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Center of Rotation - Joint moment debate

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  • Center of Rotation - Joint moment debate

    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