View Full Version : Euler angle calculation in Vaughan's book

Weixin Shen
10-25-1999, 06:07 AM
Dear All,

I have a question regarding the formulations to calculate euler
angles in the book "Dynamics of Human Gait" (by C.L. Vaughan,
B.L. Davis and J.C O'Connor).

Recently, I wrote some matlab programs as a solver for inverse
and forword dynamics problems. I used the model decribed in
the above book as a test problem. The software GaitLab was
downloaded from the ISB web site. The kinematic reconstruction and
data filtering were exactly the same. However, the results are
different for segment angular velocity, and thus angular acceleration,
and joint forces and torques.

I tried various conventions to represent segment rotation, including
rotational matrix, ZXZ euler angles, ZYX euler angles and euler
parameters. They all lead to the same angular velocity, which is
a function of euler angles (or euler parameters) and their
time derivatives.

The formulations in the book (B.72, B.73, B.74) calculate euler
angles using 'arcsin' function. This is where I am not sure if
they are correct. By default (say in ZXZ convention), the range of
three euler angles should be [0 2*pi], [0, pi] and [0 2*pi]
respectively (without considering tumbling motion). The angle
calculated from arcsin is limited between [-pi/2 pi/2] or
[0 pi] depending on the convention. Therefore, I think the
euler angles calculated from GaitLab are not correct.

Since I am new to the biomechanical area, I would appreciate if
someone can provide me the corresponding address of the authors
of the book. I will also appreciate any thoughts and suggestions
on the matter. Thanks!

Weixin Shen, Ph.D., Senior Scientist
Science and Engineering Technology Division
9775 Towne Center Drive
San Diego, Ca 92121
Tel: (858) 552-3508
Fax: (858) 552-9172
E-mail: wshen@jaycor.com

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