View Full Version : Two-step rotation - sphereical rotation coordinate system -searching for equations

10-19-2010, 03:48 AM

I have read the paper "A spherical rotation coordinate system for the
description of three-dimensional joint rotations" from PL. Cheng (Ann Biomed
Eng. 2000 Nov-Dec;28(11):1381-92).

I am working on an overview about one-step, two-step and three-step rotation
for joint angles representation.

1. The paper includes the matrix representation of two-step rotation but
unfortunatlely not in solution of the angles. It look that it is too complex
to do it by hand, but maybe it is possible. If not it should be possible based
on Groebner-Basis analysis, I think.

Has anybody done this?

2. The matrix given in the paper describes the first rotation in sperical
coordinates but I like to have it parameterized as rotation angle about the
first rotation axis which rotates the the long axis.

Has anybody done this?

I think it is good to have these formulaes. I would allow us easily to
decompose a rotation matrix given by our measurementsystems into the two
sequence-independed angles of the two-step rotation in a easy to understand
way similar to the cardan angle decomposition.

My current implementation is based on the seperate two coordinate systems of
the proximal and distal segment and includes a lot of error prone and
difficult to understand calculations steps.

Any help or dicsussion is appreciated.

best regards

Oliver Rettig