Q
UESTION
7
For the system shown in Figure 7, set up the equations in matrix form that would allow you to
determine the transfer function
(
29
(
29
L
s
s
θ
Τ
. Assume the gears are massless.
r
1
r
2
J
1
B
K
θ
L
(t)
J
L
τ
(t)
r
4
r
3
B
L
Figure 7
The Free Body Diagrams are given in Figure 7.1 below and the gear with radius
r
3
rotates with
an angular position
θ
3
. Note that the schematic between the damper and the spring is free to
rotate at a unique angular position, which is denoted
θ
2
. To analyze this portion, a rotational mass
with inertia
J
0
= 0 is inserted. For the gear set on the left the following relationship holds
2
1
1
r
r
τ
=
. For the gear set on the right the following relationships hold
3
3
4
4
3
L
r
r
=
=
. Summing the
torques applied to the inertia denoted
J
and applying the constitutive law for dampers
(
29
(
29
(
29
(
29
(
29
(
29
2
1
1
2
2
1
1
r
J
t
t
t
t
B
t
t
r
=
(1)
Summing the torques applied to the inertia denoted
J
0
and applying the constitutive laws for
springs and dampers
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 Spring '11
 LANDERS
 Rotation, Jaguar Racing, gear, Constitutive equation

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