PROBLEM 16.124
The 4–kg uniform rod ABD is attached to the crank BC and is fitted with
a small wheel that can roll without friction along a vertical slot. Knowing
that at the instant shown crank BC rotates with an angular velocity of 6
rad/s clockwise and an angular acceleration of 15 rad/s2
counterclockwise, determine the reaction at A.
PROBLEM 16.125
The 3–lb uniform rod BD is connected to crank AB and to a collar of
negligible weight. A couple (not shown) is applied to crank AB causing it to
rotate with an angular velocity of 12 rad/s counterclockwise and an angular
acceleration of 80 rad/s2 clockwise at the instant shown. Neglecting the effect
of friction, determine the reaction at D.
PROBLEM 16.125 (Continued)
Translation with B and rotation about D = Planar motion
/D B DB
= +aaa
PROBLEM 16.125 (Continued)
2
1 3 10 0.17361
12 12
()
eff
6 4 43
: ft ft
12 12 12 12
BB y x
M M D W I ma ma
a
∑=∑ − =+ −
( ) ( ) ( )
1 0.17361 3 3 1
1
0.5 3 88 74.33 10
3 34
Dgg g
−= + −
( )
1
0.5 1 82.108 , 7.10 lb
32.2
DD−= =
7.10 lb=D
PROBLEM 16.126
The 3–lb uniform rod BD is connected to crank AB and to a collar of
negligible weight. A couple (not shown) is applied to crank AB causing it to
rotate. At the instant shown, crank AB has an angular velocity of 12 rad/s and
an angular acceleration of 80 rad/s2, both counterclockwise. Neglecting the
effect of friction, determine the reaction at D.
PROBLEM 16.126 (Continued)
( ) ( )
2
43
20 15 3.333 10.00 ft/s
55
x
a=−+ =+
( ) ( )
2
34
36 15 3.333 47.67 ft/s
55
y
a=++ =+
2
2
2
1 3 10 0.17361
12 12
Igg
=+=
64 3 4
PROBLEM 16.127
The test rig shown was developed to perform fatigue testing
on fitness trampolines. A motor drives the 200–mm radius
flywheel AB, which is pinned at its center point, in a
counterclockwise direction with a constant angular velocity of
120 rpm. The flywheel is attached to slider CD by the 400-mm
connecting rod BC. The mass of the connecting rod BC is 5 kg
and the mass of the link CD and foot is 2 kg. At the instant
when
θ
= 0° and the foot is just above the trampoline,
determine the force exerted by pin C on rod BC.
PROBLEM 16.127 (Continued)
Kinematics:
Equating i–terms:
Equating j components: (6)
(7)
Substitute into (8)(9)→(3): (10)
Substitute into (2)(5)(7)(9)(10)→(4):
BA
=vv
( )
B/A
0.2
0.8
AB
AB
ω
π
+×
= ×
=
ωr
ki
j
( )
( )
C/B
0.8 –0.2 0.2 3
0.2 3 0.8 0.2
C B BC
C BC
C BC BC
v
v
πω
ω πω
= ×+
=− +−
j j+ k i j
ji j
0
BC
ω
=
2/AAB B AB
3
BC
22
,
3.2 m/s
3
c CD y
aa
π
= =
2
BC B BC
( )
/B /B
2
2
,,
16
3.2 0.1 0.1 3
3
G BC G
BC x BC y
aa
π
π
+ =− − ×− +
ij i ki j
22
,
3.2 1.6
BC x
a
ππ
=−+
2
1.6
π
3
yy
2
1.6
5 5 56.0 150.724 N
3
yy
B gB
π
= ++ ⇒ =
2
22
16
π
PROBLEM 16.127 (Continued)
2
2
16
π
PROBLEM 16.128
Solve Prob. 16.127 for
θ
= 90°.
PROBLEM 16.127 The test rig shown was developed to
perform fatigue testing on fitness trampolines. A motor drives
the 200–mm radius flywheel AB, which is pinned at its center
point, in a counterclockwise direction with a constant angular
velocity of 120 rpm. The flywheel is attached to slider CD by
the 400–mm connecting rod BC. The mass of the connecting rod
BC is 5 kg and the mass of the link CD and foot is 2 kg. At the
instant when
θ
= 0° and the foot is just above the trampoline,
determine the force exerted by pin C on rod BC.