Kinematics of Machines - Jun 2014

Mechanical Engg. (Semester 4)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1 (a) Define the following : i) Kinematics chain ii) Mechanism iii) Structure iv) Inversions v) Degrees of freedom.(10 marks) 1 (b) Sketch and explain the working of an elliptical trammel. Prove that it traces an ellipse.(10 marks) 2 (a) Explain with a neat sketch, crank and slotted lever quick return motion mechanism.(8 marks) 2 (b) Explain with a neat sketch, pantograph mechanism. State its applications.(6 marks) 2 (c) Explain with a neat sketch. Geneva mechanism.(6 marks) 3 A single slider crank mechanism shown in fig Q3 has the crank CB=100mm and connecting rod BA=300mm, with center of gravity G 100mm from B. The crank shaft has a speed of 75 rad/sec an angular acceleration of 1200 rad/sec². Find
a. The velocity of 'G' and the angular velocity of 'AB'.
b. The acceleration of 'G' and the angular acceleration of AB.
img(20 marks) 4 (a) State and prove Kennedy's theorem.(6 marks) 4 (b) Explain the analysis of velocity and acceleration of a piston in a single slider mechanism using Klein's construction.(6 marks) 4 (c) For a pin-joined four bar mechanism having the following dimension. Fixed link AD=4m, 60°, Link AB rotates at 25rpm. Determine using instantaneous center method. i) Angular velocity of link CD and ii) Angular velocity of link BC.(8 marks) 5 (a) The crank of an engine is 20cm long and the connecting rod length to crank radius is 4. determine the acceleration of the piston when the crank has turned through 45⁰ from the inner dead center position and moving towards the other center at240 RPM, counter clock wise direction using complex algebra analysis.(16 marks) 5 (b) Explain in brief Loop closure equation.(4 marks) 6 (a) Derive an equation to determine the length of path of contact by a pair of meeting spur gear.(8 marks) 6 (b) Two 20° involute spur gears have module of 10mm and addendum of one module. The number of teeth on pinion is 13 and on the spur gear is 52. docs interface occur? If it occurs to what values should the pressure angle be changed to eliminate the interface?(12 marks) 7 (a) Explain with a neat sketch the sun and planet wheel.(4 marks) 7 (b) In an epicyclic gear train an arm carries two gear. A & B having 36 & 45 teeth respectively. If the arm rotates at 15RPM in the anti clock wise direction about the center of gear. 'A' which is fixed , determine the speed of the gear B. If the gear A instead. Of being fixed makes 300RPM the clock wise direction what will be the speed of gear 'B'
img(16 marks) 8 Construct the profile of a cam to suit the following specification:
cam shaft diameter=40mm.
Least radius of cam=25mm
Diameter of roller=25mm
Angle of lift=120°
Lift of the follower-40mm
No. Of pauses are two of equal interval between motion. During the lift the motion is SHM. During the fall motion is UARM. The speed of cam shaft is uniform. The line of stroke is center of the cam.(20 marks)