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Two-step rotation - sphereical rotation coordinate system -searching for equations

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  • Two-step rotation - sphereical rotation coordinate system -searching for equations


    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