ground reaction

Can the ground reaction move for you? (competition with small prize)

Thought I’d do something different and run a little competition with the chance of winning a copy of  my book. It’s based on one of the learning exercises we give to our students on our Masters in Clinical Gait Analysis by distance learning  If you’ve got students, trainees or junior colleagues maybe you’d like to forward the URL of this post to them so that they can have a go. Our students enjoy the exercise and I assume they will too. They also learn a lot about how we walk and how to measure the ground reaction.

This exercise requires students to experiment with walking in different ways to modify the characteristics of the ground reaction. You can download  a full description here. First of all they are simply asked to walk at different speeds and record the ground reaction. They then compare the data with those in Mike Schwartz’s paper on how gait patterns in general vary with walking speed. Generally there is good agreement but occasionally we’ll find someone who doesn’t vary speed in the same way that the average person does (whoever that is!).

Then I give them a number of different graphs of theoretical ground reactions and ask them to try and walk in such a way that they match the shape of the graph. The two below, for example, are to walk with exaggerated peaks of the vertical component and then with a flat pattern.

GRF 1GRF 2

The students generally find these reasonably easy. The more alert ones spot that the flat pattern is simply what you get if you walk slowly but it can be reproduced in a normal speed walk if you think about what you are doing..

Then  come two more – one with the first peak higher than the second and finally the second peak higher than the first.

GRF 3GRF 4

Again the first is easy. It is what happens if you walk faster (but like the flat peaks there are also ways of recreating it at normal speed). The second is much harder and so far (over two years now) none of the students has come up with a convincing example of walking with a higher second peak than first.

This interests me because a few years ago Barry Meadows and some of his colleagues published a paper based on their observation that in patients with a wide range pathologies you almost always find that the second peak of the ground reaction is diminished – never the opposite. They called this Ben Lomonding, after a mountain in Scotland that has two peaks – one of which is higher than the other.

Ben Lomond

So I just wonder – is it possible to walk in this way? I’m prepared to offer a copy of my book (signed of course!) for the person who can provide the best version of the fourth graph above (2nd ground reaction considerably higher than the first) as real ground reaction data.

Part of the aim of the learning exercise is for students to think about the relationship between the ground reaction and the movement of the centre of mass and we ask them to explain how they have changed their walking pattern in order to alter the  ground reaction.

I suspect it will be a lot easier if you adopt a highly asymmetrical pattern or adjust your gait for the particular step when you hit the force plate. I’ll be more much more impressed if you can illustrate the phenomenon with a symmetrical, repeatable gait pattern.

I’ll use these last two criteria (convincing explanation, and repeatability and symmetry of gait) to judge the winner in the event that more than one person comes up with a solution.

Maybe we need a few rules. Two weeks feels like about the right time. Send entries to me (r.j.baker@salford.ac.uk) by midnight (UK time) on Monday 29th February. They should include:

  • a graph of the vertical component of the ground reaction (you might want to include the GRF from both legs if you want to impress me with your symmetry)
  • a video of you walking over the force plate (or you could send a link to one you’ve uploaded to YouTube of Vimeo or somewhere else publicly accessible – this is what I encourage our students to do). These are particularly useful if you can overlay the ground reaction vector but  I won’t insist on this as a lot of people still don’t have the technology (if all you’ve got is a smart phone then use that). Try and capture at least one step before and one step after the measurement if you want to impress me with the repeatability of your gait pattern).
  • a biomechanical explanation of how you have changed your walking pattern in order to change the ground reaction in this way.

To ensure that entries are genuine I will be try to replicate the best entries in my lab here on the basis of the explanations provided. If I can’t do this I may ask for proof that the data is real (e.g. data in a .c3d other file format that has obviously come directly from a force plate).

I’ll assume that in submitting these you’ll be happy for me to use the graphs and video  in a future post reporting the results. (Note that I won’t publish the explanations – I feel people should be free to write what they want without fear that it will get posted publicly).

Finally, if you enjoy the exercise and would like to engage more, why not think about enrolling on the Masters programme. You can do it as part time study in your current workplace and do not need to travel to Salford at all. You can find details at this link.

 

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Shear pedantry

I criticised a colleague the other day for using “shear force” to refer to the horizontal component of force measured by a force plate. He asked me “why?”  Apart from me being a miserable old pedant who’s got nothing better to do than be annoying, the simple answer is that someone did the same to me a long time ago (it might have been Chris Kirtley, but then again it might not).

I don’t always trust Wikipedia but think it is quite good in distinguishing between shear forces which occur when forces are unaligned and cause a shear deformation (see figure above) and compressive forces when they are aligned and lead to pure compression or elongation.  To distinguish between these you need to know how and where the balancing force is applied. The force plate only measures the ground reaction and I’d argue can’t therefore distinguish between shear and compressive forces. What it can do is resolve the overall force into components in different directions. I’d thus prefer to describe the components in terms of the direction in which they are acting rather than the assumed effect they are having on tissue.

If I was being really really pedantic I’d probably say that shear forces exist within a material rather than being applied to it. In most biomechanics it is actually the shear and compressive  stresses and strains that are more important. These are caused by the external forces exerted on the material but are conceptually quite different being within the material. Generally speaking the vertical component of the ground reaction will give rise to compressive stresses. Given the complex arrangements of soft tissues in the foot and the irregular shape of the bones, however, it will also cause some some shear stress. Similarly although horizontal forces will result primarily in shear they will exert some compressive (and occasionally tensile) stresses as well.

Or am I being too pedantic? Anyone like to defend the use of shear force to describe what a force plate measures? It’s certainly very common usage.

Kinetics of the inverted pendulum

One of my first posts was about the inverted pendulum and in it I promised a follow-up that I never delivered. So here it is. I commented that for all there is a lot of talk about the inverted pendulum there is little understanding of what it is and what it’s characteristics are. I’ll focus on the kinetics today.

The graph below shows the vertical component of the ground reaction under an inverted pendulum (Anderson and Pandy, 2006). You can work out the shape the curve must have from basic physics. Early on the pendulum is rising as it moves towards the vertical. As it is does so it gains potential energy and must be losing kinetic energy. Its upward velocity is thus reducing so it has a downward acceleration (i.e. an upward deceleration). If the overall force is acting downwards then the ground reaction (up) must be less than bodyweight (down). As the pendulum moves towards its highest point along a circular arc it rises less slowly, decelerates less, so the ground reaction must get closer to bodyweight.

inv pen GRF

Once it is over the highest point it starts to lose height, and accelerate downwards. Again this requires a downwards force so again the ground reaction (up) must be less than bodyweight (down). The further the mass goes around the circular arc the more quickly it loses height, the more it accelerates, so the ground reaction must be a decreasing fraction of the ground reaction. Easy eh! Appliance of science and we can predict the curve above.

The interesting thing here is that the vertical component of the ground reaction under an inverted pendulum is always less than its own weight. The inverted pendulum may be an excellent mechanism for carrying a mass from one point to another but its a pretty hopeless one for supporting that mass. On reflection this should be obvious because the vertical component of velocity is upwards at the start and downwards at the end and thus the nett acceleration during the movement is downwards and the average force must be less than bodyweight.

If the average force is less than bodyweight then you can’t possibly have a viable walking pattern simply by stringing a series of inverted pendulums together no matter how good the drawings of the kinematics look.

There are two mechanisms by which we get over this. The first is that we use our muscles so that the the ground reaction does not just mimic the mechanics of a passive inverted pendulum. In the figure below the ground reaction is under an inverted pendulum (solid line) is plotted against Winter’s data (1991)  for the vertical component of the ground reaction (grey band) from the middle of one double support phase to the next. The characteristics double bumps of the ground reaction clearly increase the average vertical force (all forces are plotted as % bodyweight).

GRF

This isn’t the whole story however. If you look more critically at this data you will see that the average vertical component of the ground reaction under the body is still considerably less than bodyweight (about 10% less) for most of us. The peaks aren’t much higher than bodyweight and they don’t last that long. How can we walk around and not support out own bodyweight?

The answer lies in two words, “double support”. During double support the forces  under both limbs combine to exceed bodyweight. The largest total vertical component of the ground reaction is actually in mid double support when relatively modest looking ground reactions under both limbs combine (you can see a graph of this in an earlier blog). By allowing the two ground reactions to combine like this we are able to rely on an inverted pendulum like movement to move the body forwards whilst achieving an average total ground reaction equal to bodyweight – a fundamental pre-requisite of cyclic walking.

A double support phase is thus an essential requirement of a gait pattern based on an inverted pendulum. It’s interesting that modelling the body as a simple inverted pendulum leads to a prediction that double support needs to last for 15% of the gait cycle. The actual value is, of course, 10%. That’s not a bad guess for such a simple model.

I put these ideas in a slightly wider context in one of the screencasts in the series “Why we walk the way we do. The whole series is linked to on my Videos page.

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Anderson, F. C., & Pandy, M. G. (2003). Individual muscle contributions to support in normal walking. Gait Posture, 17(2), 159-169.

Buczek, F. L., Cooney, K. M., Walker, M. R., Rainbow, M. J., Concha, M. C., & Sanders, J. O. (2006). Performance of an inverted pendulum model directly applied to normal human gait. Clin Biomech (Bristol, Avon), 21(3), 288-296.

Winter, D. (1991). The biomechanics and motor control of human gait: Normal, Elderly and Pathological (2nd ed.). Waterloo:: Waterloo Biomechanics.

Which bump does what?

There was some discussion at the CMAS meeting in Glasgow last week about what causes the characteristic bumps in the vertical component of the ground reaction. Before you read on it might be worth just stopping to think this through for yourself. Working from the premise that Newton declared that if there is a net force acting on an object then it must be accelerating – which acceleration does the first bump represent and which bump does the second represent?

Several of us admitted to believing that the prevailing wisdom (“what the textbooks say”) is that the first bump represents a deceleration of the centre of mass as it’s downwards movement is arrested and that the second bump is the upwards acceleration as we push off. This is not the correct explanation as Barry Meadows made clear in his presentation.

I’ve plotted some idealised data below to illustrate what is actually happening. The ground reaction under the left limb is represented in red and that under the right limb in right. One thing we  should do more often is to plot the sum of these which of course is the total force acting on the body (Chris Kirtley does do this in his book, 2006). The first interesting thing to note is that the peak total ground reaction actually occurs just before the middle of double support where two relatively modest forces from the different limbs superimpose.

GR and COM

I’ve also plotted the trajectory of the centre of mass (calculated from a double integration of the total ground reaction). It is at its highest in middle single support and lowest in early double support. The dotted black line shows its minimum value. Before this point the COM is travelling downwards and being decelerated and afterwards it is travelling upwards and being accelerated. Thus the first bump of the ground reaction is acting to accelerate the body upwards and the second bump is acting to decelerate as it falls from its peak height during middle single support. This is the opposite to “what the text books say”.

Or are we being unfair to the text books? I’ve gone back to see.

Whittle (2012) and Kaufman and Davis (writing in Rose and Gamble, 2006) get the explanation spot on.

Gage(2009, p54), on the other hand, states that the “body has been accelerating by gravity as it fell from its zenith at mid-stance to its nadir at loading response. As  a result the total force on the limb as it impacts the floor is about 120% of body weight“. This is a bit vague but essentially wrong. The body has actually been decelerating for half of its fall from zenith to nadir such that the vertical component of its speed is virtually zero at foot contact. The first peak of the ground reaction occurs well after the limb impacts the floor and is a result of the centre of mass being accelerated upwards.

Perry (2010, p459) writes that “the first peak (F1) … is increased above bodyweight by the acceleration of the rapid drop of the body mass”. This is also wrong-  the deceleration of the body mass is almost complete by initial contact and has occurred as a consequence of the GR under the trailing limb. The description of the second peak is even more confused – “the second peak (F3) … is modified by the push of the ankle plantar flexor muscles against the floor in addition to the downward acceleration of the COG as the bodyweight falls forwards over the forefoot rocker“.

So there we have it on a random sample of four books that happen to be on my shelf this afternoon two have the explanation correct and two have it essentially wrong.

There is some additional confusion because the fore-aft component of the ground reaction actually has the opposite effect.  In the first half of stance the GR is acting to decelerate the body in a horizontal direction (at the same time as accelerating it in an upwards direction). In the second half of stance the opposite is occurring as the GR is accelerating the body forwards (at the same time as it is decelerating it as it falls vertically).

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Kirtley, C. (2006). Clinical gait analysis (1st ed.). Edinburgh: Elsevier

Levine, D., Richards, J., & Whittle, M. W. (2012). Whittle’s Gait Analysis (5th ed.): Churchill Livingstone.

Rose, J., & Gamble, J. (Eds.). (2006). Human Walking (3rd ed.). Philadelphia: Lippincott Williams and Wilkins.

Perry, J., & Burnfield, J. M. (2010). Gait analysis: normal and pathological function (2nd ed.). Pomona, California: Slack.

Gage, J. R., Schwartz, M. H., Koop, S. E., & Novacheck, T. F. (2009). The identification and treatment of gait problems in cerebral palsy (1st ed.). London: Mac Keith Press.