PROBLEM 15.215
In Problem 15.205, determine the acceleration of
collar C.
PROBLEM 15.205 Rod BC and BD are each 840
mm long and are connected by ball-and–socket
joints to collars which may slide on the fixed rods
shown. Knowing that collar B moves toward A at a
constant speed of 390 mm/s, determine the velocity
of collar C for the position shown.
SOLUTION
22 2 2
PROBLEM 15.215 (Continued)
PROBLEM 15.216
In Problem 15.206, determine the acceleration of collar A.
PROBLEM 15.206 Rod AB is connected by ball-and–socket joints to
collar A and to the 16-in.–diameter disk C. Knowing that disk C rotates
counterclockwise at the constant rate
03
ω
=
rad/s in the zx plane,
determine the velocity of collar A for the position shown.
SOLUTION
PROBLEM 15.216 (Continued)
A
PROBLEM 15.217
In Problem 15.207, determine the acceleration of collar A.
PROBLEM 15.207 Rod AB of length 29 in. is connected by ball–
and–socket joints to the rotating crank BC and to the collar A.
Crank BC is of length 8 in. and rotates in the horizontal xz
plane at the constant rate
010
ω
=
rad/s. At the instant shown,
when crank BC is parallel to the z axis, determine the velocity
of collar A.
SOLUTION
PROBLEM 15.217 (Continued)
A
A
PROBLEM 15.218
In Problem 15.208, determine the acceleration of collar A.
PROBLEM 15.208 Rod AB of length 300 mm is connected by
ball–and–socket joints to collars A and B, which slide along the
two rods shown. Knowing that collar B moves toward Point D
at a constant speed of 50 mm/s, determine the velocity of
collar A when
80 mm.c=
PROBLEM 15.218 (Continued)
A
PROBLEM 15.219
In Problem 15.209, determine the acceleration of collar A.
PROBLEM 15.209 Rod AB of length 300 mm is connected
by ball–and–socket joints to collars A and B, which slide along
the two rods shown. Knowing that collar B moves toward
Point D at a constant speed of 50 mm/s, determine the velocity
of collar A when
120 mm.c=
SOLUTION
/AB
/,
AB
//
BA BA
PROBLEM 15.219 (Continued)
A
PROBLEM 15.220
A flight simulator is used to train pilots on how to
recognize spatial disorientation. It has four degrees
of freedom, and can rotate around a planetary axis
as well as in yaw, pitch, and roll. The pilot is
seated so that her head B is located at r = 2i + 1j ft
with respect to the center of the cab A. Knowing
that the cab is rotating about the planetary axis with
a constant angular velocity of 20 rpm
counterclockwise as seen from above, and pitches
with a constant angular velocity of +3 k rad/s,
determine (a) the velocity of the pilot’s head, (b)
the angular acceleration of the cab, (c) the
acceleration of the pilot’s head.
SOLUTION
B=− −+a ijk
PROBLEM 15.221
A flight simulator is used to train pilots on how to
recognize spatial disorientation. It has four degrees of
freedom, and can rotate around a planetary axis as well
as in yaw, pitch, and roll. The pilot is seated so that her
head B is located at r = 2i + 1j ft with respect to the
center of the cab A. The cab is rotating about the
planetary axis with an angular velocity of 20 rpm
counterclockwise as seen from above and is increasing
this by 1 rad/s2. Knowing that the cab rolls with a
constant angular velocity of -4 i rad/s, determine (a) the
velocity of the pilot’s head, (b) the angular acceleration
of the cab, (c) the acceleration of the pilot’s head.
B
PROBLEM 15.222
The rectangular plate shown rotates at the constant rate
2
12
ω
=
rad/s
with respect to arm AE, which itself rotates at the constant rate
19w=
rad/s about the Z axis. For the position shown, determine the velocity and
acceleration of the point of the plate indicated.
Corner B.
SOLUTION
Geometry. With the origin at A,
(0.135 m)
B
=rj
Let frame
AXYZ
rotate about the Y axis with constant angular velocity
1(9 rad/s) .
ω
= =kkΩ
Then the motion
relative to the frame consists of rotation about the X axis with constant angular velocity
22
(12 rad/s) .
ω
= =iiω
B
B
PROBLEM 15.223
The rectangular plate shown rotates at the constant rate
2
12
ω
=
rad/s
with respect to arm AE, which itself rotates at the constant rate
19
ω
=
rad/s about the Z axis. For the position shown, determine the velocity and
acceleration of the point of the plate indicated.
Corner C.
SOLUTION
Geometry. With the origin at A,
(0.135 m) (0.09 m)
C= +r jk
Let frame
AXYZ
rotate about the Y axis with constant angular velocity
1(9 rad/s) .
ω
= =kkΩ
Then the motion
relative to the frame consists of rotation about the X axis with constant angular velocity
22
(12 rad/s) .
ω
= =iiω
C
PROBLEM 15.223 (Continued)
PROBLEM 15.224
Rod AB is welded to the 0.3-m-radius plate, which rotates at the
constant rate
ω
1 = 6 rad/s. Knowing that collar D moves toward end B
of the rod at a constant speed u = 1.3 m, determine, for the position
shown, (a) the velocity of D, (b) the acceleration of D.
SOLUTION
PROBLEM 15.224 (Continued)
D=−−a ik
PROBLEM 15.225
The bent rod shown rotates at the constant rate
1
ω
= 5
rad/s and collar C moves toward point B at a constant
relative speed u = 39 in./s. Knowing that collar C is
halfway between points B and D at the instant shown,
determine its velocity and acceleration.
SOLUTION
C
PROBLEM 15.226
The bent pipe shown rotates at the constant rate
1
ω
= 10 rad/s. Knowing that a ball bearing D moves in
portion BC of the pipe toward end C at a constant
relative speed u = 2 ft/s, determine at the instant shown
(a) the velocity of D, (b) the acceleration of D.
PROBLEM 15.227
The circular plate shown rotates about its vertical diameter at the constant
rate
110 rad/s.
ω
=
Knowing that in the position shown the disk lies in the XY
plane and Point D of strap CD moves upward at a constant relative speed u
1.5 m/s,=
determine (a) the velocity of D, (b) the acceleration of D.
SOLUTION