View Full Version : Re: How to choose Euler angles sequence of rotation?

Van Den Bogert, Ton
03-12-2009, 05:10 AM
This is a question with relevance to many subscribers, so I am posting an answer to the list.

The answer depends on which joint or body you are interested in. Euler/Cardanic angles have singularities at certain postures, and the trick is to pick a sequence that never reaches the singularity.

For the lower extremity, the Cardanic joint coordinate system (Grood & Suntay 1983) is well established. Standards can be found on www.isbweb.org, click on "information services" and "standards". Those sequences always use abduction as the middle axis, and those joints never reach the singularity at 90 degrees.

For the shoulder joint it is very difficult to avoid singularities, because of its large range of motion. A very nice presentation on this can be found here:

The shoulder standard that many people seem to be using now is one where the first axis is the inferior-superior axis of the thorax, the third axis is the long axis of the humerus, and the middle axis is perpendicular to those two. This has a singularity when the arm points straight down, but no singularity when abducted.

Helical angles, attitude vectors, Euler parameters, quaternions, Rodrigues parameters have all been used as alternatives that do not have the numerical singularity of Euler/Cardanic angles. But the problem with those is that there is no good connection to clinical terminology for joint movement. The debate on this goes back to the early days of Biomch-L, a compilation can be found here: http://www.biomch-l.org/files/ANGLES3D_TOPIC.txt.

Another useful reference is Woltring HJ, J Biomech 1994.

Ton van den Bogert


A.J. (Ton) van den Bogert, PhD
Department of Biomedical Engineering
Cleveland Clinic Foundation

> -----Original Message-----
> From: * Biomechanics and Movement Science listserver
> [mailto:BIOMCH-L@NIC.SURFNET.NL] On Behalf Of siriani
> Sent: Thursday, March 12, 2009 2:02 AM
> Subject: [BIOMCH-L] How to choose Euler angles sequence of rotation?
> Dear All,
> I'm starting to working with 3-d kinematic analysis and I
> would like to share this question:
> How to choose the best Euler Angles Sequence of Rotation to
> analyse my set of data?
> I wasnt able to find a good introdutory reference to this
> issue. Also, many papers just have cited that the authors
> used Euler Angles to analyse their data, but the sequence
> wasnt provided.
> I'll be glad to have help about these topic.
> Thank you,
> Professor Anamaria Siriani de Oliveira, PT, PhD São Paulo
> University - Brazil
> ---------------------------------------------------------------
> Information about BIOMCH-L: http://www.Biomch-L.org
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