4569846498

Kinematics and dynamics of rigid bodies 73
Z 3
Z 1
Body 1
Body 2
Y 2 ,Y 3
G 3
θ
Y 1 X
Body 3
O 3
1
X 1
{ω 3 } 2/2
{ω 2 } 1/1
Fig. 2.37
Swing arm suspension dynamics
with a constant angular velocity of 100 rad/s about the axis of the revolute
joint representing the wheel bearing.
The following data may be used to represent the mass properties of the road
wheel:
m 3 16 kg
I 31 I 3xx 0.5 kg m 2
I 32 I 3yy 1.0 kg m 2
I 33 I 3zz 0.5 kg m 2
In order to determine the reaction torque on the wheel bearing when the
axle is still in a horizontal position, 0, we can use the following to give
us the required angular velocity vector { 3 } 1/3 :
⎡10⎤
⎡ 0 ⎤
⎡ 10 ⎤
{ } /
⎢
2 12 0
⎥
rad/s { } /
⎢
23 100
⎥
rad/s { } /
⎢
13 100
⎥
rad/s
⎢ ⎥
3 ⎢ ⎥
3 ⎢ ⎥
⎣⎢
0 ⎦⎥
⎣⎢
0 ⎦⎥
⎣⎢
0 ⎦⎥
In the absence of angular acceleration equation (2.233) can be adapted to
give for this problem
Σ{ M3} 13 / [ 3] 13 / [ I3] 13 / { 3}
13 /
(2.238)
Expanding this gives
∑
⎡M
⎢
⎢
M
⎣⎢
M
3x
3y
⎤
⎥
⎥
⎦⎥
3z
1/3
⎡ 0
⎢
⎢
⎢
⎣
0
3z
3y
3z
3x
3y
3x
0
⎤
⎥
⎥
⎥
⎦
1/3
⎡I3xx
0 0 ⎤
⎢
⎢
0 I
⎥
3yy
0
⎥
⎣⎢
0 0 I ⎦⎥
3zz
3/3
⎡
⎢
⎢
⎣⎢
3x
3y
⎤
⎥
⎥
⎦⎥
3z
1/3
(2.239)