GTU Mechanical Engineering (Semester 3)
Kinematics of Machines
December 2014
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


1 (a) Define and discuss: kinematic link, kinematic pair, and kinematic chain.
7 M
1 (b) Sketch and explain Whitworth quick return mechanism.
7 M

2 (a) Describe Klein's construction with an example.
7 M
Answer any one question from Q2 (b) & Q2 (c)
2 (b) The crank of a slider crank mechanism rotates clockwise at a constant speed of 300 rpm. The crank is 150 mm and connecting rod is 600 mm long. Determine 1. Linear velocity and acceleration of midpoint of connecting rod 2. Angular velocity and angular acceleration of the connecting rod, at a crank angle of 45° from inner dead centre position.
7 M
2 (c) A crank and rocker mechanism ABCD has the following dimensions. AB = 0.75m, BC = 1.25m, CD = 1m, AD = 1.5m, E is the midpoint of the coupler link BC. AD is the fixed link. Crank AB has a angular velocity of 20 rad/s counter clockwise and deceleration of 280 rad/s 2 at the instant angle DAB = 60° find 1. Instantaneous linear velocity and acceleration of midpoint E of link BC. 2. Instantaneous angular velocity and acceleration of link CD.
7 M

Answer any two question from Q3 (a), (b) & Q3 (c), (d)
3 (a) Explain the Freudenstein's Equation for four bar chain mechanism.
7 M
3 (b) Design a four bar mechanism with input link 'a', coupler link 'b' and output link 'c'. angles θ and ϕ for three successive position are given in table below:
Using Freudenstein's Equation find out other link lengths b, c and d. assume link length a = 1.
1 2 3
θ 20° 35° 50°
? 35° 45° 60°
7 M
3 (c) Explain two position synthesis of four bar chain mechanism by relative pole method.
7 M
3 (d) A double Hooke's joint is used to connect 2 shafts in the same plane and the Intermediate shaft is inclined at an angle of 20° to both the shafts. If driving shaft Rotates of 250 rpm, find maximum and minimum speed of intermediate and driven shafts.
7 M

Answer any two question from Q4 (a), (b) & Q4 (c), (b)
4 (a) Enlist different type of gear train .Explain compound gear train with neat sketch .Also derive the equation of the velocity ratio for compound gear train.
7 M
4 (b) An Epicyclic gear train is composed of fixed annular wheel "A" having 300 teeth. Meshing with A is wheel X which drives wheel Z through idle wheel Y, wheel Z being concentric with A. wheels X and Y are carried on an arm E which revolves clockwise at 120 rpm about the axis of A and Z. if the wheel X and Z have 50 and 80 teeth respectively .Determine the number of teeth on Y. and rpm of Y.
7 M
4 (c) Derive an expression for the length of path of contact for two involutes profile gear in mesh.
7 M
4 (d) A pair 20° involute gears has module of 5 mm. the pinion has 20 teeth and gear has 60 teeth. Addendum on the pinion and gear wheel in terms of module is 1.
Find the followings.
(i) Number of pairs in contact
(ii) Angle turned through by the pinion and gear wheel for one pair in contact.
7 M

Answer any two question from Q5(a), (b) & Q5 (c), (d)
5 (a) Classify followers and explain with neat sketch.
7 M
5 (b) Draw the cam operating knife edge follower from following data
(i) Follower to move out through distance of 20mm during 120°.
(ii) Follower to dwell for next 60°.
(iii) Follower to return to its initial position during 90°.
(iv) Follower to dwell for remaining cam rotation
The cam rotates at 500rpm .The minimum radius of cam is 40mm and line of follower is offset 15mm from the axis of the cam and displacement to take place with uniform acceleration and retardation both inward and outward stroke.
7 M
5 (c) Derive the condition for correct steering. Sketch and show the Davis steering.
7 M
5 (d) What is straight line motion mechanism & give its classification. Explain any one in brief.
7 M



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