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joint attitude debate......

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  • joint attitude debate......

    Dear biomch-l readers,

    I was asked by a number of you to point
    out better my opinion on the joint attitude and angles debate. I
    was also asked to give information about SPACELIB.

    I will send a personal answer to everybody but I'd also like to
    summarize my ideas here.

    I begin with SPACELIB. This is a software library I realized with
    the help of a few colleagues in order to study spatial systems of
    rigid bodies. We apply it in robotics as well as in biomechanics.
    SPACELIB is based on a matrix approach involving 4*4 matrices. We
    have six different kind of matrices to describe three kinematic
    and three dynamic entities. They are POSITION, VELOCITY AND
    ACCELERATION of bodies (or points) and ACTIONS (forces and
    torques), MASS DISTRIBUTION (inertia moments) and MOMENTUM (both
    angular and "linear"). Using this library we have written a
    program for the whole body motion analysis we presented at the
    last symposium on computer simulation in Biomechanics (DAVIS CA
    1989). This matrix approach, that can be considered being the
    extension of the homogeneous transformation approach to the whole
    kinematics and dynamics, is documented in many papers. The library
    written in C-language consists of about 40 modules which perform
    all the elementary steps necessary in developing of the analysis
    of any spatial system of rigid bodies.
    We are planing to realize in the future an academic free sharable
    version of SPACELIB.

    We will be happy to send further documentation or papers to
    anyone who is interested in.

    **** Angles debate:

    In a previous e-mail I summarized the most famous sets of angular
    coordinates. I outlined also my opinion on the fact that I don't
    believe that any of these sets are THE BEST in EVERY situation.
    Before answering to whom asked me a deep discussion I want to
    state a few points:
    1) I am interested in (three dimensional) kinematic and dynamic
    aspects of biomechanics.
    2) I am NOT an expert in smoothing raw data.
    3) I am not trying to give THE FINAL answer to the debate but I
    am just trying to point out a few relevant aspects.
    4) This mail isn't a well-organized paper but just a "hand-
    written" note edited in order to give a general idea of my

    I believe that the central idea is "if we want to study something
    (e.g. the elbow, the knee, ... the whole body ...), initially we
    create a model of that thing (e.g. we decide if we will consider
    or not the knee being a perfect revolute pair) and at last WE

    I find that the relative angular position between two bodies A and
    B generally falls in one of the following situations:

    a) The two bodies are not linked by any angular constrains. In
    this situation body B can assume any angular position with res-
    pect to A (e.g. the trunk of a man during a jump can rotate
    freely with respect to the Earth).

    b) The two bodies are connected by a non-spherical joint. Many
    situations can occur -- the most relevant are:
    b.1) The two bodies are connected by a revolute pair or an
    approximate rev.pair (i.e. arm and forearm are connected
    by the elbow (an approximate revolute pair)).
    b.2) The two bodies are connected by a "joint" which permits
    two or more degrees of freedom (e.g. the head is connected
    to the body by means of the neck (an approximately spheri-
    cal joint)).

    c) The two bodies are connected by a revolute pair or by a joint
    which can be considered the sum of two or three revolute pairs.
    (although this situation does not happen in Biomechanics, some
    joints (e.g., the elbow) can be considered as approximately be-
    longing to this category.)

    In situation a) there is no preferred direction, axis or angle, so
    it appears very obvious to choose a set of angular coordinates
    which is "neutral" or "symmetric" with respect to the body and to
    the reference frame (e.g. screw angle system (also called the
    Euler angle and axis)).
    On the contrary, in situation b.1) The movement is usually
    composed of one large rotation (around the joint axis) and
    possibly two smaller rotations. Anyway all these three rotation
    angles are always contained in a well-known range. I think that in
    this situation a system of coordinates which gives a different
    importance to the first rotation (e.g. flexion-extension of the
    elbow) with respect to the others (ab-adduction and endo-exorota-
    tion) is more significant than other angular parameter sets.
    At last in situation b.2) all the three angles can vary of about
    the same maximum range but from a "physical" point of view we can
    identify two different kinds of angular displacements. Let us
    consider, for instance, the movement of the head with respect to
    the trunk. It can be decomposed into two "flexions" and one
    "twist" of the neck. Also in this case it looks to me that the
    flexions and the twist can be considered having a different
    A further consideration is that, while in case a) the angles can
    vary from 0 to +/- 180 degrees (or 0 -/+ 360),in the cases b)
    their values are generally lower than 90 degrees.

    Situations b.1 and b.2 can be possibly handled considering the
    "joint" composed by two different joints connected in succession.
    The first joint being a two degrees of freedom joint while the
    second is a one degree of freedom joint. The first joint is a
    "semi-spherical" joint which allows the orientation of an axis "a"
    but do not permits a twist movement around the axis itself. The
    second joint is a revolute pairs which allow a rotation about axis
    "a" displaced by the previous joint. (I hope that anyone will
    invent a easy way to send pictures on e-mail).
    The three angles giving the body orientation can be: a sort of
    Latitude and Longitude angles of axis "a" plus the twist angle
    around the axis itself. These latitude and longitude angles can
    be defined giving to both of them the same importance and making
    these angles true measurable angles.

    Situation c) "requires" the adoption of a "planar" convention (one
    angle) or (sometimes) the adoption of an Euler/Cardanic convention
    if the joint is considered being constituted of a series of
    revolute pairs.

    Any of these systems of angles can originate a rotation matrix
    very useful in performing calculations.

    Summarizing: I suggest to identify a (little) number of different
    situations and to choose for each of them an appropriate
    "standard" set of angular coordinates.

    ************** At last a one million dollars question ********

    How can H. Woltring be so frequently present on e-mail, how can he
    produce so fast new papers (by the way: thanks for the
    acknowledgement) and how can he continue working at his lab at the
    same time?

    Do the days in The Nederland have more than 24 hours? Or are his
    hours longer than everywhere else?

    I'd like to have any suggestion from Herman in order to increase
    my productivity.

    have a good work.

    Giovanni LEGNANI

    P.S. Please generally excuse me for my bad English.