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PROBLEM 15.122 (Continued)
E
PROBLEM 15.123
The disk shown has a constant angular velocity of 500 rpm counter-clockwise.
Knowing that rod BD is 10 in. long, determine the acceleration of collar D
when (a)
90 ,
θ
= °
(b)
180 .
θ
= °
SOLUTION
PROBLEM 15.123 (Continued)
D
PROBLEM 15.124
Arm AB has a constant angular velocity of 16 rad/s
counterclockwise. At the instant when
90 ,
θ
= °
determine
the acceleration (a) of collar D, (b) of the midpoint G of bar
BD.
PROBLEM 15.124 (Continued)
G
PROBLEM 15.125
Arm AB has a constant angular velocity of 16 rad/s
counterclockwise. At the instant when
60 ,
θ
= °
determine
the acceleration of collar D.
PROBLEM 15.125 (Continued)
D
D=a
PROBLEM 15.126
A straight rack rests on a gear of radius r = 3 in. and is attached to
a block B as shown. Knowing that at the instant shown
θ
= 20°,
the angular velocity of gear D is 3 rad/s clockwise, and it is
speeding up at a rate of 2 rad/s2, determine (a) the angular
acceleration of AB, (b) the acceleration of block B.
SOLUTION
Let Point P on the gear and Point Q on the rack be located at the contact point between them.
PROBLEM 15.126 (Continued)
Acceleration analysis.
2
/ //
2
8.2469 5.1153 (7.74535 2.81908 )
(0.39742) (7.74535 2.81908 )
(8.2469 2.81908 1.22332)
(5.1153 7.74535 0.44526)
B Q BQ Q AB BQ AB BQ
B AB
AB
AB
a
α
α
α
= + +× −
−−
=+−
++ +
i i jk i j
ij
i
j
Equating like components of
,
a
PROBLEM 15.127
The elliptical exercise machine has fixed axes of rotation at points A
and E. Knowing that at the instant shown the flywheel AB has a
constant angular velocity of 6 rad/s clockwise, determine the
acceleration of point D.
SOLUTION
2
BD
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 15.127 (Continued)
2
D
F
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 15.128
The elliptical exercise machine has fixed axes of rotation at points A
and E. Knowing that at the instant shown the flywheel AB has a
constant angular velocity of 6 rad/s clockwise, determine (a) the
angular acceleration of bar DEF, (b) the acceleration of point F.
SOLUTION
2
( ) ( ) ( )
2
0.12 0.8 1.463 0.12 0.8
BD
DEF
α
×−−− −−
k ij ij
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 15.128 (Continued)
F
F=a
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 15.129
Knowing that at the instant shown bar AB has a constant angular
velocity of 19 rad/s clockwise, determine (a) the angular acceleration
of bar BGD, (b) the angular acceleration of bar DE.
PROBLEM 15.130
Knowing that at the instant shown bar DE has a constant angular velocity
of 18 rad/s clockwise, determine (a) the acceleration of Point B, (b) the
acceleration of Point G.
SOLUTION
.Velocity analysis
18 rad/s
DE
ω
=
( ) (15.2)(18) 273.6 in./s
D DE
DE
ω
= = =v
DD
v=v
,
BB
v=v
Point C is the instantaneous center of bar BD.
273.6 14.25 rad/s
19.2
D
BD
v
CD
ω
= = =
( ) (8)(14.25) 114 in./s
B BD
v CB
ω
= = =
114 14.25 rad/s
8
B
AB
v
AB
ω
= = =
.Acceleration analysis
0
DE
α
=
2
[( )
D DE
DE
ω
=a
2
] [(15.2)(18)=
2
] [4924.8 in./s=
]
[( )
B AB
AB
α
=a
2
] [( )
AB
AB
ω
+
]
[8
AB
α
=
2
] [1624.5 in./s+
]
/
( ) [19.2
D B t BD
α
=a
] [8 BD
α
+
]
2
/
( ) [19.2
D B n BD
ω
=a
2
] [8
BD
ω
+
]
//
( ) ( ) Resolve into components.
D B DB t DB n
=++aa a a
PROBLEM 15.130 (Continued)
PROBLEM 15.131
Knowing that at the instant shown bar AB has a constant
angular velocity of 4 rad/s clockwise, determine the angular
acceleration (a) of bar BD, (b) of bar DE.
PROBLEM 15.131 (Continued)
DE =α
PROBLEM 15.132
Knowing that at the instant shown bar AB has a constant angular velocity of
4 rad/s clockwise, determine the angular acceleration (a) of bar BD, (b) of bar
DE.
BD
PROBLEM 15.132 (Continued)
DE
