View Full Version : Instantaneous Helical Axis

Dewitt, John
06-07-1993, 08:12 AM

Dear Biomech-l Colleagues,

I am currently conducting research in kinematically defining leg motion
in chiropractic patients who have exhibited symptoms of leg length inequality
(LLI). This LLI is physiological in nature, hypothesized to be caused by
musculature imbalance somewhere in the back. It has been reported that
chiropractic adjustment results in alleviation in pain related to the LLI
phenomenon. My research partners and I are in the process of quantitatively
assessing apparent LLI cases. Since the LLI is not a structural problem,
adjustments which cause realligment of the legs should result in one of 3

1) One leg moves inferior while the other remains stationary
2) One leg moves superior while the other remains stationary
3) One leg moves superior while the other moves inferior

Regardless of which case is occuring, there must exist some translation, and
probably rotation, of one leg with respct to the other. This probably means
that some sort of pelvic rotation is involved. Nevertheless, we are
interested in determining the location of the center of rotation of one leg
with respect to the other. This is where my question arises.

I have conducted a literature review concerning the calculation of the
Instantaneous Helical Axis of rotation. Description of this variable lies in
the equation:

v = w X r

where v is the linear velocity of a point, w is the angular velocity of that
point, and r is the radius of rotation. McFayden et al. (1988) show how this
equation may be used to find the hip and ankle joint centers. There work was
conducted in 2D. Woltring expands upon this in a complex manner to find IHAs
in 3D. It seems, however, that the previous equation could be used, since
all are vector quantities. If a reference frame attached to one of the legs
is considered to be the global reference frame and the reference frame
attached to the other leg is the local reference frame, then the point of the
ICR should be able to be determined using information from both reference

My question concerns the determination of w. If a vector is constructed
from the origin of frame 1 to frame 2, movement of frame 2 wrt frame 1 will
result in some w. But frame 2 might also be "spinning" about itself. Does
this "spinning" come into play when determining w? If it does not, the the
previous equation can be utilized. If it does, then how do I calculate w?
Any responses or thoughts would be greatly appreciated.


John DeWitt
Graduate Assistant
Exercise and Sport Research Institute
Arizona State University
Tempe, Arizona USA 85287-0404
(602) 965-7528
email: dewitt@espe1.la.asu.edu