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Leendert Blankevoort
03-08-1990, 08:46 PM
Dear Biomch-L readers,

Following the discussions on the description of joint motions, I would
like to contribute the following points, which are based on the experiences
we have in our Biomechanics Lab. at the University of Nijmegen. My
intention is not to be in favor of any proposed convention, but to discuss
some items which were not directly addressed as yet and to clarify some
points.

1) JCS vs. Euler/Cardan angles

According to our analyses, the rotations in the JCS system and the Euler/
Cardan angles are equivalent, provided that the rotation sequence is
applied which is implied in the geometric definition in the JCS system.
This can be derived from the equations given in the paper of Grood and
Suntay (1983). For instance, if for the knee flexion, ad-abduction (or
varus-valgus) and internal-external rotation are specified of the tibia
relative to the femur, then in the JCS system the flexion axis is fixed to
the femur, the ad-abduction angle is the floating axis and the internal-
external rotation axis is fixed to the tibia. Using the Euler/Cardan
convention, the rotations are then specified as rotations around the body-
fixed axes of the tibia moving relative to a space fixed femur for which
the rotation sequence flexion, ad-abduction, internal-external rotation is
to be used in order to obtain the same values for the rotations as in the
JCS system. I believe that despite the controversies between Grood and
Woltring, both "chief" discussers can agree on this.

2) Translations

So far much of the attention was paid to the rotations and only little was
said on the translations, probably because the rotations are considered to
be clinically meaningful. However, the anteroposterior translations as
measured in instrumented AP-laxity tests, are important for quantifying AP
laxity and AP stiffness. The value of the translations of one bone
relative to another depend on the choice of the so-called base points,
which generally are identical with the origins of the coordinate systems in
the bones. Thus, special care is to be taken when comparing translational
data between different research groups and between different measurement
devices. When using the finite helical axis description, the translation
along the axis is independent of the choice of the coordinate systems and
represents the "true" translation of one bone relative to another for a
finite motion step. For pure translations however, the helical axis is not
defined, but then the value of the translation does not depend of the
choice of the base point.

3) Variations of the coordinate systems in experiments

As pointed out by Meglan, variations of the orientation of the coordinate
systems relative to the joint anatomy and the variations of the anatomic
reference position account, at least partly, for the differences in the
resulting rotations between joint specimens or between subjects. This was
discussed and illustrated in a paper from our group in the Journal of
Biomechanics in 1988 (Blankevoort et al., 1988). This does not mean that
as long as we are not able to uniquely define coordinate systems in
different joint specimens or different individuals, we should not bother
about the choice of the kinematic convention for the reason that the
variations between the convention are smaller than the observed variations
between joint specimens or individuals. Different kinematic conventions
will introduce systematic differences which have no relation whatsoever
with biologic variations or statistical standard deviations.

4) Mathematics and representation

The present discussion at the list was mainly focussed on how the rotations
are to be represented. Of course, if one is presenting data on joint
angles, then the mathematical background is to be specified. The reader
can then always reconstruct the motion patterns and express them with his
(or hers) own convention. However, most of the reports fail to give all
numbers, e.g. three rotations and three translations, because only those
data is reported which is relevant to the subject of the paper. Some
standardization may be necessary for commercially available measurement
systems to be used on a routine basis in the clinic. However, during the
process of data acquisition and data processing or in the formulations of
kinematic models, one is free to use any of the conventions as long as it
meets the criteria for the data processing and the mathematics of the
model. In the final stage, the kinematics data can be transformed to any
desired system. For instance in gait analysis, one can process the marker
data by some rotation convention which is found to suit best the
requirements for the subsequent dynamic analyses and can represent the
kinematics by use of the JCS or the Woltring system.

5) Future steps

Following the discussions on the list, it became clear to me that because
of the complexity of the description of 3-D joint motions, there remains a
lot of "teaching" to do in the field of Biomehcanics to make clinicians,
anatomists as well as biomechanicians aware of the difficulaties and
pitfalls of kinematics. Basic understanding seems more important than the
normalisation of motion description by adopting some standard convention,
since the consequences of any choice should be properly understood by the
users of such standard system. I am certainly in favor of producing an
extensive paper (or maybe a book?) on the ins and outs of biokinematics,
which should be aimed at a broad audience in the field of biomechanics, to
people with a poor mathematical background as well as people with poor
knowledge of (human) anatomy. I encourage Grood and Woltring to write
something (after they have cleared their confusions).


References

Grood, E.S. and Suntay, W.J. (1983) A joint coordinate system for the
clinical description of three-dimensional motions: applications to the
knee. J. Biomech. Engng 105, 136-144.

Blankevoort, L., Huiskes, R., Lange, A. de (1988) The Envelope of passive
knee joint motion. J. Biomechanics 21, 705-720.


Leendert Blankevoort
Biomechanics Section
Institute of Orthopedics
University of Nijmegen
P.O.box 9101
NL-6500 HB NIJMEGEN
The Netherlands

U462005@HNYKUN11.EARN