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MAE162A: Introduction to Mechanisms and Mechanical Systems
Exam #2 (May the Force Be With You!)
1) BB-8 is helping Rey scavenge junk on Jakku. He has found General Grievous’s
deceased body and wheel bike, link 4, and wants to tow them back to Rey. BB-8’s
body, labeled link 2, is a perfect circle with a radius of r2. At the instant shown in
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Fig. 1, BB-8 is at the top of the circular rigid mound of sand with a radius of R
rolling with a constant angular velocity of ω2=1 rad/s. Although it doesn’t appear
so in the figure, General Grievous’ wheel bike is also a perfect circle with a radius
of r4. BB-8 tows the wheel bike with a rigid link, link 3, that is attached to the
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center of his body at one end with a revolute joint and at the center of the wheel
bike on its other end with another revolute joint. The distance between these
revolute joints is L. Both the wheel bike and BB-8’s body roll with no slip on the
rigid sand floor of Jakku. The dimensions are as follows: R= 1m, r2= 0.5m ,r4=1m ,
L =2m. (35 points)
Figure 1: BB8 towing General Grievous
(a) At the instant shown, what is the angular velocity of General Grevious’ wheel
bike, ω4? (20 points)
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(b) At the instant shown, what is the angular acceleration of General Grevious’
wheel bike, α4? (15 points)
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2) The Deathstar guides and aims it’s energy beam with a flexure system shown in
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Fig. 2. The stage is connected to the ground by five wire flexures as shown in the
figure. (15 points)
Figure 2: The Deathstar’s flexure system
(a) Using the FACT chart, identify the system’s correct freedom and constraint
spaces (i.e. X DOF Type Y) and draw the freedom space on top of Fig. 2 such that it is
correctly oriented with respect to the wire flexures. (11 points)
(b) Is the design exactly-constrained or over-constrained? Why? (2 points)
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(c) Is the design under-constrained or not? Why? (2 points)
3) The Millennium Falcon, link 2, is flying through space, link 1, with a velocity of
v2/1=500m/s and an acceleration of a2/1=30m/s2 as shown in Fig. 3. It fires its
blaster turret, link 3, as it rotates counter clockwise with a constant angular
velocity of ω3/2=10rad/s. The resulting particle of energy, link 4, makes it a
distance of d=2m down the barrel of the blaser with a constant apparent velocity
of vP4/3=2000m/s. (20 points)
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Figure 3: Millenium Falcon shooting a blaster particle
(a) At the instant shown, what is the absolute velocity of the blaster particle of
energy at point P with respect to the coordinate system, link 1? (8 points)
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(b) At the same, what is the absolute acceleration of the blaster particle of energy at
point P with respect to the coordinate system, link 1? (12 points)
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4) In Obi-wan’s lightsaber duel with Darth Vader, the interlocking lightsabers can be
modeled as two rigid links joined together with a pin-in-slot joint, as shown in Fig.
4. The pin is on Obi-wan’s lightsaber, link 2, positioned a distance of d=0.6m from
the center of mass of the lightsaber’s hilt (i.e., the revolute joint shown located at
Obi-wan’s wrist) and the slot is on Darth Vader’s lightsaber, link 3. Since energy is
dissipated when the two lightsabers slide against each other, a dashpot is used to
model the scenario with a damping coefficient of c=10Ns/m as shown in the
exploded view on the right side of Fig. 4. Both Obi-wan and Darth Vader’s bodies
and arms are considered the fixed ground, link 1, and their wrists are revolute
joints which are located at the centers of mass of their lightsabers (note that
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since the laser blade of a lightsaber has no mass, the centers of mass of links 2
and 3 are at the centers of their respective hilts). The horizontal distance, a,
between the two revolute joints is 1.46m and the vertical distance, b, between
these joints is 0.18m. At the instant shown, α=45°, β=30°, and the distance
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between the revolute joint on Darth Vader’s lightsaber (i.e., his wrist) to the pin
of the pin-in-slot joint on Obi-wan’s lightsaber is 1.2m. The mass, m, of each
lightsaber is 1kg and their mass moments of inertia, IG, about their centers of
mass are 0.01kgm2. (30 points)
Figure 4: Obi-wan fighting Darth Vader
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(a) Draw and label an appropriate vector loop in the space below that captures the
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motion of both lightsabers. Assume Obi-wan’s lightsaber is the input. Write down
your vector loop equation and mark it with the appropriate symbols (I, C, ?,√). (4
points)
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(b) Find the first-order kinematic coefficients of all the unknowns identified in your
equation from part (a). (8 points)
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(c) Find the second-order kinematic coefficients of all the unknowns identified in
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your equation from part (a). (8 points)
(d) In the instant shown, Obi-wan’s lightsaber is rotating counter-clockwise with a
constant angular velocity of ω2=10 rad/s and Obi-wan’s wrist is exerting a moment of
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τ=50Nm on the lightsaber in the same direction. Use the power equation to find the
moment exerted on Darth Vader’s lightsaber by Darth Vader’s wrist. (10 points)
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