Dear Biomch-l Readers,

The Joint moment - center/axis of rotation (C of R) debate is, I
believe, most important to the fields of Biomechanics and Human Motion
science. Therefore, I am glad that the discussion initiated by Fabio Catani
which I joined lately has provoked so much discussion and debate. My own
contribution, in which I argued that the C of R is *not* an appropriate
reference point for consideration of joint moments has stimulated a number of
further contributions which have been most helpful. Some of these postings
have invited me to respond, but as fast as I have tried to collect my
thoughts, new ideas and opinions have been posted! I should add that other
contributors have more experience of this kind of biomechanics in practice,
but perhaps I have something to offer at least from a theoretical point of
view. As of today I believe I understand the following:

1. Force and moment equilibrium about joints is a common tool in biomechanics.
Many text books and many courses in biomechanics teach that the C of R is the
reference point about which we consider moment equilibrium, because the joint
force passes through it. The literature in the Journal of Biomechanics (and
elsewhere) is not consistent about this reference point - centers of curva-
ture, contact and rotation are used singly and in combination. Theoretical
considerations support all of these (with certain conditions such as neg-
ligible friction and surface compliance). We can prove this by analyzing
geometry, statics and/or virtual work.

2. Practical considerations depend on the purpose of the study/analysis.
Biomechanics studies can be divided into:
- Quasi-static vs. dynamic analyses and
- Studies of internal forces vs. studies of joints as actuators
(actuators transmit torques and generate power).
Considering dynamic analyses, use of the C of R is simpler, because relative
motion has fewer degrees of freedom about the center/axis of motion.
Therefore, the inertial terms are easier to deal with. However, the practical
problems of finding the C of R are great, so in some joints and some situa-
tions it would be better to look at the anatomy and constraints, and use other
information (fixed center of rotation, or knowledge of joint contact or center
of curvature).
Considering 'joints as actuators' (net moments) vs. 'internal forces', the
important question to ask is 'does it matter?' The objective in both cases is
to have an expression for joint moment which includes the effects of muscles,
in equilibrium with external and inertial forces. The joint force should be
excluded by considering moments about a point on its line of action.
(Ligament forces, and joints with two condyles complicate this.) It seems
that the net moment on each side of this equilibrium is sensitive to the point
about which moments are calculated, except that if the muscles forces are
nearly parallel to the joint force, as probably is often true, the sensitivity
could be small compared to other sources of errors. Certainly, in 'net
moment' measurement and reporting for any particular joint, standardization in
the biomechanics field would be very helpful.

3. As biomechanicians and teachers the most important thing we must remember
is to be critical and to be sure of the assumptions on which we base our
analyses. This is especially important in multi-disciplinary cases in which
studies/analyses may be done by one person and interpreted or applied by
another. This happens often in the clinical field where scientific findings
from studies of a few people in a controlled research situation may be applied
to a larger population. Also, sophisticated equipment, designed with known
limitations can be adapted to turn-key operation for people not necessarily
trained in all aspects of its interpretation. In anything as complex as human
joint function there are no simple answers, but the basic principles must be
clear to us before we get into the complexities. This debate certainly has
helped me.

Ian Stokes