I ndian I nstitute of S pace Science and T echnology
AE223: Kinematics and Dynamics of Mechanisms
End­semester examination Weightage: 50%
Max marks: 50
Aerospace Engineering
1330­1630
01­06­2011
This examination is closed book and closed notes
Answer all questions. Answer parts A and B in separate answer sheets.
Part ­ A
A1. Using a sketch, explain “pressure angle” for a disc cam and oscillating roller follower. What is its importance? [2marks]
A2. State Grashoff's criterion and explain how you will get different types of input­output motions (like crank­crank, crank­rocker, etc) with a four­bar which satisfies Grashoff's criterion. [3 marks]
A3. Euler's equation of rotational motion is M = [I] alpha + w x ([I] w), where alpha is the angular acceleration. Explain what each term means. What is the advantage of using principal inertia axes for writing the equation? [3 marks]
A4. A cam follower mechanism with a reciprocating follower has to use a half return motion from zero velocity, as part of its displacement. If the starting acceleration is not zero and the end acceleration is zero, what standard curve can will you use, if the speed is high? What do you understand by “high speed”? [3 marks]
A5. A mass of 1 Kg is hanging by a spring of stiffness 100 N/m. Determine its frequency. Also determine the position and velocity of the mass at t=2 s, if at t=0, x=0.1 m, dx/dt=­0.1 m/s. [5 marks]
A6. Figure A­6 shows a portion of the mechanism of a back hoe. Identify joints and links and determine the degrees of freedom. Explain how you will actuate the mechanism to lower the bucket from the current position, and scoop up some soil. You can use sketches to describe the operation. Indicate which actuators are to be operated in various stages, and in which directions. Also explain how you will determine the cylinder extension required to rotate the bucket (keeping other links fixed), by a specified angle. [6 marks]
A7. The mechanism shown in figure A­7 is subjected to known forces at a known position. At this instant, it also has some known velocity. Write the relevant equations for finding the acceleration of the follower, and explain how you will find the acceleration. Assume there is no friction. [6 marks]
Figure A­6
Figure A­7
Part ­ B
B 1 a). Derive the relation connecting semi cone angle, shaft angle and gear ratio for power transmission between a pair of bevel gears? (2 Marks)
b). A pair of bevel gears has 20 teeth and 32 teeth. Determine the semi cone angles for both the gears, if the shafts intersect at right angles. (1 Marks) B 2. Sketch any one configuration of a four speed planetary gear train? (2 Marks)
B 3. a) A car driver found that one tire was not rotating properly, due to imbalance. As an engineer how will you conclude whether the tire is balanced or not? Would you choose static or dynamic balancing to make it perfectly balanced, if it is not balanced. Justify your answer.
(3 Marks)
b). A circular disc mounted on a shaft carries three attached weights of 40N, 30N and 25N at radial distances of 75mm, 85mm and 50mm and at the angular positions of 450, 1350 and 2400 respectively. The angular positions are measured counterclockwise from the reference line along the x­axis. Determine the amount of the countermass at a radial distance of 75mm required for the static balance.
(3 Marks) B 4. In a typical spur gear drive it was reported that there is a problem of interference. What are your suggestions to over come this problem? Justify your answer. (2 Marks)
B 5. The mechanism shown in Fig b.5 is a marine Steering gear called Rapson’s slide. O2P is the tiller and AC is the actuating rod. If AC is moving to the right with a constant velocity of 25units/s, find the acceleration of P. Note that the angular velocity of link 4 is 0.1667rad/s, and link3 slides along link 4 with a relative velocity of 12.5 units/s. (6 Marks)
B 6. Bevel gear 2 is driven by the engine in the reduction unit shown in fig.b.6. Bevel planet 3 mesh with crown gear 4 and are pivoted on the spider (arm) connected to the propeller shaft B. find the percent speed reduction. Given gear 4 is fixed; the number of teeth in gear 2, 3 and 4 are 36, 21 and 52 respectively.
(3 Marks)
Fig.b.5
Fig.b.6
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