Biomedical Engineering Reference
In-Depth Information
TABLE 7.2
Tracking Markers during Walking
m
T
1
m
T
2
m
T
3
Frame
X
Y
Z
X
Y
Z
X
Y
Z
5
20.65
33.87
35.95
1.30
25.74
32.14
26.52
44.43
28.10
6
25.46
34.47
35.95
6.60
25.32
31.86
30.94
45.31
28.22
7
30.18
34.97
35.94
11.98
24.64
31.60
35.08
46.10
28.36
y
m
=
(z
m
×
a
)
: [115
.
065,
−
168
.
201,
−
154
.
30]
x
m
=
(y
m
×
z
m
)
: [3696
.
709,
−
3336
.
825, 6394
.
162]
The normalized axis for this leg [G to M] matrix for frame 6 is:
⎡
⎤
0
.
4561
−
0
.
4117
0
.
7889
⎣
⎦
0
.
4501
−
0
.
6580
−
0
.
6037
0
.
7677
0
.
6305
−
0
.
1148
7.2.1.3 Calculation of [Global to Anatomical] Matrix.
From Figure 7.2,
the final step is to calculate the [G to A] matrix that is the product of the
fixed [M to A] matrix and the variable [G to M] matrix; for frame 6 this
product is:
⎡
⎤
⎡
⎤
0
.
7164
0
.
6954
−
0
.
0552
0
.
4561
−
0
.
4117
0
.
7887
⎣
⎦
⎣
⎦
0
.
0760
0
.
0008
−
0
.
9971
0
.
4501
−
.
6580
0
.
6037
0
.
6935
0
.
7186
−
0
.
0522
0
.
7677
0
.
6305
−
0
.
1148
⎡
⎤
0
.
5974
−
0
.
7873
0
.
1515
⎣
⎦
=
0
.
8000
0
.
5969
−
0
.
0550
−
0
.
0472
0
.
1544
0
.
9868
From Equation (7.5), this [G to A] matrix is equal to:
⎡
⎤
c
2
c
3
s
3
c
1
+
s
1
s
2
c
3
s
1
s
3
−
c
1
s
2
c
3
⎣
⎦
−
c
2
s
3
c
1
c
3
−
s
1
s
2
s
3
s
1
c
3
+
c
1
s
2
s
3
s
2
−
s
1
c
2
c
1
c
2
We now solve this matrix to get
θ
1
,
θ
2
, and
θ
3
. Equating the three terms in
the
bottom
row:
s
2
=−
0
.
0472,
−
s
1
c
2
=
0
.
1544,
c
1
c
2
=
0
.
9868
.
∴
θ
2
=
2
.
71
◦
177
.
29
◦
;
2
.
71
◦
,
−
or
assuming
θ
2
=−
c
2
=
0
.
99888
or
−
0
.
99888,
8
.
92
◦
or
8
.
92
◦
.
c
1
c
2
=
0
.
9868,
∴
c
1
=
0
.
9868
/
0
.
99888
=
0
.
9879, and
θ
1
=
−
8
.
92
◦
because
∴
s
1
=
0
.
1550 or - 0.1550. We now validate that
θ
1
=−
−
s
1
c
2
≈
0
.
1544. We now use the first two terms in the first column to calculate
and
validate
θ
3
:
c
2
c
3
=
0
.
5974,
−
c
2
s
3
=
0
.
8000.
c
3
=
0
.
5974
/
0
.
99888
Search WWH ::
Custom Search