5.7.26.11.2 Centre of pressure calculations
Centre of pressure (CoP) calculations were made from the output from two force plates inset in the
laboratory floor. Figure 5.18 demonstrates the x, y and z axes of the force plates.
Appendix 1
Figure 6.18 Force plate axes
Centre of pressure calculations
5.7.26.11.2 Centre of pressure calculations
Centre of pressure (CoP) calculations were made from the output from two force
Centre of pressure (CoP) calculations were made from the output from two force plates inset in the
plates inset in the laboratory floor. The figure below demonstrates the x, y and z
floor. Figure
5.18Yellow
demonstrates
x, y and z axesthe
of the
force plates.
axeslaboratory
of the force
plates.
arrowtherepresents
x-axis;
green arrow, the y-axis;
and orange
arrow, the z-axis.
Figure 6.18 Force plate axes
Yellow arrow represents the x-axis; green arrow, the y-axis; and orange
arrow, the z-axis.
The x-coordinate of the CoP was calculated under each limb from the moments and forces produced
Yellow arrow represents the x-axis; green arrow, the y-axis; and orange
byThe
eachx-coordinate
plate with arrow,
respect
toz-axis.
the origin
the laboratory
space,
follows:
of the
the
CoP
was of
calculated
under
eachaslimb
from the moments and
forces produced by each plate with respect to the origin of the laboratory space, as
The x-coordinate of the CoP was calculated under each limb from the moments and forces produced
follows:
by each plate with respect to the origin of the laboratory space, as follows:
−𝑀 _
+ 𝑝𝑙𝑎𝑡𝑒 𝑜𝑟𝑖𝑔𝑖𝑛
𝐹 _
𝑥
_
=
𝑥 𝑥
_
_==
𝑥
_
=
−𝑀 _
−𝑀
_ + 𝑝𝑙𝑎𝑡𝑒 𝑜𝑟𝑖𝑔𝑖𝑛
𝐹 _ + 𝑝𝑙𝑎𝑡𝑒 𝑜𝑟𝑖𝑔𝑖𝑛
𝐹 _
−𝑀 _
+ 𝑝𝑙𝑎𝑡𝑒 𝑜𝑟𝑖𝑔𝑖𝑛
𝐹 _
where
of the
CoPCoP
under
the left
right
at time
i, and
where𝑥 xCoPl_i,
arex-x-coordinates
coordinates
of the
under
theand
left
andfeet
right
feetpoint
at time
_ , 𝑥xCoPr_i
_ are
, Fzl_i, Fzr_icomponents
are directional
the acting
moments
yr_idirectional
𝑀point
𝑀 i, _ and
,𝑥𝐹 _M
, 𝐹yl_i, M
are
of thecomponents
moments and of
forces
on theand
body
_ , where
_ , 𝑥 _ _ are x- coordinates of the CoP under the left and right feet at time point i, and
forces acting on the body from each force plate. These coordinates are expressed
𝑀 _ ,𝑀
are coordinates
directional components
of the moments
andthe
actingcoordinates
on the body of the
from
each
forceplate.
relative
_ , 𝐹 _ , 𝐹These
relative
to
the
global_ coordinates
ofare
theexpressed
laboratory
spaceto
byforces
a global
translation
between
each
These
coordinates
areorigin
expressed
to the global
coordinates
the from
origin
offorceplate.
the force
plate
and the
of relative
the laboratory
(plate
originofxl,the
plate
originxr) .
144
144
The x-coordinate of the CoP of the whole body was calculated by multiplying the xcoordinate of the CoP for each limb by the fraction of the total vertical force (Fz)
acting through that limb, and adding the two terms together, as follows:
x-coordinate of the CoP of the whole body was calculated by multiplying the x-coordinate of the
the twoThe
terms
together, as follows:
for each limb
by the
of the body
total vertical
force (Fz)by
acting
through the
thatx-coordinate
limb, and adding
The CoP
x-coordinate
of the
CoPfraction
of the whole
was calculated
multiplying
of the
as follows:
CoPthe
fortwo
eachterms
limbtogether,
by the fraction
of the total vertical force (Fz) acting through that limb, and adding
the two terms together, as follows:
𝑥
= 𝑥
_
𝑥
𝑥
where 𝑥
_
_
_
_
= 𝑥
∗
∗
_
= 𝑥
_
𝐹 _
𝐹 _ 𝐹+ 𝐹
_
_
𝐹
+ 𝐹
_
𝐹 _
∗
𝐹 _ + 𝐹
+𝑥
+𝑥
_
+𝑥
_
𝐹 _
𝐹𝐹 _ + 𝐹
∗
_
_
_
∗
_
𝐹 _
∗
𝐹 _ + 𝐹
𝐹
_
+ 𝐹
is the x-coordinate of the CoP of the whole body.
_
_
_
where
𝑥 x_CoP_i
is the
x-coordinate
of theofCoP
the whole
where
is the
x-coordinate
theofCoP
of thebody.
whole body.
where 𝑥 _ is the x-coordinate
of the of
CoPthe
of theroot
wholemean
body. squared error of the centre of
5.7.2.16.11.2.1
5.7.2.16.11.2.1 Calculation
Calculation
of the
root
mean
squared error of the centre of
Calculation
of the
root
mean squared error
of the(CoP
centre
of
pressure
in
the
antero-posterior
direction
(CoP
pressure
in the
antero-posterior
direction
) AP) in the anteroRMSE
RMSE
APpressure
posterior direction (CoP
)
RMSE AP of the root mean squared error of the centre of
5.7.2.16.11.2.1
Calculation
The root mean squared error of the CoP in the antero-posterior direction (x-direction) is given by:
The root mean
squaredinerror
of the CoP in the antero-posterior
direction
(x-direction) is given by:
the
antero-posterior
(CoP
RMSE
AP)
Thepressure
root mean
squared
error of thedirection
CoP in the
antero-posterior
direction (x-
direction) is given by:
The root mean squared error of the CoP in the antero-posterior direction (x-direction) is given by:
𝐶𝑜𝑃
𝐶𝑜𝑃
𝑥
=
_
_
𝑥
=
_
𝐶𝑜𝑃
𝑥
=
_
_
−𝑥 _
_𝑁 − 𝑥
𝑁
−𝑥
𝑁
_
_
where 𝑥 _ is the mean position of the x-coordinate of the CoP, and N is the number of time points
in the trial.
where 𝑥 _ is the mean position of the x-coordinate of the CoP, and N is the number of time points
where
is the
meanofposition
of the x-coordinate
of Nthe
CoP,
and N
is the
where
𝑥 _ isxCoP_i
the mean
position
the x-coordinate
of the CoP, and
is the
number
of time
points
in the
trial.
5.7.2.26.11.2.2
Calculation of centre of pressure velocity in the antero-posterior
number of time points in the trial.
in the trial.
direction (CoP VEL AP)
5.7.2.26.11.2.2
of centre ofdirection
pressure
velocity
in the
The mean velocity ofCalculation
the
CoP in the antero-posterior
(x-direction)
is given
by: antero-posterior
5.7.2.26.11.2.2
Calculation
of
centre
of
pressure
velocity
in
the
antero-posterior
Calculation
of centre
of pressure velocity in the antero-posterior direction (CoPVEL
direction (CoP
VEL AP)
AP)
direction (CoP VEL AP)
𝑥 direction
− 𝑥 _(x-direction)
The The
mean
velocity
the
antero-posterior
(x-direction)
is given
The
meanofvelocity
of in
the
CoP
in the antero-posterior
direction
(x-direction)
given
_ direction
mean
velocity
of
theCoP
CoP
inthe
the
antero-posterior
is given
by: isby:
by:
𝐶𝑜𝑃
_
=
where fs is the data sampling𝐶𝑜𝑃
frequency.
=
_
𝐶𝑜𝑃
_
=
∗𝑓
𝑁
𝑥𝑥
𝑥
_ _− −
145
where fs is the data sampling frequency.
fs is the
data sampling
frequency.
where fs iswhere
the data
sampling
frequency.
145
145
𝑥_
𝑁𝑁
_
∗ 𝑓∗ 𝑓