View Full Version : Inertial parameters and their role in joint loading

Zvi Ladin
06-01-1994, 06:26 AM
In recent postings Brian Davis and Paul Devita discussed the role of
the inertial parameters in the determination of joint moments, suggesting
that even large errors in the inertial parameters will lead to relatively
small errors in the calculated moments. I would like to address two
issues that are related to this discussion - the overall magnitude of
the inertial loads (i.e. forces and moments that arise from the motion
of the body segments), and the role of the inertial parameters in the
determination of the inertial loads.

In a study that Ge Wu (who is now at Penn State) and I conducted a few
years ago, we used the kinematometers (devices that combine position
markers, linear accelerometers and angular velocity sensors) to monitor the
kinematics of the lower limb during physical activities ranging from
slow walking to jumping. We then compared the magnitudes of inertial
and static components of the joint loads (forces and moments). The
results were presented last year, during the Second International
Symposium on 3-D Analysis of Human Movement (Poitiers, France), and
in summary we found that the inertial effects are largest in the
transverse plane and that they increase in magnitude in the proximal
direction and with an increase in the speed of the activity.

We compared the ratios of the maximum inertial forces to the maximum
static forces (i.e. the forces needed to maintain equilibrium).
In SLOW WALKING the maximum inertial forces for the ankle were on the
order of 3-6% (of the maximum static forces) in the vertical direction,
16% in A-P direction and 60-80% in the M-L direction.
The corresponding values for the hip were 20% in the vertical direction,
100-110% in the A-P direction and 200-300% in the M-L direction.

As the speed of the activity increased, we saw the expected increase in
the inertial effects, leading to inertial forces that were either HIGHER
than or similar to the static components in the A-P and M-L directions,
and are on the order of 10-20% in the vertical direction. These results
would be linearly affected by errors in the segmental masses.

The corresponding values for the moments were generally smaller, however
even there we saw values that were on the order of 20-40% in the medial
direction for running.

As both Devita and Davis suggest, the results of the moments will
be very sensitive to errors in the locations of the joints, however,
since the accepted practice of the inverse dynamic solution of the moment
equations invovles conducting the calculations in a Body Coordinate
System centered at the segmental center of mass, any errors in the location
of the COM would have just as grave consequences as errors in the locations
of the joint centers (since the equations contain terms that are the radii
vectors from the segmental COM to the joint centers).


Ge Wu and Zvi Ladin. The effect of inertial load pm human joint force
and moment during locomotion. Proceedings of the Second International
Symposium on Three-Dimensional Analysis of Human Movement, 6/30-7/3/1993,
Poitiets, France, pp 106-107.

Zvi Ladin
Biomedical Engineering Department
Boston University
e-mail: ZL@buenga.bu.edu