Biomedical Engineering Reference
In-Depth Information
Figure 4.9
Technique used to calculate the axis of rotation between two adjacent
segments
x
c
,
y
c
. Each segment must have two markers in the plane of movement. After
data collection, the segments are rotated and translated so that one segment is fixed in
space. Thus, the moving-segment kinematics reflects the relative movement between
the two segments and the axis of rotation can be located relative to the anatomical
location of markers on that fixed segment. See text for complete details.
segments. Figure 4.9 shows two segments in a planar movement. First, they
must be translated and rotated in space so that one segment is fixed in space
and the second rotates as shown. At any given instant in time, the true axis
of rotation is at (
x
c
,
y
c
) within the fixed segment, and we are interested in
the location of (
x
c
,
y
c
) relative to anatomical coordinates (
x
3
,
y
3
) and (
x
4
,
y
4
)
of that segment. Markers (
x
1
,
y
1
) and (
x
2
,
y
2
) are located as shown; (
x
1
,
y
1
)
has an instantaneous tangential velocity
V
and is located at a radius
R
from
the axis of rotation. From the line joining (
x
1
,
y
1
)to(
x
2
,
y
2
), we calculate
the angular velocity of the rotating segment
ω
z
. With one segment fixed in
space,
ω
z
is nothing more than the joint angular velocity,
V
=
ω
z
×
R
(4.16
a
)
or, in Cartesian coordinates,
=
R
y
ω
z
i
V
x
i
V
y
j
(R
x
ω
z
) j
+
−
Therefore,
V
x
=
R
y
ω
z
and
V
y
=−
R
x
ω
z
(4.16
b
)
Since
V
x
,
V
y
, and
ω
z
can be calculated from the marker trajectory data,
R
y
and
R
x
can be determined. Since
x
1
,
y
1
is known, the axis of rotation
x
c
,
y
c
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