Biomedical Engineering Reference
In-Depth Information
driven by an externally applied force, and point P is reached in the force versus
y-position curve, the y-coordinate of point B will suddenly move to point Q with
equal force magnitude. During the reverse path a snap through will occur from
point R to point T.
Example 4.3
The Achilles tendon is attached to the rear of the ankle (the calcaneus) and is
connected to two muscle groups: the gastrocnemius and the soleus, which, in turn,
are connected to the tibia, see Fig.
4.12
(a). A schematic drawing of this, using a
lateral view, is given in Fig.
4.12
(c). If the ankle is rotated with respect to the
pivot point O, i.e. the origin of the coordinate system, the attachment point A
is displaced causing a length change of the muscle system. The position of the
attachment point A is given by
x
A
=−
R
sin(
α
)
e
x
−
R
cos(
α
)
e
y
,
where R is the constant distance of the attachment point A to the pivot point. The
angle
is defined in clockwise direction. The muscles are connected to the tibia
at point B, hence:
α
x
B
=
He
y
,
with
H
the distance of point B to the pivot point. The positions in the undeformed,
unstretched configuration of these points are
x
0,A
=−
R
sin(
α
0
)
e
x
−
R
cos(
α
0
)
e
y
B
1
tibia
H
1
2
2
e
y
e
x
o
R
4
5
6
3
α
3
A
calcaneus
(a) The ankle and foot.
(1) tibia, (2) fibula,
(3) medial malleolus,
(4) lateral malleolus,
(5) talus, (6) calcaneus
(b) Ankle muscles, pos-
terior view. (1) gastroc-
nemius, (2) soleus,
(3) Achillles tendon
(c) Location of muscle
Figure 4.12
Muscle attached to tibia and calcaneus.
