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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:
http://www.udel.edu/HNES/faculty/richards/BluePresentation_files/frame.htm
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
http://www.lerner.ccf.org/bme/bogert/
> -----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
> To: BIOMCH-L@NIC.SURFNET.NL
> 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
> Archives: http://listserv.surfnet.nl/archives/Biomch-L.html
> ---------------------------------------------------------------
>
>
===================================
P Please consider the environment before printing this e-mail
Cleveland Clinic is ranked one of the top hospitals
in America by U.S. News & World Report (2008).
Visit us online at http://www.clevelandclinic.org for
a complete listing of our services, staff and
locations.
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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:
http://www.udel.edu/HNES/faculty/richards/BluePresentation_files/frame.htm
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
http://www.lerner.ccf.org/bme/bogert/
> -----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
> To: BIOMCH-L@NIC.SURFNET.NL
> 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
> Archives: http://listserv.surfnet.nl/archives/Biomch-L.html
> ---------------------------------------------------------------
>
>
===================================
P Please consider the environment before printing this e-mail
Cleveland Clinic is ranked one of the top hospitals
in America by U.S. News & World Report (2008).
Visit us online at http://www.clevelandclinic.org for
a complete listing of our services, staff and
locations.
Confidentiality Note: This message is intended for use
only by the individual or entity to which it is addressed
and may contain information that is privileged,
confidential, and exempt from disclosure under applicable
law. If the reader of this message is not the intended
recipient or the employee or agent responsible for
delivering the message to the intended recipient, you are
hereby notified that any dissemination, distribution or
copying of this communication is strictly prohibited. If
you have received this communication in error, please
contact the sender immediately and destroy the material in
its entirety, whether electronic or hard copy. Thank you.