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Joint moment reference frame

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  • Joint moment reference frame


    I am currently trying to analyze data from gait and stairs trials.
    I would like to report the lower limb joint moments. However, unlike for kinematics, I did not find any standards for the reference frame to compute the joint moments.

    I have read several papers like:
    Schache AG, Baker R. On the expression of joint moments during gait. Gait Posture. 2007 Mar;25(3):440-52.
    Brandon SC, Deluzio KJ. Robust features of knee osteoarthritis in joint moments are independent of reference frame selection. Clin Biomech (Bristol, Avon). 2011 Jan;26(1):65-70.

    It seems that I could use any reference frame (with maybe JCS as the preferred one).

    I was wondering if there is recent paper/advancement/discussion about standardization to report kinetics data.

    Thank you.

  • #2
    Re: Joint moment reference frame

    Hi Yoann,

    This question is regularly rised in the forum.

    You can look at the previous discussion in the Biomch-L archive :
    Standardization of reporting gait kinetics? Started by pshull, 10-31-2011

    Many references were listed there and other references have been published on the topic:
    O'Reilly OM, Sena MP, Feeley BT, Lotz JC.On representations for joint moments using a joint coordinate system. J Biomech Eng. 2013 Nov;135(11):114504.
    Kristianslund E, Krosshaug T, Mok KM, McLean S, van den Bogert AJ. Expressing the joint moments of drop jumps and sidestep cutting in different reference frames--does it matter? J Biomech. 2014 Jan 3;47(1):193-9.
    Dumas R, Cheze L. Letter to the editor: Joint moments in the joint coordinate system, Euler or dual Euler basis. J Biomech Eng. 2014 May;136(5):055501

    As I was saying in 2011, I am using the expression of the joint moment in the JCS using a non-orthogonal projection. The orthogonal projection may seem attractive for its simplicity and the possible interpretation of the projected joint moment in terms of “motor torque” but I am thinking that the related “dual Euler basis” of the JCS can be confusing.

    Any other comments?

    Raphael Dumas
    Université de Lyon
    LBMC UMR_T 9406 - Laboratoire de Biomécanique et Mécanique des Chocs
    Université Lyon 1 - IFSTTAR


    • #3
      Re: Joint moment reference frame

      I am going to have a look to these references.

      Thank you very much!

      Yoann Dessery


      • #4
        Re: Joint moment reference frame

        Some quick thought on expressing moments relative to JCS.

        I have always held the traditional view that joint forces, moments and powers should be expressed relative to the body fixed axes of the proximal segment. These being body fixed orthogonal axes aligned with the segment’s anatomical planes. As mentioned by Schache & Baker (2007) and Dumas & Cheze (2014) all calculations should be done using the orthogonal body fixed axes of the respective segment (such as inverse kinematics), however the argument is that we can express results relative to a set of non-orthogonal axes to aid in anatomical interpretation.

        When we describe joint rotations (distal segment relative to proximal) using an ordered Cardan sequence (eg x,y,z) we do use a non-orthogonal set of axes (e1 – proximal flex/ext; e3 – distal ext/int; e2 perpendicular to e1 and e3) to describe anatomical meaningful rotations. Here the two respective orthogonal axes remain fixed in the segments (ideally) regardless movement. Such that changes in the three rotations about the non-orthogonal axes are dependent on the joint position and reflect changes in movements. So long as you don’t go and add or subtract joint rotations or remove offsets as if they were vectors.

        I am not entirely convinced that this notion can be applied to expressing joint moments relative to the same non-orthogonal e1,e2,e3 axes used to describe joint rotations. Joint moments vary during movement due to numerous other internal and external factors besides joint position. Expressing moments relative to the body fixed proximal orthogonal axes gives a consistent reference frame (ideally) regardless of joint position about which to express moments. However the non-orthogonal axes e1,e2,e3 vary orientation relative to one another and to adjacent segments with movement. Such that there is not a consisted reference frame that the moments are expressed relative to within the same movement (task) or across different movements. Therefore limiting direct comparisons between movements unless the movements are near identical (both moments and axes are changing relative to the segments during movement).

        I am less convinced with the practice described in O'Reilly et al (2013) that invents another non-orthogonal axes where e2 remains the same but e1 and e3 are redefined relative to e2 so all axes are floating.

        Also the Cardan rotational sequence and derived axes and rotations are identical to the Grood and Suntay convention. The later just has a roundabout way of achieving the same results as classical mechanics.

        Again it is my opinion but I am not totally convinced on expressing moments relative the non-orthogonal and floating (e1,e2,e3) JCS.

        Allan Carman


        • #5
          Re: Joint moment reference frame

          I think both the body relative frame and the laboratory reference frame are important in describing the moments and the kinematics and they can be used in a complimentary manner and not as alternatives of each other. In such a comprehensive description the directions of e1 e2 e3 in space should also be specified to complete the kinematic and kinetic picture.


          • #6
            Re: Joint moment reference frame

            Anyone can, of course, use whatever reference frame they prefer but there are good reasons for trying to standardize this. That way, there is a common terminology and you don't have to do 3D coordinate transformations in your head while reading an article that uses a different standard.

            This was quite successful in kinematics, with the adoption of the generalized Joint Coordinate System in the ISB standard. Not yet for kinetics.

            The proximal segment frame (as Allan Carman suggested) could be a good standard for joint moment representation, but this introduces a terminology and interpretation problem. The hip abduction motion is measured with a floating axis, and the hip abduction moment is measured with a pelvis-fixed axis. These axes can be far apart in joints with a large 3D range of motion. And, of course, you can't multiply the angular velocity and moment anymore to get the power, if motion and moment use different axes.

            Of course, you can always convert back and forth between different representations. If you are interested, you can find the equations here:

            These days I work more in dynamics and control, and less in load analysis. For this, it is very convenient to define moments on the same axes as the rotations. BTW, moments should be projected (not decomposed) on these axes. This makes the moments equal to the generalized forces that correspond to the generalized coordinates. This makes it easier to use energy methods to derive multibody dynamics. The drawback is that the dynamics does not include forces and moments that are not associated with motion, i.e. reaction loads that do no work.

            For load analysis, I would admit that it is easier to express joint loads as a full 3D force and moment vector in a segment-fixed reference frame. Then you can use that as input for an FE model, etc.

            For clinical movement analysis, standardization is important so this is an important discussion.

            Ton van den Bogert