Biomedical Engineering Reference
In-Depth Information
z
0
and
the coefficients in the expression for
e
faz
represent the cosines of the angles between
,
z
0
and
,and
z
0
and
. Consequently, these relationships can be transposed as
x
y
z
977
i
0
þ
0815
j
0
þ
195
k
0
i
¼
0
:
0
:
0
:
102
k
0
0624
i
0
þ
993
j
0
j
¼
0
:
0
:
0
:
975
k
0
202
i
0
þ
0877
j
0
þ
k
¼
0
:
0
:
0
:
In this form, these relationships can be used to transform vectors expressed in terms of
lab coordinates:
A
¼
A
x
i
þ
A
y
j
þ
A
z
k
into foot coordinates:
¼
A
x
i
0
þ
A
y
j
0
þ
A
z
k
0
A
To demonstrate this process, consider the foot angular velocity vector
v
¼
0
:
042
i
þ
2
:
22
j
0
:
585
k
rad
=
s
foot
Substituting the relationships for the lab coordinate system in terms of the foot coordi-
nate system,
v
foot
becomes
v
foot
977
i
0
þ
0815
j
0
þ
195
k
0
Þ
¼
0
:
042
ð
0
:
0
:
0
:
0624
i
0
þ
993
j
0
102
k
0
Þ
þ
2
:
22
ð
0
:
0
:
0
:
202
i
0
þ
0877
j
0
þ
975
k
0
Þ
0
:
585
ð
0
:
0
:
0
:
789
k
0
rad
0210
i
0
þ
16
j
0
¼
0
:
2
:
0
:
=
s
In a similar manner, the other vectors required for the computation are transformed into
the foot coordinate system:
r
1
¼
0
:
032
i
þ
0
:
002
j
þ
0
:
002
k
032
i
0
004
k
0
m
¼
0
:
0
:
r
2
¼
0
:
033
i
0
:
005
j
0
:
054
k
0435
i
0
007
j
0
0457
k
0
m
¼
0
:
0
:
0
:
F
g
¼
3
:
94
i
15
:
21
j
þ
242
:
36
k
16
i
0
þ
47
j
0
þ
62
k
0
N
¼
44
:
6
:
238
:
T
g
¼
995
k
¼
0
:
201
i
0
þ
0873
j
0
þ
970
k
0
Nm
0
:
0
:
0
:
F
A
¼
3
:
18
i
þ
15
:
1
j
239
k
2
i
0
23
j
0
235
k
0
N
¼
44
:
6
:
v
¼
0
:
0420
i
þ
2
:
22
j
0
:
585
k
foot
021
i
0
þ
16
j
0
789
k
0
rad
¼
0
:
2
:
0
:
=
s
a
¼
0
:
937
i
þ
8
:
85
j
5
:
16
k
foot
425
i
0
þ
26
j
0
116
k
0
rad
s
2
¼
0
:
8
:
6
:
=
