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ME 352  Machine Design I
Name of Student___________________________
Fall Semester 2010
Lab. Div. Number__________________________
FINAL EXAM. OPEN BOOK AND CLOSED NOTES.
Wednesday, December 15th, 2010.
Use the blank paper provided for your solutions. Write on one side of the paper only. Where
necessary, use the given figures to show vectors. Any work that cannot be followed is assumed to
be in error. Staple each problem separately and attach your crib sheet to the end of Problem 1.
Problem 1
(25 Points)
. For the mechanism in the position shown in Figure 1, the constant angular
velocity of the input link 2 is
2
3krad/s
ω=
with a torque
12
T1
.
5
k
N

m
=−
acting at bearing
2
O. The
length of link 2 is
2
OA 0
.12m
,
=
22
O G
0.045 m,
=
23
O G
0.09 m,
=
and the free length of the spring
attached between ground pin O
1
and pin A is 0.5 m. A viscous damper is attached between pin O and
link 3. There is a horizontal force
P acting at pin A, gravity is acting vertically downward, and the
effects of friction in the mechanism can be neglected. The known data (where
23
R
is the vector from
bearing O
2
to the mass center
3
G
and
3
R
is the vector from the ground pin O to the mass center
3
G
) is:
23
R
′
3
R
′
23
R
′′
3
R
2
m
3
m
2
G
I
3
G
I
K
C
m/rad
m/rad
m/rad
2
m/rad
2
kg
kg
kg.m
2
kg.m
2
N/m Ns/m
+ 0.052
+ 0.104
+ 0.150
+ 0.120
7
12
0.75
2.25
15
75
Determine: (i) the firstorder kinematic coefficients of the linear spring and the viscous damper.
(ii) the potential energy of the spring.
(iii) the equivalent mass moment of inertia of the mechanism.
(iv) the magnitude and direction of the external force P.
Figure 1. A planar mechanism.
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ME 352  Machine Design I
Name of Student
_____________________________
Fall Semester 2010
Lab
.
Div. Number
____________________________
Problem 2 (25 Points).
Part A.
A rotating shaft is simply supported by two bearings at A and B as shown in Figure 2. Gears 1,
2, and 3 are rigidly attached to the shaft at locations C, D, and E, respectively. Gear 1 at location C
weighs 165 N, gear 2 at location D weighs 255 N, gear 3 at location E weighs 90 N, and the weight of
the shaft can be neglected. If the first critical speeds of the shaft with each gear attached separately are
11
ω
190 rad/s,
=
22
ω
105 rad/s,
=
and
33
ω
280 rad/s,
=
respectively, then determine:
(i) The first critical speed of the shaft with all three gears using the Dunkerley approximation.
(ii) Numerical values for the influence coefficients
11
22
a,a,
and
33
a.
(iii) If gear 2 is now moved to location E and gear 3 is moved to location D, then determine the first
critical speed of the new system using the Dunkerley approximation.
Figure 2. A rotating shaft with three gears rigidly attached.
Part B.
The weights of three flywheels rigidly attached to a shaft rotating with a constant angular
velocity are
1
W4
5
0
N
=
,
2
W
325 N,
=
and
3
W7
6
0
N
.
=
The nine influence coefficients of the shaft are:
6
11
a2
.
2
5
x
1
0
m
/
N
−
=
,
6
22
a1
.
6
2
5
x
1
0
m
/
N
−
=
,
6
33
.
5
x
1
0
m
/
N
−
=
,
6
12
21
a
a
0.95 x 10
m/N
−
==
,
6
13
31
aa0
.
6
5
x
1
0
m
/
N
−
, and
6
23
32
.
8
5
x
1
0
m
/
N
−
. Determine:
(i) The deflections of the shaft at each flywheel.
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 Fall '08
 Staff
 Angular Momentum, Force, Machine Design, Moment Of Inertia, pistons

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