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2.007 Design and Manufacturing I
Spring 2009
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2.007 –
Design and Manufacturing I
Draft Exam on Drawing, CAD, Motors, Pneumatics, and Mechanisms
You have 1.5 hours to answer the following 9 questions.
Please show your work to the extent
possible given the allotted time.
Point allocations (out of 100 total) are listed for each question.
1.
(10 points) What tension,
T
, must be applied to raise the 4 N weight at a constant rate?
pulley
10
cm
Going up!
First, I deal with the right side which is a capstan and NOT a pulley
Going down!
5N
By the capstan equation F
between
=5N*e^(
*
)=5N*e^(0.3*
/2)=3.12N
NOTE the sign in the exponent. It is nagative because the 5N weight is going down and the
frictional forces oppose the motion resulting in a lower tensile force in the rope in between the
capstan and the pulley than was applied by gravity.
Next, I deal with the left side which is a pulley and NOT a capstan
Sum of moments about the pivot SM=4N*10cmF
between
*10cmT*5cm=0
T=1.76N
4N
F
between
F
between
T
Page 2 of 8
2.
(5 points) How many degrees of freedom does this mechanism possess?
4 Bodies each with 3 DOF = 12 DOF
5 full pin joints eacg remove 2 DOF = 10 DOF
Leaving
2 DOF
of the mechanism
One of the DOF is associated with the parallelogram linkage
Comprised of the base, two links extending from the base, and
the triangular piece near the top of the lamp.
The other degree of freedom is associated with the lamp head itself which
Is free to rotate about its pivot.
Some students thought perhps some of the elements of the mechanism were
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This note was uploaded on 02/23/2012 for the course MECHANICAL 2.007 taught by Professor Fry during the Spring '11 term at MIT.
 Spring '11
 Fry

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