Biomedical Engineering Reference
In-Depth Information
The force vector acting on the spring at point B is written as
F
B
=
c
(
λ
−
1)
a
.
The stretch
λ
of the spring follows from
(
0
cos(
α
0
))
2
+
y
2
0
=
λ
=
.
0
The orientation of the spring as represented by the unit vector
a
is given by
0
cos(
α
0
)
e
x
+
ye
y
x
B
−
x
A
|
x
B
−
x
A
|
=
y
2
.
So, in conclusion the force vector applied to the spring at point B,
F
B
, equals
F
B
=
c
(
a
=
(
0
cos(
α
0
))
2
+
−
1
0
cos(
α
0
))
2
+
y
2
0
cos(
α
0
)
e
x
+
y
e
y
(
y
2
.
0
0
cos(
α
0
))
2
+
Given an initial length
0
=
1 [mm], a spring constant
c
=
0.5 [N] and an initial
4, the force components of
F
B
in the
x
- and
y
-direction (
F
x
and
F
y
, respectively) are represented in Fig.
4.11
as a function of the
y
-location
of point B. Notice that, as in the previous example, both
F
x
and
F
y
are non-linear
functions of
y
even though the spring is linearly elastic. It is remarkable to see that
with decreasing
y
, starting at the initial position
y
0
orientation
α
0
=
π/
=
0
sin(
α
0
), the magnitude
of the force in the
y
-direction
first increases and thereafter decreases. This
demonstrates a so-called snap-through behaviour. If the translation of point B is
|
F
y
|
F
x
[N]
F
y
[N]
0.1
R
T
0.05
0
Q
P
-0.05
-0.1
-0.15
-1
-0.5
0
0.5
y
0
1
y
[mm]
Figure 4.11
Forces in the horizontal and vertical direction exerted on the spring to displace point B in the
y
-direction. Snap-through behaviour.
