Biomedical Engineering Reference
In-Depth Information
4.
The third coordinate axis is computed to be orthogonal to the first two axes. Compute the
vector cross product
e
ttz
e
ttx
to determine the medial-lateral direction, or
y
-axis, of the thigh
technical coordinate system:
e
tty
¼
e
ttz
e
ttx
¼
0
:
012
i
þ
0
:
943
j
þ
0
:
332
k
For this example, the technical coordinate system for the thigh can be expressed as
2
4
3
5
¼
2
4
3
5
2
4
3
5
e
ttx
e
tty
e
ttz
0
:
996
0
:
040
0
:
079
i
j
k
f
e
tt
g¼
0
:
012
0
:
943
0
:
332
0
:
088
0
:
330
0
:
940
computed during the standing subject
calibration can also be computed from each camera frame of walking data. That is, its computa-
tion is based on markers (the lateral femoral condyle and thigh wand markers) and an anatomical
landmark (the hip center) that are available for both the standing and walking trials. Conse-
quently, the technical coordinate system
Note that this thigh technical coordinate system
f
e
tt
g
becomes the embedded reference coordinate system
to which other entities can be related. The thigh anatomical coordinate system
f
e
tt
g
f
e
ta
g
can be related
to the thigh technical coordinate system
by using either direction cosines or Euler angles, as
described in Section 4.2.2. Also, the location of markers that must be removed after the standing
subject calibration (e.g., the medial femoral condyle marker MK), or computed anatomical loca-
tions (e.g., the knee center) can be transformed into the technical coordinate system
f
e
tt
g
f
e
tt
g
and later
retrieved for use in walking trial data reduction.
Segment and Joint Angles
Tracking the anatomical coordinate system for each segment allows for the determi-
nation of either the absolute angular orientation, or attitude, of each segment in space or
the angular position of one segment relative to another. In the preceding example, the three
pelvic angles that define the position of the pelvic anatomical coordinate system
e
pa
g
relative to the laboratory (inertially fixed) coordinate system can be computed from the
Euler angles, as described in Section 4.2.2 with Eqs. (4.32)-(4.34). Note that in these equa-
tions the laboratory coordinate system represents the proximal (unprimed) coordinate sys-
tem, and the pelvic anatomical coordinate system
f
f
e
pa
g
represents the distal (triple primed)
coordinate system. Consequently, Eq. (4.32)
k
000
y
x
¼
arcsin
ð
j
Þ
becomes
y
x
¼
arcsin
ð
e
paz
j
Þ
¼
arcsin
ðð
0
:
188
i
0
:
024
j
þ
0
:
982
k
Þ
j
Þ
¼
arcsin
ð
0
:
024
Þ
1
of pelvic obliquity
¼
