View Full Version : Joint centers (was: Wobbling mass model)

unknown user
02-23-1991, 12:03 PM
Dear BIOMCH-L readers,

In his discussion of the 'wobbling mass' model, Herman Woltring has
raised the question whether the assumption of fixed joint centers would
cause significant errors in the estimation of joint contact forces. I
think it will, because an essential step before joint forces are
calculated, is the calculation of muscle forces. This involves two
basic problems: the distribution criterion and the moment arms of the
muscles. The moment arms have usually been calculated with respect to a
fixed joint center, and we all know that such a thing does not exist in
the knee joint. Estimated forces will contain relative errors as large
as the error in the joint center location, divided by the moment arm.

An elegant way to get rid of fixed joint centers has been demonstrated
in the December (1990) issue of the Journal of Biomechanics by Cees Spoor
and co-workers from the University of Leiden, Netherlands. The
instantaneous moment arm of a muscle (conventionally defined as the
perpendicular distance from the line of action to the instantaneous
joint center) can also be defined as the partial derivative of the
muscle length with respect to the angle of the joint. So, you only need
to know how the length of a muscle depends on joint angles (from cadaver
measurements), and *not* the location of the actual joint center at each
instant in time. The method also solves another problem: that of a
muscle not following the shortest path from origin to insertion when it
curves around bone or other muscles. Conventional models have great
difficulty describing this.

If this principle (of virtual work) is also used to determine the
moment arm of an external (ground reaction) force, assumptions on the
kinematical properties of joints will no longer be a source of error in
inverse dynamics analysis. Inertial forces require some special
attention though.

Sometimes, e.g. in a 'forward' simulation, we *do* want to describe
exactly how the segments are kinematically coupled, but modern multibody
software packages (e.g. DADS) contain a rather extensive library of
kinematic connections.

-- Ton van den Bogert
Faculty of Veterinary Medicine
University of Utrecht