Biomedical Engineering Reference
In-Depth Information
is a nonlinear element—that is, there may be other nonlinear or linear elements missing in
the model—or, perhaps, some of the assumptions made in the development of the model
are wrong. For the moment, consider that the analysis is correct and assume that some
elements are missing. This topic will be revisited in Section 13.7.
13.5.3 Elasticity
The normal operating point (at primary position),
, is much shorter than the length at
which maximum force occurs at approximately 30
. Even when the effects of the passive
muscle are removed, a relationship between length and tension is still evident, as previ-
ously described. Let us introduce a new elastic element into the model to account for the
relationship between length and tension as shown in Figure 13.16, which is described by
the following equation.
L
p
T
¼
F
K
pe
x
Kx
ð
13
:
22
Þ
, accounts for the slope of the subtracted curve shown as
the dashed line in the graph on the left in Figure 13.15. The slope of the line,
The new elastic element,
K
K
, at primary
position, is approximately 0.8 g/
¼
40.86 N/m (a value typically reported in the literature).
The slope for each of the curves in Figure 13.14 can be calculated in the same manner at
primary position with the resultant slopes all approximately equal to the same value as
the one for 15
N. At this time, the introduction of additional experiments will provide
further insight to the development of the muscle model.
Series Elastic Element
Experiments carried out by Levin and Wyman in 1927 and Collins in 1975 indicated the
need for a series elasticity element, in addition to the other elements previously presented
in the muscle model. The experimental setup and typical data from the experiment are
shown in Figure 13.17. The protocol for this experiment, called the quick release experi-
ment, is as follows. (1) A weight is hung onto the muscle. (2) The muscle is fully stimulated
at time
t
2
, the muscle changes length almost
instantaneously when the weight is released. The only element that can instantaneously
change its length is a spring. Thus, to account for this behavior, a spring, called the series
elastic element,
t
1
. (3) The weight is released at time
t
2
. At time
K
se
, is connected in series to the active-state tension element. While some
T
x
K
K
pe
F
FIGURE 13.16
A muscle model consisting of an active-state tension generator,
F
, passive elastic element,
K
pe
,
and elastic element,
K
. Upon stimulation of the active-state tension generator, a tension
T
is exerted by the muscle.
