Biomedical Engineering Reference
In-Depth Information
0
-0.005
-0.01
-0.015
-0.02
-0.025
F
Fy
-0.03
-0.035
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
α
Figure 4.13
Force in muscle.
and
x
0,B
=
H
e
y
.
Hence, the stretch of the muscle follows from
(
R
sin(
))
2
H
)
2
x
B
|
|
x
0,A
−
x
0,B
|
=
|
x
A
−
α
+
(
R
cos(
α
)
+
λ
=
(
R
sin(
α
0
))
2
+
H
)
2
,
+
(
R
cos(
α
0
)
while the orientation of the muscle is given by
R
sin(
α
)
e
x
+
(
R
cos(
α
)
+
H
)
e
y
a
=
(
R
sin(
H
)
2
.
))
2
α
+
(
R
cos(
α
)
+
From these results the force acting on the muscle at point B may be computed:
F
B
=
c
(
λ
−
1)
a
.
The force components in the
x
- and
y
-direction, scaled by the constant
c
,are
depicted in Fig.
4.13
in case
R
=
5[cm],
H
=
40 [cm] and an initial angle
α
0
=
π/
4.
4.5
Small fibre stretches
As illustrated by the above example the finite displacements of the end points
of a spring may cause a complicated non-linear response. In the limit of small
displacements of the end points a more manageable relation for the force in the
spring results. To arrive at the force versus displacement expression the concept
of displacement first needs to be formalized.
