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

JAYCOR, Inc

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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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

JAYCOR, Inc

9775 Towne Center Drive

San Diego, Ca 92121

Tel: (858) 552-3508

Fax: (858) 552-9172

E-mail: wshen@jaycor.com

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------