Biomedical Engineering Reference
In-Depth Information
B ant ¼ F ant ANT a
x 2 ANT b
ð
13
:
34
Þ
where
are parameters based on the asymptotes for contracting
(agonist) or stretching (antagonist), respectively.
AG a
,
AG b
,
ANT a
, and
ANT b
13.5.5 A Linear Muscle Model
At this time, we will put all of the elements that have been discussed into a model of
muscle as shown in Figure 13.27 (left), and then we will analyze this model to determine
the tension created by the muscle. Note that in the muscle model, we have subtracted out
the effects of passive elasticity and assumed that
x
> x
:
Thus, starting with the free body diagram in Figure 13.27 (right), we have our two node
equations as
2
1
T ¼ K se x
ð
x
Þ
2
1
F ¼ B x
þ K lt x
þ K se x
ð
x
Þ
2
2
2
1
¼ T
We solve for
x 2 from the node 1 equation as
x
K se þ x
1 , and we substitute it into the
2
node 2 equation, giving us
T
K se þ x
F ¼ Bx
þ K se þ K lt
ð
Þ x
K se x
¼ B x
þ K st
K se x
2
2
1
2
1
1
For convenience, we will let
K st ¼ K se þ K lt
, and we will multiply the previous equation by
K se
and rearrange terms, so we have
K se F ¼ K se Bx 2 þ K st T þ K se K lt x 1
or
T ¼ K se F
K st K se K lt
x 1 K se B
K st
x 2
K st
.
Bx 2 + K LT x 2 + K SE ( x 2 - x 1 )
T
F
K lt
B
x 2
K se
x 1
K SE ( x 2 - x 1 )
F
T
FIGURE 13.27 (Left) Updated model of muscle with active-state tension generator, length-tension elastic
element, series elastic element, and viscosity element. (Right) Free body diagram of the system on the left.
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