MIME 3300
Final Exam
Fall 2000
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Joke: Exerted from a student's comments about a professor: "The professor is very
comprehensive. Whatever he does not cover in class he includes it in the exam"
1) Consider the four bar linkage shown on the next page. The angular velocity of link 2 is
2=10 rad/sec.
a) Find the angular velocity of link 4, 4.
b) The velocity of point A at the end of link 2.
c) Find the angular velocity of link 3, 3.
1.506
4.701
B
3.861
3
4.895
link 3
link 4
A
2.560
2.000
4
2
link 2
O2
link 1
.885
6.000
Figure for problem 1
O4
2) The link shown rotates with constant angular speed =4 rad/sec2. The acceleration of
point A is horizontal, and has magnitude 1 m/sec. Calculate the acceleration of point B.
Since acceleration is a vector you must calculate both the magnitude and the orientation
angle of the acceleration or equivalently its x-component and y-component.
AB
B
r=1 m
1)
A
 = 4 rad/sec
=450
AA=1 m/sec2 (horizontal)
Figure for problem 2
2
3). a) Determine the module of a pair of gears whose center distance is 100 mm. The gears
have 20 and 40 teeth respectively.
b) What are the diametral pitch and the pitch diameter of a 40-tooth gear whose circular
pitch is 3.5 in?
c) Consider the pinion-gear set in the figure. Distances O2B and O3A are 150 mm and 450
mm, respectively. The angular velocity of rotation of the pinion is 1 rad/sec, and it is
constant with time. Find the velocity and acceleration of point A.
O2
2=1 rad/sec
B
A
O3
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4) Answer to the following questions. You do not need to explain your answers to truefalse questions (marked T-F) but you can do so if you think that a question is vague.
a) Consider a rigid straight bar one end of which is pinned. The bar rotates with constant
angular velocity  rad/sec. The velocity of the other end of the bar is equal to the length
of the bar multiplied by the angular velocity square. (T-F)
b) In a) the velocity of the tip is directed toward the center of the bar. (T-F)
c) In a) The acceleration is normal to the axis of the bar. (T-F).
d) The angular velocity of a body is a vector that is normal to the plane of rotation. (T-F)

e) The velocity of a point is: V  5  5 j . The orientation angle is 45 degrees. (T-F)
f) The larger the diametral pitch of a gear the larger the thickness of its teeth is. (T-F)
g) The fundamental law of gearing stipulates that the velocity ratio must be constant
through the mesh. (T-F)
h) If the line of action of the gears does not change as the gears rotate then the velocity
ratio is constant. (T-F)
i) A cam-follower system is usually a single-degree-of-freedom system. (T-F)
j) 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)
k) If the follower is a roller then the base circle is smaller than the prime circle. (T-F)
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