Dear Biomch-L readers,

Now that Herman Woltring has shown us the mathematical
relationships between various definitions of joint
moments/forces, as well as the 3-dimensional generalization, I
want to point out a difference between two views on dynamic
analysis. In my view this is important to clarify the discussion.

Herman is deliberately limiting the discussion to *net* joint
kinetics, i.e. the model consists of rigid links with one force
and one moment transmitted by each joint. These variables are
calculated, plus sometimes the joint powers (moment x angular velocity).
The analysis essentially stops there, and individual muscles are
not part of the model. This is probably a good method for clinical
gait analysis, because no detailed information on muscle lines of
action is needed, and no assumptions on load sharing of muscles have to
be made. However, these joint forces and moments are not physical
quantities but mathematical abstractions: they do not exist at all
anywhere in the system. When I say 'not exist', I mean that there
is no anatomical structure loaded by (= deformed as a function of)
either the force or the moment. Is that not a good definition of
'physical existence' of a force: that it produces a deformation
somewhere that has a one-to-one relationship to the force? Hmm,
you could even say that force is then also a mathematical
abstraction, and that only stresses 'exist'. But let's accept the
concept of force (muscle force, ligament force, contact force...)
for now.

Another way to look at 'net kinetics' analysis is as a
transformation of the original kinematic, kinetic and
anthropomorphic measurements, intended to facilitate the
(clinical) quantification of 'gait quality' or the recognition of
certain abnormalities. A mechanical interpretation of the
resulting 'net kinetics' variables is not the real purpose of the
analysis (apart from the fact that, strictly speaking, it is not
even allowed - see above). Looking at it this way, I must agree
with Ian Stokes that it does not really matter which reference
point is used to calculate the joint moment. Just as long as you
use the same reference point when comparing results, and the
variables obtained still contain useful information. In fact,
using a fixed point is to preferred above the elusive ICR. The
ICR can only be estimated when the kinematic data are of
sufficient quality, and even then requires sophisticated filtering
and analysis methods. For such a 'net kinetic' analysis it might
be more reliable to use the lateral epicondyle as reference at the
knee, rather than the ICR, because it can be marked directly and
measured by the measuring system. The choice of reference point
does require standardization however, to avoid problems when
comparing published results.

Many biomechanicians however, *are* interested in real muscle
forces and real joint forces, and try to estimate them as well as
possible. These forces are not mathematical but physical
quantities. There are of course the well-known indeterminacy
problems because the equilibrium equations for moment and force
often have too many unknowns. For some situations however, such an
analysis is the right tool for the job. In that case, the reasoning
of my previous posting applies: the ICR is the only point about which the
moment arms of muscle forces (dL/dA) and joint forces (zero) are easy to
obtain. (For simplicity I limit the discussion to 2D). Note that the
'net joint force' resulting from this type of analysis is not the same
as in the 'net kinetics' analysis, but is much larger (and more
realistic). This force may also be only a resultant of several physical
(contact & ligaments) forces, but the muscle forces that have been
obtained are real physical quantities.

So my revised opinion is: use the ICR as reference point when
estimating muscle and joint forces. For a 'net kinetic' analysis,
only standardization is required; there is no preferred reference
point. Clinical usefulness seems to be more important than mechanical
interpretation in that case.

Finally, this is probably a very academic discussion without
practical implications; the various definitions reviewed by Ian
Stokes produce very similar results. But sometimes it is
enlightening to think about why you do things one way, and not the
other way.

-- Ton van den Bogert
University of Utrecht, Netherlands