Biomedical Engineering Reference
In-Depth Information
feedbacks and other interaction devices, it seems to be difficult to address this problem
without introducing metaphors.
An alternative might be using a force plate under the feet which can bring relevant
information of the user's gait. In biomechanics, force plates are used to measure the
ground reaction force (GRF) below the feet, the moment of this force around the
main ground axes and the location of the instantaneous center of pressure (COP).
The ground reaction force is used to compute the acceleration of the center of mass
if no other force than gravity and GRF occur. For the global mechanical system
(restricted to its center of mass):
W
+
GRF
=
m
q
¨
where W stands for the body weight, m is the mass and q is the center of mass
position. If we can estimate q and its derivative at some times (especially the initial
value but it is sometimes possible to get these values for each foot-strikes event) it
is thus possible to integrate the signal:
t
1
m
2
q
(
t
)
=
W
+
GRF
(τ )
d
τ
t
0
where t
0
states for the beginning of the studied sequence. Practically, the initial
center of mass velocity
.Asa
consequence these two values should be either measured or imposed at the beginning
of the motion (such as starting straight with a null velocity). With a simple Euler
integration scheme, this equation becomes:
q
˙
(
t
0
)
and position
q
(
t
0
)
are required to compute
q
(
t
)
1
m
(
t
n
˙
)
=˙
)
+
+
))
q
(
n
q
(
0
W
GRF
(
i
i
=
1
n
q
(
n
)
=
q
(
0
)
+
1
˙
q
(
i
)
t
i
=
where
t stands for the sampling frequency.
A force plate is generally calibrated at the beginning of the sequence so that
the value is set to zero when nothing is placed over it. However, if the user jumps
over the forceplate or goes out and in several times, the initial calibration could be
inappropriate. From the numerical point of view, we obtain:
⎧
⎨
t
s
−
i
=
1
1
1
q
˙
(
0
)
+
m
(
W
0
+
GRF
(
i
))
×
tift
<
t
s
q
˙
(
n
)
=
t
s
−
i
=
1
1
i
=
t
s
n
m
W
t
s
+
)
×
⎩
1
1
q
˙
(
0
)
+
m
(
W
0
+
GRF
(
i
))
×
t
+
GRF
(
i
t
