MIME 3300 Exam 2 Spring 2002

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1)(40 points, each question has equal weight)

a. Using an algebraic approach find the angle of the connecting rod, 3, the distance d and the distance AC, of the mechanism in the figure below. All angles are in degrees and the lengths are in meters.

b. How many instant centers does this mechanism have? Where are the centers? You may show the centers on the above sketch or on a separate sketch. If an instant center is at infinity then simply say so.

c. If the angular velocity of the crank is 2=1 rad/sec, find the velocities of points A, B and the angular velocity of the connecting rod, 3.

2) (40 points)

It takes 0.1 sec for the small cylinder to make one complete rotation around the big circle. Find:

a)(5 points) The velocity of the center of the small cylinder, C

b)(5 points) The velocity of the contact point, P

c)(10 points) The acceleration of the center of the small cylinder

d)(10 points) The acceleration of the contact point P.

e)(10 points) Generally, if the radius of the big circle is an order of magnitude larger than the radius of the small circle, say R>10r, then the acceleration of the contact point is much larger than that of the center, C. Briefly explain why. Your answer should be less than 50 words.

3) (20 points) Answer to the following questions briefly (up to 100 words). Do not justify your answers to true-false questions (Marked T-F). However, you can do so if a true-false question is vague or ambiguous in your opinion.

a)A cam-follower system is usually a single-degree-of-freedom system. (T-F)

b)Consider a cam with a uniform motion displacement diagram. The velocity of the follower is constant if the cam rotates with constant velocity. (T-F)

c)If the follower is a roller then the base circle is smaller than the prime circle. (T-F)

d)Consider a cam-follower set. If the shape of the cam is derived from a harmonic displacement profile, then the acceleration is always continuous. (T-F)

e)The ratio of the velocities of a follower and a cam is always constant as the cam rotates. (T-F)

f)A four-bar linkage has four instant centers. (T-F)

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