Biomedical Engineering Reference
In-Depth Information
7.1.1 Global Reference System
For purposes of convenience, we will be consistent in our axis directions
for the GRS: X is the forward/backward direction, Y is the vertical (gravita-
tional) axis, and Z is the left/right (medial/lateral) axis. Thus, the XZ plane
is the horizontal plane and, by definition, is orthogonal to the vertical axis.
The directions of these GRS axes are the same as those of the axes in the
force plate. To ensure that this is so, a spatial calibration system (a rigid
cubic frame or a rigid 3D mechanical axis) is instrumented with markers
and is placed on one of the force plates and aligned along the X and Z
axes of the force platform. The position of each of the markers relative to
the origin of the force plate is known and fed into the computer. If more
than one force platform is used, the origin of each additional platform is
recorded by an X and Z offset from the primary platform. An additional
offset in the Y direction would be necessary if the additional platform were
at a different height from the first (as would be necessary for a biomechan-
ical analysis of stairway or ramp walking). Many laboratories have a fixed
arrangement of cameras, so there is no need to recalibrate the GRS every day;
such is the case in clinical gait laboratories. Such a system is illustrated in
Chapter 3; see Figure 3.12. However, in many research situations, the cam-
eras are rearranged to best capture the new movement and, therefore, require
a new calibration of the GRS. Once the calibration is complete, the cameras
cannot be moved, and care must be taken to ensure they are not accidentally
displaced.
7.1.2 Local Reference Systems and Rotation of Axes
Within each segment, the anatomical axis system is set with its origin at
the center of mass (COM) of the segment, and its principal y -axis usually
along the long axis of the segment or, in the case of segments like the
pelvis, along a line defined by skeletal landmarks such as PSIS and ASIS.
The other local axis system is constructed on the segment by using a set of
surface markers. A total of two transformations are necessary to get from
the GRS to the marker axis system and from the marker to the anatomical
axis system. Figure 7.1 shows how one of those rotations is done. The axis
system x , y , z needs to be rotated into the system denoted by x , y , z .
Many sequences of rotation are possible; here, we use the common Cardan
sequence x - y - z . This means that we rotate about the x axis first, about the
new y axis second, and about the new z axis last. The first rotation is θ 1
about the x axis to get x , y , z . Because we have rotated about the x axis,
x will not be changed and x =
x , while the y axis changes to y and the z
axis to z . The second rotation is θ 2 about the new y
axis to get x , y , z .
Because this rotation has been about the y
y . The final rotation is
θ 3 about the new z axis to get the desired x , y , z . Assuming that we have
a point with coordinates x 0 , y 0 , z 0 in the original x , y , z axis system, that same
axis, y =
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