Problem 6.169
At the instant shown, bar
AB
rotates with a constant angular velocity
!AB D24 rad=s
. Letting
LD0:75
m and
HD0:85
m, determine the
angular acceleration of bar
BC
when bars
AB
and
CD
are as shown, i.e.,
parallel and horizontal.
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Dynamics 2e 1401
Problem 6.170
A slender bar
AB
of length
LD1:45 ft
is mounted on two identical
disks
D
and
E
pinned at
A
and
B
, respectively, and of radius
rD
1:5 in:
The bar is allowed to move within a cylindrical bowl with center
at
O
and diameter
dD2ft
. At the instant shown, the center
G
of the
bar is moving with a speed
vD7ft=s
. Determine the angular velocity
of the bar at the instant shown.
2r2
22
Therefore, the angular velocity of the bar is
O
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Problem 6.171
The bucket of a backhoe is the element
AB
of the four-bar linkage
system
ABCD
. The bucket’s motion is controlled by extending or
retracting the hydraulic arm
EC
. Assume that the points
A
,
D
, and
E
are fixed and that the bucket is made to rotate with a constant
angular velocity
!AB D0:25 rad=s
. In addition, suppose that, at
the instant shown, point
B
is vertically aligned with point
A
, and
point
C
is horizontally aligned with
B
. Letting
dEC
denote the
distance between points
E
and
C
, determine
P
dEC
and
R
dEC
at the
instant shown. Let
hD0:66 ft
,
eD0:46 ft
,
`D0:9 ft
,
wD1:0 ft
,
dD4:6 ft, and qD3:2 ft.
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permission of McGraw-Hill, is prohibited.
Acceleration analysis.
The figure defining the
xy´
and
x0y0´0
frames is repeated here for convenience.
Since !AB is constant, we can immediately write
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Dynamics 2e 1405
and the remaining terms on the right side of Eq. (25) have been found previously. Substituting expressions
for
EvCrel
,
E
˝
, and
ErC=E
found earlier, as well as Eqs. (9), (15), and (26) into Eq. (25), we obtain the following
BC C.h w/!2
CD
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Problem 6.172
An overhead fold-up door with height
HD30 ft
consists of two
identical sections hinged at
C
. The roller at
A
moves along a horizon-
tal guide, whereas the rollers at
B
and
D
, which are the midpoints
of sections
AC
and
CE
, move along a vertical guide. The door’s
operation is assisted by a counterweight
P
. Express your answers
using the component system shown.
If at the instant shown, the angle
D55ı
and
P
is moving
upward with a speed
vPD15 ft=s
, determine the velocity of point
E, as well as the angular velocities of sections AC and CE.
Solution
Referring to the figure at the right, the origin of the
xy
coordinate
system is at point
O
. Given that the length of the segment
AB
is
H=4, we can parameterize the xposition of Ausing
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Dynamics 2e 1407
Problem 6.173
An overhead fold-up door with height
HD30 ft
consists of two
identical sections hinged at
C
. The roller at
A
moves along a horizon-
tal guide, whereas the rollers at
B
and
D
, which are the midpoints
of sections
AC
and
CE
, move along a vertical guide. The door’s
operation is assisted by a counterweight
P
. Express your answers
using the component system shown.
If at the instant shown,
D45ı
, and
A
is moving to the right
with a speed
vAD2ft=s
while decelerating at a rate of
1:5 ft=s2
,
determine the acceleration of point E.
Solution
We are given that motion of Aas
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We aren’t given xAat this instant, we are given that D45ı. We can relate and xAvia
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Dynamics 2e 1409
Problem 6.174
A vertical shaft has a base
B
that is stationary relative to an inertial reference frame with vertical axis
Z
.
Arm
OA
is attached to the vertical shaft and rotates about the
Z
axis with an angular velocity
!OA
and an
angular acceleration
˛OA
. The
xy´
frame is attached at
C
, such that
Z
and
´
are always parallel and the
x
axis of the rotating reference frame coincides with the axis of the arm
OA
. At this instant, the collar
C
is at a distance
d
from the
Z
axis, is sliding along
OA
with a constant speed
vC
(relative to the arm
OA
),
and is rotating with a constant angular velocity
!C
(relative to the
xy´
frame). Point
D
is attached to the
collar and is at a distance
`
from the
x
axis. At the instant shown, point
D
happens to be in the plane that
is rotated by an angle
from the
x´
plane. Compute expressions for the inertial velocity and acceleration
of point
D
at the instant shown in terms of the parameters given, and express them relative to the rotating
coordinate system.
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