Biomedical Engineering Reference
In-Depth Information
Similarly, Eq. (4.33)
k
000
ð
Þ
cos y
x
i
y
y
¼
arcsin
becomes
0
@
1
A
ð
e
paz
i
Þ
y
y
¼
arcsin
cos y
x
0
@
1
A
ð
0
:
188
i
0
:
024
j
þ
0
:
982
k
Þ
i
¼
arcsin
cos 1
0
@
1
A
0
188
cos 1
:
¼
arcsin
11
of anterior pelvic tilt
¼
and Eq. (4.34)
i
000
ð
Þ
cos y
x
j
y
z
¼
arcsin
becomes
0
1
ð
e
pax
j
Þ
@
A
y
z
¼
arcsin
cos y
x
0
1
ð
0
:
974
i
0
:
123
j
0
:
190
k
Þ
j
@
A
¼
arcsin
cos 1
0
@
1
A
123
cos 1
0
:
¼
arcsin
7
of pelvic rotation
This Euler angle computation may be repeated to solve for the three hip angles that
define the position of the thigh anatomical coordinate system
¼
f
e
ta
g
relative to the pelvic
anatomical coordinate system
. For the hip angles, the proximal (unprimed) coordinate
system is the pelvis and the distal (triple-primed) coordinate system is the thigh. Substitut-
ing the values of
f
e
pa
g
f
e
pa
g
and
f
e
ta
g
from Example Problems 4.10 and 4.11 into Eq. (4.32) yields:
y
z
¼
arcsin
ð
e
taz
e
pay
Þ
¼
arcsin
ðð
0
:
137
i
þ
0
:
175
j
þ
0
:
975
k
Þð
0
:
125
i
þ
0
:
992
j
þ
0
:
000
k
ÞÞ
¼
arcsin
ð
0
:
156
Þ
9
of hip abduction-adduction
¼
