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  • ISB Recommendation for Standardization

    Subject: DISCUSSION-FORUM on the ISB Recommendations for
    Standardization in the Reporting of Kinematic Data

    In the October-1995 issue of the Journal of Biomechanics appeared on
    pages 1257-1260 the "ISB RECOMMENDATIONS FOR STANDARDIZATION IN THE
    REPORTING OF KINEMATIC DATA" presented by G. Wu and Peter R. Cavanagh
    on behalf of the ISB-Standardization and Terminology Committee. The
    recommendations are followed by an EDITORIAL COMMENT written by R.A.
    Brand.

    Among other proposed definitions are the recommended directions of the
    global (resp. local segmental) right-handed Cartesian axes: the
    +Y-axis pointing upward and parallel with the field of gravity
    (+Yi-segmental axes pointing towards the proximal joint of a
    segment), the +X-axis pointing in the forward direction to the right
    (the +Xi-axes in the anterior direction), and the +Z-axis sidewards
    and perpendicular to the XY-plane (and similarly the +Zi-axes).

    This proposed convention ignores and contradicts all international
    standards and commonly accepted practices in physics, mechanical
    engineering, Lagrangian dynamics, applied mathematics and, most
    important, also in biomechanics. The following spatial (and hence also
    segmental) Cartesian coordinate system(s) is (are) commonly adopted:
    the X-axis points sidewards (in the direction of the ISB-proposed
    Z-axis), the Y-axis in the forward direction, and the Z-axis upwards
    in the vertical direction.

    Here follows a small sample of English (American)-language and
    internationally renowned textbooks and works in which this spatial
    coordinate system is used: L.K. Branson:ENGINEERING MECHANICS, Simon
    and Schuster, New York, 1970, p. 3; R.Resnick and D. Halliday:
    PHYSICS (parts I and II), John Wiley, New York, 1966, p. 302; D.A.
    Wells: LAGRANGIAN DYNAMICS, Schaum Publ., New York, 1967, p. 181; H.
    Goldstein: CLASSICAL MECHANICS, Addison-Wesley, 1969, p. 94; J.L.
    Synge, B.A. Griffith: PRINCIPLES OF MECHANICS, Mc Graw-Hill, New
    York, 1959; P. Allard, I.A.F. Stokes, J. Blanchi: THREE-DIMENSIONAL
    ANALYSIS OF HUMAN MOVEMENT, Human Kinetics, 1995, p. 147; J.
    Wittenburg: DYNAMICS OF SYSTEMS OF RIGID BODIES, Teubner, Stuttgart,
    1977, p. 21.

    I am unable to understand why the ISB can make recommendations which
    not only grossly contradict international standards but also ignore
    the e-mail discussions of a few years ago, in which a number of
    colleagues (including me) proposed this universally accepted
    coordinate system which has already been used in the creation of
    three-dimensional human body models. In addition, the ISB-recommended
    coordinate system necessitates an awkward sequence of rotations in
    obtaining the rotation matrix: rotation about the Z-axis first,
    followed by Y and X, while the common and logical sequence is (e.g.
    for Cardan angles) X, Y, Z. Finally, it should be pointed that most
    manufacturers of force plates also use this reference frame for
    defining ground reaction force components.

    Any biomechanist, who uses the ISB-proposed coordinate system in
    publications submitted to international engineering, mechanics,
    mathematics or similar journals runs the risk of being heavily criticized
    for not adhering to international conventions.

    I feel that this issue is certainly worth being discussed in this
    forum. In fact, in my opinion, it would have been wiser to discuss the
    ISB-recommendations within the scientific community before their
    publication in the Journal of Biomechanics.

    H. Hatze, Ph. D.
    Professor of Biomechanics, University of Vienna, Austria.

  • #2
    ISB RECOMMENDATIONS FOR STANDARDIZATION

    SUBJECT: ISB RECOMMENDATIONS FOR THE STANDARDIZATION
    OF THE REPORTING OF KINEMATIC DATA - RESUME OF
    THE BIOMCH-L DISCUSSION FORUM OPENED BY
    H. HATZE ON 28 SEPT. 1995

    Instead of presenting a summary listing of all BIOMCH-L contributions


    to the above topic, I shall attempt to give an objective resume.

    A total of 19 contributions was received which includes those
    directed to my personal e-mail address. Of these 19 contributions, 15


    (or 79%) expressed outright rejection of the proposed ISB recommend-
    ations, in some cases rather emphatically ("We have no intention of
    ever using the proposed (ISB) conventions"). Of the remaining 4
    contributions only one (that of Dr. Jack Crosbie of the University of


    Sydney) expressly supported the ISB standard, while in 3
    communications (those of Barbara van Geems, South Africa, Hamid
    Rassoulian, Dr. J. H. Lawrence III, University of Kentucky) arguments


    were presented that could possibly be classified as partial support
    for some aspects of the ISB recommendations.

    I shall now briefly react to the arguments put forth in the 4
    communications that could be seen as support for the proposed ISB
    conventions.

    Dr. Crosbie's argument rests on the 2D-presentation of motions in
    the plane of progression which, in his opinion, should be the
    XY-plane. A similar argument is also used by Wu and Cavanagh on page
    1258 of their J. of Biomechanics paper with the addition that such a
    presentation "... will be consistent with the three-dimensional
    convention." If the internationally adopted 3D-convention for
    Cartesian axes systems is meant then this statement is not true as I
    have shown by means of many examples from the international
    literature. In addition, and in complete agreement with the opinion
    expressed by Dr. Scott Tashman of Case Western Reserve University
    ("3D analysis is a completely different world than 2D analysis" and
    "... basing a 3D standard on 2D conventions makes little sense"), 3D
    analysis and simulation are the dominating techniques in todays
    biomechanical research which fact should be used as point of
    departure for any standardization attempt. Also, in any
    two-dimensional (sideward) motion in the CORONAL PLANE, the YZ-plane
    (in the ISB convention) would be the plane of progression and
    therefore the XY-plane argument completely breaks down, although such


    a motion analysis would certainly qualify as a ligitimate 2D-motion
    analysis, albeit in the coronal plane. The remarks just made also
    pertain
    to the opinion expressed by Hamid Rassoulian ("the plane of
    progression
    should always be labelled XY").

    The arguments advanced by Barbara van Geems of the University of Cape


    Town and based on photogrammetric considerations are also not
    convincing. Again, she assumes the recording of a 2D motion executed
    in the sagittal plane only, in which case the photographic XY-plane
    would coincide with the spatial ISB standard XY-plane. However, in
    3D-recording more than one camera are used of which most will be
    situated in oblique positions relative to the spatial coordinate
    system and certainly not such that the spatial Z-axis always
    coincides with the optical axis of the camera concerned. Quite to the


    contrary, the optical (z-)axis of a head-mounted camera would be in
    line with the ISB-standard-proposed Y-axis.

    Finally, the opinion expressed by Dr. J. H. Lawrence III of the
    University of Kentucky also (implicitly) assumes ONE plane of
    activity ("I believe that the key to maintaining convention when
    setting up a 3-D orthogonal measurement system is to establish
    Cartesian coordinates in the plane of the activity"). It must be
    reiterated that, by definition, 3D-motion analysis and simulation is
    not restricted to one plane of activity and, in general, not even to
    a
    plane of "major activity" that could be clearly identified. Moreover,


    such a scheme would again contradict the idea of standardization,
    whether desirable or not.

    In summary, then, it would appear that the arguments advanced in
    support of the proposed ISB convention are not convincing. Also, the
    opinion aired by the Editor-in-Chief of the Journal of Biomechanics,
    Richard A. Brand, in his EDITORIAL COMMENT on the ISB
    recommendations that these represent "a thoughtful approach..." and
    "a compilation of commonly accepted practices" may not be shared by
    too many biomechanists. In this context it is also noteworthy and
    most
    remarkable that responses from the members of the ISB Standards and
    Terminology Commitee (notably from Ge Wu, Peter Cavanagh, John Paul,
    Don Grieve, and others) were conspicuously absent from the present
    discussion. The reasons for this strange silence remain clouded in
    mystery and forces everyone into speculation.

    To conclude, a rejection rate of 79% (in this discussion forum) for
    the
    proposed ISB convention does not augur well for future acceptance of
    these standards. In my opinion, the ISB Standardization and
    Terminology Committee would be well advised to withdraw the present
    recommendations and revise them in accordance with internationally
    accepted conventions and, most important, in collaboration with the
    scientific community of biomechanists.

    I thank all of you who have contributed to this discussion and
    thereby to the clarification of an important issue.

    Herbert Hatze, PhD.
    Professor of Biomechanics
    University of Vienna

    Comment


    • #3
      Standardization and the ISB

      Dear Biomch-L readers:

      It has been rewarding to see the discussion over the last two weeks
      regarding the ISB Recommendations for Standardization in the Reporting=
      of
      Kinematic Data. This shows that there is a continued interest in=
      this
      area, which is why the ISB has moved forward with this project. =
      The vigor
      of the responses that this topic seems to engender may come as a=
      surprise
      to some new readers, but I can assure you that this is indeed "par=
      for the
      course". Any venture into the area of standardization is definitely=
      not
      for the faint-hearted!

      The Recommendation (J. Biomech pp 1257-1260, October 1995) evolved=
      through
      many versions, and has been developed based on consideration and=
      comment
      from members of the ISB and from readers of this list. The first=
      public
      airing of the proposed recommendation was at the XIIIth Congress=
      of the
      International Society of Biomechanics, December 9-13, 1991, in Perth,
      Australia. On behalf of the committee, I presented an outline of=
      the
      proposed recommendation to approximately 300 ISB members. A lively
      discussion ensued and the comments were incorporated into Draft version=
      4.0
      which was reproduced in the February/March ISB Newsletter #45. BIOMCH-L
      readers may want to consult the BIOMCH-L archives for May 4, 1992,=
      where
      the draft was also posted to all subscribers. Comment was invited=
      and a
      summary of the comments received was published in the ISB Newsletter=
      #47
      Aug/Sept 1992. After two further drafts, the recently published
      Recommendation emerged. Those of you who missed the earlier posting=
      might
      find this a good reason (one of many!) to join the ISB in order to=
      keep
      abreast of these and other current issues.

      It is worth noting that a number of other groups such as the Scoliosis
      Society, the CAMARC group, the Clinical Gait Analysis Group are also
      working on standards and ISB maintains working relationships with=
      all of
      these groups. There is also a listing under "Standardization" on=
      the
      Biomechanics Home Page (http://dragon.acadiau.ca/~pbaudin/biomch.html)
      which at present points only to ISO. The soon to be released ISB=
      home page
      will also contain complete details of existing, proposed, and in=
      progress
      Recommendations and Standards from the ISB.

      The debate in the last two weeks has reiterated some of the issues,=
      and
      reinforced some of the motivations, that led to the pursuit of a=
      standard
      form of reporting that is specific to Biomechanics:

      =80 Within our own field, many different conventions are used for=
      reporting
      kinematic information so that the reader of each paper has to start=
      by
      working out which were used by the author (and perhaps holding graphs
      upside down or in a mirror!)

      =80 Outside our field, we find that there is indeed a number of different
      systems for describing the SAME thing. Each of the various sub-disciplines
      consider their method to be "standard". =20

      =80 We all tend to be very resistant to change from what we have=
      used in the
      past as "standard".

      =80 We have a tendency, if doing more complex analysis, to suggest=
      that the
      needs of those doing less complex analysis are less important.

      =46rom these reasons, the Recommendation was born. A key phrase=
      in the title
      of the Recommendation is "for the reporting of". The notion here=
      is that
      no one should have to use a system of computation that they are not
      comfortable with or simply do not like. However, once the results=
      are to
      be communicated to others, then there is a real need for standardization.=
      =20
      Converting to the ISB axis system could be seen as applying a filter.=
      The
      input of the filter is specific to each user while the output is
      understandable to all. This goes not just for the direction of the
      coordinate axes, but also for such things as the conventions used=
      for
      flexion/extension etc.

      The ISB exists for its members, and standardization is something=
      that
      members have asked us to pursue. No recommendation is cast in stone=
      and we
      will always move in a direction that the majority of our almost 1000
      members are comfortable with. We welcome input from all quarters=
      but we
      ask you to realize that any decision will leave in its wake a significant
      number of disaffected individuals who simply like the way they are=
      doing
      things at present.=20

      As the debate continues, those of you who feel so inclined might=
      try using
      the ISB conventions in reporting your data. =20


      Peter R. Cavanagh
      ISB President

      Comment


      • #4
        ISB Standardisation Document

        The following message is the outcome of email discussions on the topic of
        standardisation by Fred Yeadon, Ton van den Bogert and Giovanni Legnani.
        Since the standardisation proposal is "on the table" interested parties
        should (a) accept it as it stands (b) propose changes. We think that changes
        are needed and as an initial step have made some comments on the proposal.

        Comments on the document:

        Standardization and Terminology in Biomechanics.
        Volume 1. Section A.
        Recommendations for standardization in the reporting of kinematic data.

        It should be borne in mind that the purpose of standardisation is to have a
        common convention for REPORTING data so that the results of different
        researchers can be interpreted and compared more easily. Any discussion on
        this document should bear this in mind and avoid issues of what conventions
        are best used for data analysis. It is the reporting of results that is the
        present focus of the standardisation document.

        In the "Recommendations" document:-

        Part 1. X, Y, Z axes for displacements

        It should be recognised that there IS general agreement on the directions of
        the three Cartesian axes in that they are mutually perpendicular, one axis is
        vertical, and the directions of the remaining two horizontal axes are not
        usually contentious. There is some disagreement as to the NAMING (XYZ) of the
        three axes. There is also the issue of the senses of the axes in that there is
        general agreement that "up" is positive whereas "left" may be positive or
        negative. The system proposed in the standardisation document seems to be
        supported by people who have initially used 2D analysis and have added the a
        horizontal Z axis for 3D in order to preserve consistency between 2D and 3D.

        Unfortunately the majority of researchers in biomechanics seem to favour a
        system in which the Z axis is vertical. This does not augur well for the
        acceptance of the standardisation proposal in its present form.

        However, since there is general agreement on the directions of the axes and the
        focus is on the reporting of data, standardisation could take the form of naming
        these axes with words rather than with letters. For example, it might be
        possible to use "forward", "lateral", and "vertical" to name these directions.
        The point is not that particular names be cast in stone but that it become
        common practise to use appropriate words rather than XYZ.

        Another issue is that the XYZ system used should fit well with the system used
        to describe rotations. This will be addressed after the comments on Part 4 and
        Part 5.

        Part 2. Definition of segmental reference frames

        The system proposed in the standardisation document is consistent with the
        system proposed for the absolute reference frame in Part 1. However, as noted
        above, most researchers are not in agreement with the adoption of the proposed
        Part 1. An alternative will be proposed after considering relative orientation
        in Part 5.


        Part 4. Absolute Orientation

        In the standardisation document it is proposed that the absolute orientation of
        a body segment be defined by successive rotations about lateral, longitudinal
        and frontal axes. Since the system for defining the orientation of the whole
        body has not yet been published the present proposal prejudges the issue.
        Recommendations have been made to the Standardization Committee on whole body
        orientation as detailed in:

        Yeadon, M.R. 1990. The simulation of aerial movement. Part I: The determination
        of orientation angles from film data. Journal of Biomechanics 23, 59-66.

        In this system successive rotations are made about the lateral, frontal and
        longitudinal axes. This order of rotations has the advantage that the Cardan
        angles of somersault, tilt and twist agree with the nomenclature used by
        gymnasts and coaches. Since the focus is on the reporting of data such
        considerations of the established use of terminology are of great relevance.

        Part 5. Relative Orientation

        The description of the system proposed here appears to be somewhat ambiguous but
        our interpretation is that successive rotations about lateral, frontal and
        longitudinal axes bring one segment from initial alignment with a more proximal
        segment to its final relative orientation. That is we interpret the proposal
        as stating that the system described in the cited publication (Grood and Sunday,
        1983) is to be adopted. If this is so then we are in agreement with this part
        of the proposal and expect that most researchers will also find it acceptable.
        On the other hand this definition is in conflict with that proposed in Part 4,
        suggesting again that Part 4 be changed.

        Part 1 and Part 2.

        It would be attractive to think that articles could use Tables in which axes
        were labelled with words rather than X, Y and Z but since this is unlikely to
        occur there is a case for having a standard system. One rationale would be to
        let the definition of orientation dictate the axes nomenclature by requiring
        sequential rotations about the X, Y and Z axes. This leads to the adoption of
        a system with Z vertical (longitudinal).

        One final note of caution on the subject of standardisation:

        There is a danger if recommendations were to be adopted formally by an academic
        journal. Any standardised system will need to be able to adapt to various needs
        and changing circumstances. For different types of arm movements it may be
        helpful to use different systems of describing orientation. It will not be
        helpful if systems are cast in stone from on high. Researchers need the freedom
        to choose what they think is best bearing in mind the conventions prevalent at
        the time. For example even if whole body orientation is "standardised" in some
        way, it should not be imposed on all activity. What is a sensible system for
        gymnastics may not necessarily be sensible for high jumping. It should rest
        with the researchers of high jumping to arrive at a useful system bearing in
        mind what already exists.

        Fred Yeadon
        Ton van den Bogert
        Giovanni Legnani

        --
        M.R. (Fred) Yeadon
        M.R.Yeadon@lut.ac.uk

        Comment


        • #5
          Standardization and the ISB - Clean version

          The following message was corrupted during a Mac to Eudora transfer.=
          Here
          is a 'clean' version:

          ----------------------
          Dear Biomch-L readers:

          It has been rewarding to see the discussion over the last two weeks
          regarding the ISB Recommendations for Standardization in the Reporting=
          of
          Kinematic Data. This shows that there is a continued interest in=
          this
          area, which is why the ISB has moved forward with this project. =
          The vigor
          of the responses that this topic seems to engender may come as a=
          surprise
          to some new readers, but I can assure you that this is indeed "par=
          for the
          course". Any venture into the area of standardization is definitely=
          not
          for the faint-hearted!

          The Recommendation (J. Biomech pp 1257-1260, October 1995) evolved=
          through
          many versions, and has been developed based on consideration and=
          comment
          from members of the ISB and from readers of this list. The first=
          public
          airing of the proposed recommendation was at the XIIIth Congress=
          of the
          International Society of Biomechanics, December 9-13, 1991, in Perth,
          Australia. On behalf of the committee, I presented an outline of=
          the
          proposed recommendation to approximately 300 ISB members. A lively
          discussion ensued and the comments were incorporated into Draft version=
          4.0
          which was reproduced in the February/March ISB Newsletter #45. BIOMCH-L
          readers may want to consult the BIOMCH-L archives for May 4, 1992,=
          where
          the draft was also posted to all subscribers. Comment was invited=
          and a
          summary of the comments received was published in the ISB Newsletter=
          #47
          Aug/Sept 1992. After two further drafts, the recently published
          Recommendation emerged. Those of you who missed the earlier posting=
          might
          find this a good reason (one of many!) to join the ISB in order to=
          keep
          abreast of these and other current issues.

          It is worth noting that a number of other groups such as the Scoliosis
          Society, the CAMARC group, the Clinical Gait Analysis Group are also
          working on standards and ISB maintains working relationships with=
          all of
          these groups. There is also a listing under "Standardization" on=
          the
          Biomechanics Home Page (http://dragon.acadiau.ca/~pbaudin/biomch.html)
          which at present points only to ISO. The soon to be released ISB=
          home page
          will also contain complete details of existing, proposed, and in=
          progress
          Recommendations and Standards from the ISB.

          The debate in the last two weeks has reiterated some of the issues,=
          and
          reinforced some of the motivations, that led to the pursuit of a=
          standard
          form of reporting that is specific to Biomechanics:

          =80 Within our own field, many different conventions are used for=
          reporting
          kinematic information so that the reader of each paper has to start=
          by
          working out which were used by the author (and perhaps holding graphs
          upside down or in a mirror!)

          =80 Outside our field, we find that there is indeed a number of different
          systems for describing the SAME thing. Each of the various sub-disciplines
          consider their method to be "standard". =20

          =80 We all tend to be very resistant to change from what we have=
          used in the
          past as "standard".

          =80 We have a tendency, if doing more complex analysis, to suggest=
          that the
          needs of those doing less complex analysis are less important.

          =46rom these reasons, the Recommendation was born. A key phrase=
          in the title
          of the Recommendation is "for the reporting of". The notion here=
          is that
          no one should have to use a system of computation that they are not
          comfortable with or simply do not like. However, once the results=
          are to
          be communicated to others, then there is a real need for standardization.=
          =20
          Converting to the ISB axis system could be seen as applying a filter.=
          The
          input of the filter is specific to each user while the output is
          understandable to all. This goes not just for the direction of the
          coordinate axes, but also for such things as the conventions used=
          for
          flexion/extension etc.

          The ISB exists for its members, and standardization is something=
          that
          members have asked us to pursue. No recommendation is cast in stone=
          and we
          will always move in a direction that the majority of our almost 1000
          members are comfortable with. We welcome input from all quarters=
          but we
          ask you to realize that any decision will leave in its wake a significant
          number of disaffected individuals who simply like the way they are=
          doing
          things at present.=20

          As the debate continues, those of you who feel so inclined might=
          try using
          the ISB conventions in reporting your data. =20


          Peter R. Cavanagh
          ISB President

          -----------------





          /-------------------------------\
          | Peter Cavanagh |
          | Center for Locomotion Studies |
          | Penn State University |
          | University Park |
          | PA 16802 USA |
          | -x- | =20
          | Voice +1 814 865 1972 |
          | FAX +1 814 863 4755 |
          | Email PRC@PSU.EDU |
          \_______________________________/

          Comment


          • #6
            Re: ISB Standardisation Document

            To the Biomch-L readership:

            I agree wholeheartedly with the Yeadon/Bogert/Legnani
            counterproposal for standardization.

            Comment #1: Cardan angles in the order X-Y-Z (i.e., successive
            rotations about the mediolateral, anteroposterior and longitudinal axes)
            should be a good and logical way to express segment orientations. I believe
            that this should be the "standard", which should be used ***almost***
            always. At the same time, we have to keep in mind that such an order (like
            any other order) will produce "gimbal lock" at certain orientations. (This
            is where some of the angles "go crazy" because there are two very different
            combinations of numerical values of the three angles that produce very
            similar physical orientations of the segment.) Gimbal lock should be
            avoided. A different Cardan angle order will achieve this. That is why I
            consider it very important also that the new proposal allows for deviations
            from the standard when necessary. There is no angle order that will prevent
            gimbal lock everywhere. Any angle order has a "ugly orientation" that
            produces gimbal lock. That is why we should not force any given order on
            every situation.

            Comment #2: I would like to recommend that the X axis generally
            should point toward the right, and the Y axis forward, instead of the
            alternative (X axis forward and Y axis toward the left). This is not really
            a very critical issue, but here is why I think that X toward the right and Y
            forward is somewhat better:

            When I am analyzing a person walking or running forward, I generally
            think of myself as an observer that is traveling with the subject. I feel
            that this helps me to gain a more intuitive understanding of what the
            subject is experiencing. When I am considering the values of forces or
            velocities in the horizontal plane, I think of myself as the subject looking
            downward at this plane. Then, if I am using the X=right/Y=forward
            convention relative to the direction of motion, when I look at the ground I
            will see the positive X direction pointing toward the right and the positive
            Y direction pointing forward, which is how I generally draw these axes when
            I make any graph on a piece of paper: I am in familiar territory. But if I
            use the alternative convention X=forward/Y=left, then when I look at the
            ground I see the X direction pointing forward and the Y pointing toward the
            left, which is more unfamiliar. I think most people would probably feel
            more comfortable with X=right/Y=forward.

            Jesus Dapena

            Comment


            • #7
              ISB STANDARDIZATION RECOMMENDATION

              SUBJECT: ISB STANDARDIZATION RECOMMENDATION

              The standardization proposals recently made by Yeadon/Bogert/Legnani
              (16 October) and endorsed by J. Dapena (19 Oct.), are in full
              agreement with my original proposal of 28 September 1995 concerning
              the use of Cardan angles to describe 3D whole-body and segment
              orientation, and the use of the internationally accepted 3D coordinate
              system XYZ. In fact, my three-dimensional 17-segment human body
              model first published in 1980 ("A mathematical model for the
              computational determination of parameter values of anthropomorphic
              segments", J. of Biomechanics 13, 833-843) and then used repeatedly
              in subsequent papers ("Neuromusculoskeletal control systems modeling -
              a critical survey of recent developments", IEEE Transactions on
              Automatic Control AC-25, 375-385, 1980, "HOMSIM: a simulator
              of three-dimensional hominoid dynamics", CSIR - Special Report
              SWISK 23, 1981, "Computerized optimization of sports motions: an
              overview of possibilities, methods and recent developments", J. of
              Sports Sciences 1, 3-12, 1983, etc.) already employs Cardan angles
              for describing 3D whole-body and segment orientations and, as
              spatial and segmental coordinate system, a Cartesian XYZ reference
              frame with the X-axis pointing towards the PASSIVE observer (or
              to the right of the subject IF THE PLANE OF FORWARD
              PROGRthe right of the PASSIVE observer (or in the direction of the
              subject moving forward in the sagittal plane), and the Z-axis normal
              to the other two axes in a right-handed Cartesian coordinate system.

              My reasons for selecting Cardan angles (also called Bryant angles)
              were similar to those of Fred Yeadon and Jesus Dapena. While the
              critical case (gimbal lock) occurs for Cardan angles at PHI2=PI/2+n*PI
              (n=0,1,2,...), this is the case at THETA=n*PI (n=0,1,2,...) for Euler
              angles. However, for most situations arising in biomechanics it is
              more advantageous to have the critical case occurring at a larger
              angle and not near THETA=0. This makes also possible the derivation
              of particularly simple expressions for the elements of a Cardan
              transformation matrix for the case where all three angles are near
              zero, which can not be done if Euler angles are used. This was an
              additional reason why I selected Cardan angles.

              As far as the XYZ labelling of the spatial and segmental coordinate
              axes is concerned, the overriding criterion for me was to adhere
              to internationally accepted norms. As already pointed out in my
              original e-mail of 28 Sept. 1995, this implies that the XYZ-axes
              system described above and also agreed upon by Yeadon, Bogert,
              Legnani, Dapena, and many others be used. Exceptions to this
              standard should be possible for specific purposes.

              I might also mention that I have sent summaries of the present
              ISB-standardization e-mail discussions to Dr. R. Brand in his
              capacity as editor of the Journal of Biomechanics. I am sure that he
              also wants to contribute to the present discussion.

              Herbert Hatze, Ph.D.
              Professor of Biomechanics, University of Vienna

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