Kinematics of Machines - Dec 2013
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 degrees of freedom. Find the degrees of freedom for the following mechanism as shown in fig Q1(a)
img(10 marks) 1 (b) Define the following terms with examples: i) Kinematics pair ii) Mechanism iii) Structure iv) Inversions(10 marks) 2 (a) Describe with neat sketch two inversion of double slider-crank chain mechanism.(10 marks) 2 (b) Derive an expression for necessary condition of correct steering and explain Ackermann steering gear with neat sketch.(10 marks) 3 (a) A four bar mechanism shown in fig Q3 crank BC rotates with an angular velocity of 100 rad/sec and an angular acceleration of 4400 rad/sec2 at the instant when the crank makes an angle 53° to the horizontal. Draw the acceleration polygon and determine the liner acceleration of points E and the angular acceleration of link 3.
img(20 marks) 4 (a) Write a note on Kennedy's theorem.(5 marks) 4 (b) List the properties of instantaneous center of rotation.(5 marks) 4 (c) In a slider crank mechanism shown in fig Q4(c) the crank OA=300 mm and connecting rod AB=1200mm the crank. If the crank rotates at 15 rad/sec clockwise, find i) velocity of slider B and ii) Angular velocity of connecting rod AB
img(10 marks) 5 (a) Derive an expression for displacement analysis of a 4 bar mechanism using complex algebra method.(10 marks) 5 (b) For a single slider mechanism of fig Q5(b) determine the velocity and acceleration of piston, angular acceleration of connecting rod. Take crank length=50mm, connecting rod=200mm crank speed=300 RPM(Constant). Crank angle 30°.
img(10 marks) 6 (a) Derive an equation to determine length of are of contact for mating of 2 spur gear.(8 marks) 6 (b) Two gear wheel mesh externally and are to give a velocity ratio of 3. the teeth are of involute form of module 6mm and standard addendum one module. Pressure angle=18°. Pinion rotates at 90 RPM. Find
i) Number of teeth on each wheel so that interference is just avoided.
ii)Length of path of contact
iii) Maximum velocity of sliding between teeth.
iv) Number of pairs of teeth in contact.(12 marks) 7 (a) Explain with neat sketch classification of gear trains.(6 marks) 7 (b) In a epicyclic gear train, the internal wheels A,B and the compound wheel C and D rotate independently about the axis '0'. the wheel E and F rotate on a pin fixed to the arm G. E gear with A and C, and F gears with B and D, and D. All the wheels have same pitch and the number of teeth on. E and F are 18, C and D are 28,26 respectively.
i)Sketch the arrangement
ii) Number of teeth on A and B
iii) If arm (G) makes 200RPM clockwise and gear A is fixed, find speed of gear B.
iv) If arm (G) makes 100rpm clockwise and gear A makes 50rpm CCW, find the speed of gear B.(14 marks) 8 A cam rotating at uniform Speed of 300rpm operates a reciprocating follower through a roller 1.5 cm diameter. The follower motion defined as below:
i) Outward during 150°.with UARM.
ii)Dwell for next 30°
iii) Return during next 120° with SHM.
iv) Remaining dwell period.
Stroke of the follower is 3 cm. Minimum radius of cam is 3 cm. Draw the cam profile when the follower axis is offset to the left by 1 cm and determine maximum velocity and maximum acceleration during outstroke.(20 marks)