978-0073380308 Chapter 6 Solution Manual Part 22

subject Type Homework Help
subject Pages 9
subject Words 3772
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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page-pf1
Problem 6.149
Bar
AB
rotates about point
A
with angular speed
!1
and angular
acceleration
˛1
, both in the directions shown. The curved bar
BC
is pinned to bar
AB
at
B
and rotates with angular speed
!2
and
angular acceleration
˛2
about the pin at
B
in the directions shown,
relative to bar
AB
. At this instant, collar
D
is at the top of the
curved bar
BC
. The speed and acceleration of
D
relative to bar
BC
are given by
v0
and
a0
, respectively. Express your answers in
the
xy´
frame that is attached to bar
BC
with its origin at
B
.Hint:
As we will see in Eq. (10.14),
E!BC D E!AB C E!BC=AB D E!1C E!2
.
Determine the acceleration of the collar
D
in terms of
d
,
R
,
!1,!2,˛1,˛2,v0, and a0.
Solution
Using the given rotating reference frame, we can determine the acceleration of Dusing
or,
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permission of McGraw-Hill, is prohibited.
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Dynamics 2e 1361
Problem 6.150
The reciprocating rectilinear motion mechanism consists of a disk pinned
at its center at
A
that rotates with a constant angular velocity
!AB
, a slotted
arm
CD
that is pinned at
C
, and a bar that can oscillate within the guides
at
E
and
F
. As the disk rotates, the peg at
B
moves within the slotted
arm, causing it to rock back and forth. As the arm rocks, it provides a slow
advance and a quick return to the reciprocating bar due to the change in
distance between Cand B.
For the position shown, determine
(a)
The angular velocity of the slotted arm
CD
and the velocity of the
bar
(b)
The angular acceleration of the slotted arm
CD
and the acceleration
of the bar
Evaluate your results for !AB D120 rpm, R=h D0:5, and dD0:12 m.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
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Solving these two equations for !CD and PrB=C results in
Writing sin and cos in terms of given quantities
the solutions in Eq. (6) become
h2CR2D.R= h/2!AB
1C.R= h/2D2:513 rad=s and PrB=C DhR!AB
where we have used
!AB D120 rpm D120
30 rad=s
and
R= h D0:5
to obtain the numerical result.
Therefore, the angular velocity of the slotted arm CD is
If
Q
is the contact point in common between the gear and the bar at this instant, the velocity of the bar is
where we have used the fact that O
KDO
kand dD0:12 m.
Part (b).
We first determine the acceleration of point
B
by relating it
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pf4
Dynamics 2e 1363
Equation (13) is equivalent to the following two scalar equations
AB
Solving these two equations for ˛CD and RrB=C and substituting for sin and cos from Eq. (7), we obtain
AB
AB
30 rad=s
Therefore, the angular acceleration of the slotted arm CD is
If
Q
is the contact point in common between the gear and the bar at this instant, the acceleration of the bar is
equal to the tangential acceleration of the point Qon the arm CD, that is,
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pf5
Problem 6.151
The reciprocating rectilinear motion mechanism consists of a disk pinned
at its center at
A
that rotates with a constant angular velocity
!AB
, a slotted
arm
CD
that is pinned at
C
, and a bar that can oscillate within the guides
at
E
and
F
. As the disk rotates, the peg at
B
moves within the slotted
arm, causing it to rock back and forth. As the arm rocks, it provides a slow
advance and a quick return to the reciprocating bar due to the change in
distance between Cand B.
For the position shown, determine
(a)
The angular velocity of the slotted arm
CD
and the velocity of the
bar
(b)
The angular acceleration of the slotted arm
CD
and the acceleration
of the bar
Evaluate your results for !AB D90 rpm, R=h D0:5, and dD0:12 m.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pf6
Dynamics 2e 1365
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pf7
Problem 6.152
The reciprocating rectilinear motion mechanism consists of a disk pinned
at its center at
A
that rotates with a constant angular velocity
!AB
, a slotted
arm
CD
that is pinned at
C
, and a bar that can oscillate within the guides
at
E
and
F
. As the disk rotates, the peg at
B
moves within the slotted
arm, causing it to rock back and forth. As the arm rocks, it provides a slow
advance and a quick return to the reciprocating bar due to the change in
distance between Cand B.
For the position shown, determine
(a)
The angular velocity of the slotted arm
CD
and the velocity of the
bar
(b)
The angular acceleration of the slotted arm
CD
and the acceleration
of the bar
Evaluate your results for !AB D60 rpm, R=h D0:5, and dD0:12 m.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pf8
Dynamics 2e 1367
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pf9
If
Q
is the contact point in common between the gear and the bar at this instant, the acceleration of the bar is
equal to the tangential acceleration of the point Qon the arm CD, that is,
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pfa
Dynamics 2e 1369
Problem 6.153
The reciprocating rectilinear motion mechanism consists of a disk pinned
at its center at
A
that rotates with a constant angular velocity
!AB
, a
slotted arm
CD
that is pinned at
C
, and a bar that can oscillate within
the guides at
E
and
F
. As the disk rotates, the peg at
B
moves within
the slotted arm, causing it to rock back and forth. As the arm rocks, it
provides a slow advance and a quick return to the reciprocating bar due to
the change in distance between Cand B.
For the arbitrary position shown, determine
(a)
The angular velocity of the slotted arm
CD
and the velocity of the
bar
(b)
The angular acceleration of the slotted arm
CD
and the acceleration
of the bar
as functions of ,ıDR= h,d, and !AB
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.

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