View Full Version : Axis convention

Young-hoo Kwon
10-10-1995, 01:43 PM
Dear colleagues on Biomch-L:

I have read the debate about the axis convention issue with interest since
I've felt uncomfortable with the axis convention proposed by ISB which seems
more gait-oriented. It may be because of my background (Astronomy) or because
I daily deal with complex human motions commonly observed in sports settings.
Anyway, first of all, I disagree with ISB on setting the Y axis as the
vertical axis. At the same time I agree with Young Hui Chang on the use of
anatomical terms to explicitly express the directions.

Rather than forcing someone to use certain axis convention, I'd like to
introduce you the convention I am using in research and programming. I set
the Y axis vertical and the X axis horizontal (to the right) in 2-D, while
setting the Z axis vertical and the Y axis to the right in 3-D. In other
words, I set the X axis in 3-D to the direction of the observer and the YZ
plane becomes the sagittal plane. There are several reasons in doing this:

(a) In 3-D mechanics, the X axis is normally drawn to the observer with the Y
axis drawn to the right. Then, moving upward, to the right or toward you will
become positive. The human motion occurs mostly in the sagittal plane
(flexion-extension), thus it is reasonable to me to identify the YZ plane as
the sagittal plane.

(b) I'd like to keep the axes on the sagittal plane in the increasing cyclic
order in both 2-D and 3-D: X -> Y in 2-D and Y -> Z in 3-D. In essence, my
3-D axis convention is the same to what ISB proposed since axes are arranged
in the increasing cyclic order (mine: X -> Y -> Z, ISB: Z -> X -> Y). The
only difference is the starting axis.

(c) As far as the rotation in the main movement plane (sagittal plane, about
the transverse axis) is concerned, I'd like to keep the counter-clockwise
rotation as positive. I am reluctant to having the XZ axis as the sagittal
plane. Assuming the base for using the Z axis as the vertical axis is the
convention being used in physics and mechanics, it is hard to believe that
the XZ system used for the sagittal plane is also from the same base. The
axes are in the decreasing cyclic order.

(d) Let's imagine the subject is facing in the Y axis in anatomical position.
Keeping the axes of the segmental reference frames in the same direction to
the global frame, the X(seg) axis becomes the axis for the flexion-extension,
while the Y(seg) and Z(seg) axes become the axis for the adduction-abduction
and rotation, respectively. In computing the internal orientation angles of a
segment (segment i) to its adjacent proximal segment (segment j), one can
rotate the j frame to match to the i frame in the sequence of
flexion-extension (X) -> adduction-abduction (Y) -> rotation (Z). This
sequence will give you an Eulerian rotation of XYZ type. This sequence is
pretty simple to deal with and to memorize. So I align the X(i) axis to the
medio-lateral axis of the segment, while setting the Y(i) and Z(i) axes to
the antero-posterior axis and the longitudinal axis of the segment,
respectively. In the ISB system, the sequence is ZXY.

I have written many programs ranging from digitizing to complex angular
kinematics and graphics. I have enjoyed using this axis convention. But
things I take as advantages could be perceived as disadvantages to others. I
welcome any kind of comments regarding my axis convention.


Young-Hoo Kwon, Ph.D.
Korea Sport Science Institute
223-19, Gongneung-2-Dong
Seoul, 139-242 KOREA
Phone: +82-2-9709-555
Fax: +82-2-9709-502
Internet: y-hkwon@kssisun.kssi.re.kr