60 years of the determinants of gait: a misconception

The month of July 2013 marks the 60th anniversary of the publication of The Major Determinants of Normal and Pathological Gait by J B dec M Saunders, Verne Inman and Howard Eberhart.  This is a seminal paper in the history of gait analysis which was revered for many years and is the foundation of the description of normal walking in many text books.  More recently, however, it has come in for substantial criticism.

three determinants

The first named author, John Bertrand deCusance Morant Saunders, was a medically trained Professor of Anatomy at the University of California who was born in South Africa of Scottish descent. The story is that he needed his name on a paper to justify a trip to the Joint Meeting of the Orthopaedic Associations in London in 1952 and Inman and Eberhart obliged. There is little doubt that the ideas were those of Inman, a pioneering Orthopaedic Surgeon, and Eberhart,  an engineer. (Inman first met Eberhart when amputating his leg after a wartime accident at the time when he had been asked to establish the National Research Council Advisory Committee on Artificial Limbs. He invited Eberhart, originally a civil engineer, to join him and the partnership continued for the next thirty years).

Over the month I intend to write a series of posts celebrating this anniversary by looking at different aspects of the paper.  In this post I’d like to dispel one of the myths about the paper which is that it states that the aim of walking is to minimise the excursion of the centre of mass. In a significant review article, for example, Art Kuo (2007) writes “The six determinants of gait theory proposes that a set of kinematic features help to reduce the displacement of the centre of mass. It is based on the premise that the horizontal and vertical displacements are energetically costly”. 

An earlier paper by Ortega and Farley (2005) starts with an almost identical quote which drove the authors to train participants to walk with a nearly flat trajectory of the centre of mass. They then showed that it took nearly twice as much energy (oxygen) to walk a given distance with the flattened trajectory than with the normal trajectory. Gordon, Ferris and Kuo (2009 – who I think did the work earlier but published it considerably later than Ortega and Farley) conducted a very similar study and came up with essentially the same results. The introduction of that paper is interesting in describing how “at least a dozen text books have interpreted [Inman’s] work as meaning it is desirable to minimise or reduce COM movement during walking” and giving an overview of how the ideas have developed through these.

What is interesting though is that nowhere in the original paper (nor in the extended versions that have appeared in the three editions of the book Human Walking) can I find any statement by the  authors that minimisation of the COM movement is the aim of walking. What thy actually said was this:

Translation of a body in straight line with the least expenditure of energy may be achieved mechanically by the use of a wheel, but it is quite impossible by means of bipedal gait. The next most economical method would be the translation of the body through a sinusoidal pathway of low amplitude in which the deflections are gradual. Since force is equal to mass times acceleration and acceleration is a function of time, abrupt changes in the direction of the centre of motion compel a high expenditure of energy. In translating the centre of gravity through a smooth undulating pathway of low amplitude the human body conserves energy; and, as we shall see in considering pathological gait, the body will make every attempt to continue to conserve energy.

What they are proposing is that the body acts to ensure a smooth trajectory not necessarily one of minimal vertical displacement. They start off by describing compass gait, moving with fixed knee with no foot and the problem that they identify with this is that “at the point of intersection with the arcs, the abrupt change in the direction of the forward acceleration [I think they actually mean vertical component of velocity – RB] would require the application of a force of considerable magnitude”. This is actually extremely close to the hypothesis of the Dynamic Walking Group that one of the principal energy costs of walking is the requirement to redirect the centre of mass velocity during step to step transitions (Kuo et al. 2005) despite a contention that  their approach is the antithesis of Inman and Eberhart’s (see Kuo  2007). The six determinants proposed in the original paper are then strategies to smooth the trajectory of the COM but not necessarily to reduce it.

So where did the original and perfectly sensible views of Inman and Eberhart get distorted? Gordon et al. (2009) quote Perry (1992) as saying “minimising the amount that the centre of gravity is displaced from the line of progression is the major mechanism for reducing the muscular effort of walking, and consequently, saving energy”. Perry, of course, trained under Inman, and it may be that like so many pupils it is she that has misrepresented the ideas of her teacher. As an engineer myself, however, I’d take the personal side out. I’d see the original and valid ideas as indicative of the potential for progress when clinicians and engineers come together to address the challenges of clinical biomechanics. The misrepresented and invalid ideas appear when clinicians think they can go it alone!

That’s it for this post. I’ve emphasised one particular aspect in which I think the work has been unfairly criticised. In later posts I’ll look at some aspects where criticism may have been more justified as well as examining the popular appeal of the approach


Gordon, K. E., Ferris, D. P., & Kuo, A. D. (2009). Metabolic and mechanical energy costs of reducing vertical center of mass movement during gait. Arch Phys Med Rehabil, 90(1), 136-144.

Kuo, A. D., Donelan, J. M., & Ruina, A. (2005). Energetic consequences of walking like an inverted pendulum: step-to-step transitions. Exerc Sport Sci Rev, 33(2), 88-97.

Kuo, A. D. (2007). The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective. Hum Mov Sci, 26(4), 617-656.

Ortega, J. D., & Farley, C. T. (2005). Minimizing center of mass vertical movement increases metabolic cost in walking. J Appl Physiol, 99(6), 2099-2107.

Perry, J. (1992). Gait Analysis. Thorofare: SLACK.

Saunders, J. D. M., Inman, V. T., & Eberhart, H. D. (1953). The major determinants in normal and pathological gait. Journal of Bone and Joint Surgery, 35A(3), 543-728.



  1. OK, I’ll bite.
    First, Saunders, Inman, Ralston, Eberhart et al. were amazing pioneers.
    I am amazed by what they accomplished with the equipment they had in that era.
    Conversely, I am amazed by how little we have accomplished given the power of today’s technology.

    Saunders, Inman & Eberhart 1953 definitely recognized that the foot ground collision work was important. It took 5 decades for people to measure that work (Mont Hubbard & R McN Alexander recognized it and then Kuo, Donelan etc. measured it). Today, I think many of us recognize that step to step transition work is a major “determinant” of the metabolic cost of walking.

    But together with their foresight into the cost of cog redirection during double support, Saunders, Inman and Eberhart do state:

    page 548 regarding compass gait: “The energy cost to a person using the compass gait would be exceedingly high. … the center of gravity would have to be elevated approximately three and three quarter inches which is double the normal vertical displacement.”

    Further down page 548 re: Pelvic Tilt
    “Thus the summit of the arc of its translation falls and still further flattening of the pathway results. The savings in energy by the cutting of the vertical displacement of the center of gravity in half is obvious.”

    Page 550 under the knee flexion determinant:
    The summit of the arc described by the passage of the center of gravity is still further lowered with the conservation of energy by reduction of its vertical displacement.

    While none of these exactly say “minimization is best”, I read them as repeated implications (or direct statements) that less vertical displacement of the cog reduces the energy cost (mechanical or metabolic).

    The studies by Ortega & Farley and Gordon et al. took this idea to a logical extreme and in doing so point out its flaws. I never met Inman, Ralston or Eberhart but I would like to think that they would have appreciated the simple approaches of the more recent investigators. I can imagine that they would be surprised and amused that folks are still debating/discussing their paper.

    1. Rodger,

      Thanks for these comments that have really made me think about the original article. On reflection I agree with you that whilst the authors state that the purpose of walking is to smooth the CoM trajectory, there are parts of the text where the authors do clearly seem to be describing mechanisms to reduce the excursion. It’s almost as if they’ve stated one axiom but applied another.

      For a long time I assumed, with everyone else, that the aim of reducing the excursion of CoM trajectory was explicitly stated in the paper. What I could never understand was how a classical engineer like Eberhart could sign up to this (read his obituary if you want evidence of his engineering credentials). There are all sorts of conservative systems (balls on slopes, common and inverted pendula, oscillating springs etc.) in which potential energy (gravitational or elastic) is exchanged with kinetic energy and the centre of mass moves without any work being done. How could any competent engineer have been drawn into the assumption that reducing the CoM excursion was a prerequisite for energy efficiency?

      How about a bit of wild (and unprovable) conjecture to answer this question. Although it is entirely conjecture it is based on 25 years’ experience of discussing biomechanics within a clinical environment?

      Suppose that someone who only had a partial grasp of biomechanics actually came up with the concept of the determinants of gait originally on the basis that the aim of walking is
      to reduce the vertical excursion of the total body CoM. The concepts are extremely elegant, appear plausible (if not examined too closely) and fill a vacuum because no-one has really thought about the problem in detail since the Weber brothers in Germany over 100 years earlier (translation published in 1991).

      This sophisticated yet elegant theory is then explained to someone who really does understand mechanics. They appreciate its elegance and plausibility but recognise that the fundamental premise about the vertical excursion of the centre of mass is ridiculous. The work begins to find a more rigorous hypothesis on which to base the same concepts. The work fails but a compromise, that a smooth trajectory is an energy efficient one, is found and this rescues the original ideas (I say compromise because even this is not rigorous – an ideal ball bouncing is a clear example of conservative system in which the CM trajectory is not smooth).

      This leads to any explicit mention of the original axiom being removed from the formal published description but it still being implicit in the description of several of the determinants (as Rodger has observed). It is also quite possible that, despite the published version being corrected, the originator continued to stick to the original description when passing on his ideas less formally. (I’ve certainly seen examples of this in contemporary clinical biomechanics.) I pointed out in the last post that Perry, Inman’s trainee, does make explicit reference to reducing centre of mass excursion. Maybe she picked this up because it was what she was being taught! This might explain the persistence of the idea despite it never being stated in the original article.

      As I’ve said this is all conjecture but it seems quite plausible to me and appears to explain several of the facts. An interesting observation which might lend support to this is that when an extended version of the article was published as the first chapter of Human Walking (1981) it was attributed to Inman, Ralston and Todd. Why was Eberhart’s name dropped? This certainly suggests he only had a minor role in developing the original ideas. Might is also suggest that he was not entirely in agreement with what was written?
      Inman, V., Ralston, H., & Todd, F. (1981). Human Walking (1st ed.). Baltimore: Williams and Wilkins.

      Weber, W., & Weber, E. (1991). Mechanics of the Human Walking Apparatus (P. Maquet & R. Furlong, Trans.). Berlin: Springer-Verlag.

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