View Full Version : coordinate axis controversy

John Lawrence
10-01-1995, 11:12 PM
It appears to me that the main point of contention in this debate
over 3-D axis conventions is centered, quite literally, on the question of
When studying "vertical" systems (i.e., a ground-based force plate as
the focus of some biomechanical study), it seems most reasonable (to me) to
establish X and Y in the plane of the force plate. By making Z orthogonal
to X and Y, the Z-axis then represents the vertical direction. When studying
"lateral" systems (those parallel to the plane of the observer, such as
locomotion and other whole body studies), the logical approach is to place
X and Y in the plane of movement or in some plane parallel to the upright
I use the words "reasonable" and "logical" in an effort to remind
us all of the common convention from whence 3-D measurement systems arose.
Remember the old Cartesian plane? X and Y are always represented at some
lateral distance (Z) from the OBSERVER! X represents translations towards the
right or left of the observer and Y represents translations towards the
top or bottom of the observer.
I believe that the key to maintaining convention when setting up a 3-D
orthogonal measurement system is to establish Cartesian coordinates in the
plane of the activity. Then, establish Z as orthogonal to X and Y, thus
representing translations away from or towards the activity plane. In
this way, everyone is using the same "standard", since orientation in itself
cannot be considered global when trying to answer questions about
inherently different mechanical systems which express their own "points of
I hope this wasn't too wordy, but I feel that we do need to
simplify things a bit -- and the best way to do that is to use the same
starting point.

J. H. Lawrence III, Ph.D.
Assistant Professor
Center for Biomedical Engineering
University of Kentucky
Lexington, KY 40506-0070