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Power flow calculations using Inverse Dynamics

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  • Power flow calculations using Inverse Dynamics

    Dear Biomch-L readers,

    I have completed many 3D multi-segment rigid body models of the human body to
    calculate the joint (F*v) and muscle powers (M*w) during human movement. I am
    familiar with Winter's work who emphasised the usefulness of this approach in
    biomechanics. He believed that a typical power analysis would show the distinct
    patterns of energy generation and absorption by the muscles, and this could have
    significant implications for training and conditioning.

    Winter's calculations are relatively simple. In his book "Biomechanics and
    Motor Control of Human Movement (2nd Ed, 1990), he intially stated that muscle
    power is the produce to net muscle moment (M) and angular velocity (w) yielding
    the formula P = Mw, where P is power in watts. This power could be therefore
    positive or negative depending on whether the muscles were performing a positive
    rate of change or negative change of work. Hence the terms muscle power
    generation and muscle power absorption were conceptualised mechanically. A
    little later on Winter says that the aforementioned formula should be modified
    to include the angular velocities of the adjacent segments in order to partition
    the transfer component so that w is repaced by (w1 - w2) and the muscle power
    equation now becomes P=M(w1-w2), where if w1 and w2 have the same polarity, the
    rate of transfer is the lesser of the two power components.

    In Zajac et al. (2002). Biomechanics and muscle coordination of human walking.
    Part 1: Introduction to concepts, power transfer, dynamics and simulations. Gait
    and Posture 16 (2002), 215-232, states the following:

    (i) any one muscle may effect the acceleration and power of ALL body segments
    because of dynamic coupling.

    (ii)the net power instantaneously delivered by a muscle to either the segment of
    origin or insertion must be found from COUPLED EQUATIONS OF MOTION and cannot be
    found from the dot product of its force vector at the origin (insertion) with
    the velocity vector of the origin (insertion) OR from the dot product of the net
    joint moment vector with the segment angular velocity vector. The reason is that
    the effects of the contributions of net joint moment to the joint intersegmental
    forces and the muscle contributions to joint intersegmental forces are not

    (iii) It is often erroneously stated that or inferred that a muscle delivers
    power to or absorbs power from only the segments to which it attaches.

    (iv) This error (iii) seems to arise because of the lack of recognition that the
    terms in the coupled dynamic equations are correct for computing muscle power to
    the entire sustem, but incorrect when used separately to find the net
    contribution to the segments to which they attach.

    Therefore, I have the following questions that I would like resolved:

    (a) From the inverse dynamics solution of two or more coupled rigid bodies, what
    would the value of just the net joint torque multiplied the corresponding
    segment angular velocity compute (i.e. just P = Tw)? Anything meaningful?

    (b) If the net joint torque (from inverse dynamics) multiplied by the difference
    in angular velocities of the adjacent segments was calculated would this
    satifactorily give the values of THE TOTAL SUM OF active muscle power flows in
    or out of the segment (i.e. P=T(w2-w1)). Is this always necessary or could
    sometimes P=Tw used?

    (c) Can joint muscle power or absorption be calculated accurately using Winter's
    approach using the joint torques found from an inverse dynamics solution? Is
    this what Winter meant or did he mean as in (ii) above? Is the methodology for
    calculating power flows correct in Winter?

    (d) Can the power flow equations easily applied to the 3D case since power is a
    scalar quantity?

    (e) How should power flows into or out of a segment be described taking into
    account statement (iv) by Zajac et al. Does this mean that P=T(w2-w1) give the
    net joint power which represents the SUMMED power by the net joint moment
    to/from ALL the segments?

    Your replies would be greatly appreciated, and a summary of replies posted.

    Thank you.

    Rene Ferdinands

    Department of Physics &
    Electronic Engieering
    University of Waikato
    New Zealand

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