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Unformatted text preview: II6 Chapter II: Planar Rigid Body Kinematics Homework
Planar Kinematics Homework Problems ME 274 Problem II.4 Given: The compound wheel assembly shown below is driven by a cable attached to the outer rim
Problem II4
of the assembly at point A. The wheel rolls without slip at point B, and the acceleration at point
A isThe compound xwheel ˆassembly shown below is driven by a cable attached to the outer
given by = a ˆ + ay j
a
i rim of the assembly at point A. Assuming that the wheel rolls without slip about point B,
and the acceleration at point A is given by a A = ax i + ay j , determine the acceleration of Find: Determine the acceleration of the center point C of the pulley. point C. y A !
x C 0.025 m B
0.1 m
Use Use following parameters in your analysis: sec 2 0,ndx a 8m/sec2sec 2 . ay = 12m/sec2 .
the the following: ! = 36.87° , a = 8 m / φ = a a = = 6 m / and
x y II8 Chapter II: Planar Rigid Body Kinematics Homework Planar Kinematics Homework Problems ME 274 Problem II.6 Problem II6 Given: At the instant shown, the piston has velocity A = vAˆ.
v
i If, at the instant shown, the piston has velocity v A = vA i , determine the resulting angular Find: Determine the resulting angular velocity ωBC of the crankshaft.
velocity ! CB of the crankshaft. B
0.06 m
C y !
A
x 0.03 m
Use the following parameters in your analysis: φ = 30◦ and vA = −50m/sec. Use the following: ! = 53.13° and vA = !20 m / sec . v Chapter II: PlanarHomework Problems
Planar Kinematics Rigid Body Kinematics Homework II15
ME 274 Problem II.1010
Problem II
Given: The mechanism below is drivenby a motor at point A,A, which produces angular velocity
The mechanism below is driven by a motor at point which produces an an angular
of ωAB and angular acceleration of αAB . BCE and CD are horizontal and vertical, respectively, at
velocity of ! A and angular acceleration of ! AB . Provided BCE and CD are horizontal
the instant shown. B and vertical, respectively, at the instant shown, find the velocity and acceleration vectors
of Determine the velocity and acceleration vectors of point E.
Find: point E. 0.3 m Use the following parameters in your analysis: ωAB = 3rad/sec, αAB = 0 and φ = 36.87◦ . Use the following: ! AB = 8 rad / sec , ! AB = "5 rad / sec 2 and ! = 53.13° . Chapter II: Planar Rigid Body Kinematics Homework II21 Problem II.16
Given: The orientation angle θ for the circular disk of radius R is given by: θ (t) = π sinπ t (with
3
θ in radians and t in seconds).
Find: Determine the velocity and acceleration vectors for point A on the outer edge of the disk
for:
• t=0
mework Problems • t = 1/3seconds ME 274 Make sketches of these vectors for the above two instants in time. ngle ! for the circular disk of radius R is
"
sin" t (with ! in radians and t in
3
ine the velocity and acceleration vectors
e outer edge of the disk for: A !
R O conds
these vectors for the above two instants
Use the following parameter in your analysis: R = 0.5m our analysis. II22 Chapter II: Planar Rigid Body Kinematics Homework Problem II.17
Given: Thin bar AB (having a length of L) moves in a way that ends A and B slide along straight,
ﬁxed guides as shown in the ﬁgure. End A has a constant speed of vA to the right as the bar moves.
omework Problems ME 274 Find: Determine the velocity and acceleration of end B. ving a length of L) moves in a way
B slide along straight, fixed guides as
ure. End A has a constant speed of
s the bar moves. B elocity and acceleration of end B. L ! ! A vA Use the following parameters in your analysis: L = 2f t, vA = 4f t/sec, θ = 36.87◦ and φ = 120◦ . rs , vA = 3 m / sec , ! = 90° and ! = 36.87° in your analysis. II28 Chapter II: Planar Rigid Body Kinematics Homework Problem II.23 Planar Kinematics Homework Problems ME 274 Given: 23
Problem IIA mechanism is made up of links AB and BD, with point A being pinned to ground and
point B being a pin joint connecting links AB and BD. A slider is connected to BD at pin D with A mechanismbeing constrained to AB and BD, with point A being radius of R. At the position shown
the slider is made up of links move on a circular path with a pinned to ground and
point B being aAB is vertical, link BD is horizontal andA slider is connected to BD at pin position,
below, link pin joint connecting links AB and BD. D is directly above point O. At this
D with the slider being constraineda constant speed of vD path with a radius of 2.5 meters.
D is traveling to the right with to move on a circular .
At the position shown below, link AB is vertical, link BD is horizontal and D is directly
above point O.this this position, D is traveling to the right with a constant speed of 5
Find: For At position:
m/sec. For the position shown, find:
• determine the angular velocities of links AB and BD. Write your answers as vectors. i) the angular velocity of links AB and BD, and ii) t• determine the angularoaccelerations of BD. AB and BD. Write your answers as vectors.
he angular acceleration f links AB and links y
x A
d vD D L
B R O Use the following parameters in your analysis: R = 0.5m, L = 2m, d = 1.5m and vD = 5m/sec. Planar Kinematics Homework Problems ME 274 Problem II26
Given: II: Planar Rigid Body Kinematics Homework BC and a wheel pinned to
A mechanism is made up of links AB and
Chapter
BC at the wheel’s center C. The wheel rolls without slipping on a
horizontal surface. Link AB rotates counterclockwise with a constant
Problem rate of 3 rad/sec. At the instant shown, link AB is vertical.
II.26 II31 Find: A At the instant shown, links AB and BC and a wheel pinned to BC at the wheels center
Given: mechanism is made up of
C. The wheela) determine the angular velocities surface. BC and the wheel.
rolls without slipping on a horizontal of link Link AB rotates counterclockwise with
a constant rate of ωAB . At the instant shown, link AB is vertical.
b) determine the angular accelerations of link BC and the wheel.
c) determine the velocity and acceleration of point E on the perimeter
Find: For this position:
of the wheel (at the instant shown, E is on the same horizontal line as C).
• determine the angular velocity of links AB and BC. Write your answers as vectors.
• determine the angular acceleration of links AB and BC. Write your answers as vectors. Write your answers as vectors. B
r d
!AB E
no slip L A
C Use the following parameters in your analysis: r = 0.5m, L = 2m, d = 1m and ωAB = 3rad/sec. II32 Chapter II: Planar Rigid Body Kinematics Homework PProblem II.27
lanar Kinematics Homework Problems ME 274 Given: I 27
ProblemAImechanism is made up of links OA, AB and BD. At the instant shown, link OA is
vertical and links AB and BD are horizontally aligned. At this instant, link BD is rotating CW at
Given: A mechanism is made up of at α OA, AB and BD. At the instant shown, link
links .
ωBD with this angular speed changing
BD
OA is vertical and links AB and BD are horizontally aligned. At this instant,
2
Find: Forlink BD is rotating CW at 6 rad/sec with this rate increasing at 4 rad/sec .
this position: Find: showFthethe instant shown,
or location of the instant center for link AB in the ﬁgure below.
•
a) show the location of the instant center for link AB in the figure below.
• determine the angular velocity of links OA and AB.
b) determine the angular velocity of links OA and AB.
• determine the angular the angular accelerationandlinks OA and AB.
c) determine acceleration of links OA of AB. A L B d D !BD
r O Use the following parameters in your analysis: r = 2f t, L = 3f t, d = 1f t, ωBD = 6rad/sec and
αBD = 4rad/sec2 . II34 Chapter II: Planar Rigid Body Kinematics Homework Planar Kinematics Homework Problems ME 274 Problem II.29 Problem II29 Given: A mechanism shown is made up of links OA and AB with a slider pinned to link AB at
Given: A mechanism shown is made up of links OA and AB with a slider pinned to
B. The slider is constrained to move within a ﬁxed slot at a constant speed of vB in the direction
link AB at is oriented at constrained to move within a fixed the at a
shown. The slotB. The slider isan angle θ from the horizontal. At slot instant shown, link OA is
constant speed of vB = 2
vertical and AB is horizontal. 0 ft/sec in the direction shown. The slot is oriented at a 36.87° angle from the horizontal. At the instant shown, link OA is vertical
a For this horizontal.
Find: nd AB is position: Find: • For the instant shown, velocity of links OA and AB.
determine the angular d) determine the angular velocity of links OA and AB.
e) determine the angular acceleration of links OA and AB. • determine the angular acceleration of links OA and AB. A B L ! vB r O Use the following parameters in your analysis: r = 2f t, L = 3f t, θ = 36.87◦ and vB = 20f t/sec. Chapter II: Planar Rigid Body Kinematics Homework
Planar Kinematics Homework Problems II35
ME 274 Problem II.30 Problem II30
Given: The simple mechanism shown below consists of a ﬂywheel pinned at O and an attached
Given: The simple mechanism shown below consists of a flywheel pinned at O and
member AB pinned on the outer edge of the ﬂywheel at A. At this moment in time the ﬂywheel
an attached member AB pinned on the outer edge of the flywheel at A. At this
has a constant angular velocity of ω in the clockwise direction, and OA is horizontal. Assume that
moment in time the flywheel has a constant surface aligned of ! in the
point B remains in contact with the horizontalangular velocity with the bottom of the ﬂywheel, as
clockwise direction, and OA is horizontal . Assume that point B remains in
shown below.
contact with the horizontal surface aligned with the bottom of the flywheel, as
shown below.
Find: For this moment in time:
Find: • this moment in time,
For determine the velocity of B.
a) determine the velocity of B (write your answer as a vector).
• show the location of the instant center of link AB in the ﬁgure below. Use this location to
b) show the location of the instantof B foundlink AB in the figure below.
verify the direction of the velocity center of above.
Use this location to verify the direction of the velocity of B found in a)
above.
• determine the acceleration of B.
c) determine the acceleration of B (write your answer as a vector). ...
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 Fall '09

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