane is found to be 230 N. Determine the
weight of the body and the coefficient of friction. (8)
Or
(b) A compressor requires 90 kW to operate at 250 rpm. The drive is by V
belts from an electric motor running at 750 rpm. The diameter of the
pulley on the compressor shaft must not be greater than 1 meter while
the center distance between the pulleys is limited to 1.75 m. The belt
speed should not exceed 1600 m/min. Determine the number of V belts
required to transmit the power if each belt has a cross sectional area of
375 mm2; density 1000 kg/m3 and an allowable tensile stress of 2.5 MPa.
The groove angle of the pulley is 35°. The coefficient of friction between
the belt and the pulley is 0.25. Also calculate the length of each belt.