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Summary of Responses: Kinetic COM Calculation

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  • Summary of Responses: Kinetic COM Calculation

    Dear All,

    Thank you to everyone that responded to my query about how to
    calculate the centre of mass from kinetic data. And a
    particular thanks to Drew Smith who gave me much help. From
    the responses, I found the best was to calculate the COM
    using kinetic data without knowing the initial position or
    velocity is to calculate the acceleration from the force
    data, and then use double integration, finding the area under
    the graph to give velocity, and then finding the area under
    that graph to give the displacement. Finding the area can be
    done using the trapezoidal rule (2-point Newton-Cotes rule).
    It should be noted this only gives the COM in relation to the
    centre of the force plates, not in relation to starting
    point. There seems to be a number of variations on how you
    can calculate COM, with each method making different
    assumptions. However, the method I used appeared to be the
    simplest whilst still giving a reasonable answer.

    Below is the initial question I posted, followed by the
    individual responses I received. Thank you all again, it was
    of great help.

    Katrina McDonald

    Initial Posting:

    Hello All, I am trying to calculate the centre of mass of
    sprinters running over the first two steps after exiting the
    blocks. I am using kinetic data from 2 force plates, having
    only obtained force, moment and centre of pressure data
    collected at 990Hz. I have calculated the centre of mass
    using the kinetic double integration method considering the
    initial velocity and initial displacement to be zero. I used
    this method as it was described in the biomch L archives:
    Chris Kirtley’s - CoM from force plate: Summary of responses.
    The results I obtained seem unrealistic and I am having
    trouble interpreting them. I would very much appreciate any
    help with a correct method to use, how to calculate the
    integration constants (if they should be non-zero) and any
    information on what to expect or how to interpret them.
    Thanks for any help.

    From: Danik Lafond, Ph.D < >

    see Lafond et al. (2004) Journal of Biomechanics.

    From: Young-Hoo Kwon, Ph.D. <>

    It is impossible to compute accurate CoM position from
    acceleration if the initial position and velocity are
    unknown. When you integrate acceleration twice, you only get
    the position change due to acceleration. You are missing the
    contribution of initial velocity and initial position.
    It may be OK, however, not knowing the initial position if
    the main focus is on the position change (displacement)
    during the two steps. In this case, simply start the
    integration from the stationary on-block position (initial
    velocity = 0). This will give you the initial velocity of the
    CoM at the beginning of the two steps. You will be able to
    get the displacement due to acceleration and that due to the
    initial velocity. I hope it helped.

    From: Omar Feix do Nascimento

    Try this Reorganisation of human step initiation during acute
    experimental muscle pain. Gait Posture. 1999 Dec;10(3):240-7.

    From: Drew Smith, PhD

    It's difficult to assess where your errors/problems may lie
    from your posting, so forgive me if I am stating some things
    you consider obvious. The double integration method is good
    in that integration will also smooth your COM kinematic data.
    So, the resulting curves are likely to be fairly smooth. The
    downside of using this method is that the COM displacement
    data are in force platform coordinates, ie, the 0,0,0 will be
    the centre of the force platform and typically some 20mm
    below the surface (depending on the type of force platform -
    the specs will confirm this). This means you will need to
    know where the centre of the force platform is relative to
    your actual measurement space, eg, the blocks or the start
    line, to make sense of the kinematics. This is especially
    true for multiple platforms, since each will have its own
    0,0,0. A second problem is that as soon as your sprinter
    touches the second platform (I am assuming from your posting
    that you have 2 platforms) while still having a foot on the
    first platform, things get a bit hairy, since the forces are
    now being distributed two platforms. There are methods for
    determining the overall COP from two platforms, but I have
    never seen this method combined with determining COM
    displacement data. However, if you in fact have only one
    platform, then your COM data will only be valid until just
    before the other foot lands on the ground. If you have some
    actual GRF data that you could send me, eg, in a spreadsheet,
    I'd probably be able to give you some more specific advice.

    From: Aguinaldo, Arnel"

    I encourage you to read the methods described by Donelan JM,
    Kram R, Kuo AD. Simultaneous positive and negative external
    mechanical work in human walking. J Biomech. 2002, 35(1):117-
    24 Traditional kinetic methods of COM estimation often
    underestimate the double integrals due to summation of GRFs
    of both the trailing and leading limbs before integration.
    Donelan et al. describe a more logical calculation that may
    give you a more appropriate answer. Also, check out the
    methods outlined by Eames et al. Comparing methods of
    estimating the total body centre of mass in three-dimensions
    in normal and pathological gaits. Human Movement Sci 1999,
    18: 637-646