Biomedical Engineering Reference
In-Depth Information
for the anatomical knee vector and for the anatomical vectors of the three
tracking markers
m
T
1
,
m
T
2
and
m
T
3
, we would calculate the following:
Anatomical knee
vector
Anatomical
m
T
1
vector
Anatomical
m
T
2
vector
Anatomical
m
T
3
vector
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
0
13
.
86
≈
≈
4
.
139
2
.
371
0
.
197
0
.
000
−
1
.
770
13
.
974
−
⎣
⎦
⎣
⎦
⎣
⎦
⎣
⎦
−
17
.
991
−
0
3
.
833
5
.
508
We are now ready to calculate the constant marker-to-anatomical matrix
([M to A] in Figure 7.2). The three tracking markers form a plane in the GRS,
and we can now define our maker axes in that plane.
m
T
2
is chosen as the
origin of the marker plane, and the line joining
m
T
2
to
m
T
3
is chosen to be
the
z
axis, labeled
z
m
. The line joining
m
T
2
to
m
T
1
is a vector labeled
a
(an
interim vector to allow us to calculate
y
m
and
x
m
).
y
m
is normal to the plane
defined by
z
m
and
A
and
x
m
, is normal to the plane defined by
y
m
and
z
m
.
z
m
=
local
m
T
3
−
local
m
T
2
:[
−
1
.
770, 31
.
965,
−
1
.
675]
A
vector
=
local
m
T
1
−
local
m
T
2
:[4
.
139, 20
.
362, 4
.
030]
y
m
=
168
.
344]
x
m
=
(y
m
×
z
m
)
: [5380
.
78, 570
.
87, 5208
.
25]
(z
m
×
A
vector
)
: [162
.
925, 0
.
200,
−
The normalized axis for this leg anatomical-to-marker matrix [LA to M] is:
⎡
⎤
0
.
7164
0
.
0760
0
.
6935
⎣
⎦
0
.
6954
0
.
0008
−
0
.
7186
−
0
.
0552
0
.
9971
−
0
.
0522
The fixed leg marker-to-anatomical matrix [LM to A] is the transpose of
[LA to M]:
⎡
⎤
0
.
7164
0
.
6954
−
0
.
0552
⎣
⎦
0
.
0760
0
.
0008
0
.
9971
0
.
6935
−
0
.
7186
−
0
.
0522
7.2.1.2 Tracking Markers — Calculation of [Global to Marker] Matrix.
We are now ready to calculate the [G to M] matrix in Figure 7.2. Table 7.2
lists representative GRS coordinates for the leg segment for three successive
frames of walking taken during the swing phase. The procedure to calculate
this [G to M] matrix is exactly the same as the latter part of the calculation
of the [M to A] matrix. Consider the coordinates for frame 6:
z
m
=
(m
T
3
−
m
T
2
)
:[
X
z
=
24
.
34,
Y
z
=
19
.
99,
Z
z
=−
3
.
64]
a
vector
=
(m
T
1
−
m
T
2
)
:[
X
a
=
18
.
86,
Y
a
=
9
.
15,
Z
z
=
4
.
09]
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