View Full Version : Re: Normalisation of joint torques

David Smith
02-07-2007, 11:11 PM

Quote "I am keen to get a better understanding of why you would normalise
your data to body height (and body mass) as surely the height of the
subject/ body
segment has already been taken into account during initial calculations."

That's a good question, these are my thoughts:

Normalisation is not normal. What I mean by that is that usually publishers
only semi normalise data into a rate or ratio IE Nm/kg or watts/kg. This may
be because it is more intuitive to read and understand that information than
if the data were fully normalised into a dimensionless figure, which has no
meaning on its own. This may be overcome if everybody fully normalised data.
However it is probably beyond the ken of some to do this and it is not
always useful. How one normalises data (or not) may depends on what it is
you need to conclude from the results.
IE it is pointless normalising pressure data for the plantar foot pressure
if you are interested in peak pressure or pressure /time curves. Heavier or
taller people are not likely to require higher pressures to cause tissue
pathology as in diabetes for instance.

In your case however I would think that normalising moments to height and
weight may be advantageous ie Nm/ (kg x H). H = height or limb length (I
like limb length better). If you required to look at the powers for the
subjects then normalising power would look something like this
(Watts/kg*(g*h)^1/2). g = gravity h = height.

So if your subjects had a very wide range of hieght it is also likely that
they also would have a wide range of limb length from shortest to longest.
If you apply 100N to a 1000mm arm length then you have 100Nm external moment
about the shoulder and a reciprocal internal moment produced by the muscle
of 100Nm. But the same force on a short arm of 500mm has only 50Nm internal
moment to produce the same effect. In this case there is static equilibrium
and so no work or power is taking place in terms of physics. If you
normalise to weight it might be likely that the smaller person is lighter
but not necessarily proportionally. What if the short person is very fat and
the tall person very lean and skinny and weights are the same eg 80kg.
Normalised by weight the tall person achieves 100/80 = 1.25Nm/kg and the
small person 50/80 = 0.625Nm/kg. Normalised by weight and height though, the
tall person achieves (I'll use arm length here) 100/(80* 1) =1.25 and the
small person achieves 50/(80*0.5) = 1.25. Are any of these values useful in
terms of characterising how easily, or if, the subject is able to rise from
the chair?

So if we look at the torque produced by the elbow extensors about the elbow
our 80kg subjects must produce min (40 * (9.81+acc of CoM)) Newtons of
vertical force at the hand per arm to start to raise the bodyweight. Lets
say this force is 420N i.e.10.5m/s/s*40kg => 420N * external Moment arm
(forearm = 500mm and 250mm) = 210Nm and 105Nm external moments respectively.
So therefore the extensors produce the equal and opposite torque or Internal
Moments to balance for equilibrium. Are the muscles producing more force in
the tall subject, perhaps not since the extensor lever arm is twice the
length of the short arm. Let's say 50mm and 25mm so the muscles produce
210/0.05 and 105/0.025 = 4200N. So the lifting force is equal and the muscle
forces are equal but the moments are double for the tall man. (Four times if
the small subject were half the tall subject's weight) So if you produce a
table or graph that only shows values normalised to Nm/kg it might be
intuitive to think that the tall subject could more easily raise his body
weight than the short subject. You can see from the above however, that they
both have the same acceleration of CoM. By normalising with weight and
height or limb length the values are equal and it would be more intuitive to
think that they have equal ability to raise their body weight.

If the small subject were half the weight of the tall subject then half the
force to raise the body would be required so therefore 20kg*10.5m/s/s = 210N
* 0.25m = Ext moment of 52.5Nm. 52.5Nm/(40*0.25)= 5.25 and the same equation
for the tall subject of 80kg = Ext moment 210Nm - 210Nm/(80*0.5)= 5.25.

If the small subject is the same weight as the tall subject then the
normalised value = 105Nm/80 = 1.31Nm/kg fully normalised value =
105Nm/(80*0.25) = 5.25.

Notice that Torque = 210Nm V's 105Nm V's 52.5Nm

Semi normalised Torque = 2.625Nm/kg V's 1.31Nm/kg V's 1.31Nm/kg (notice the
limb length variation make a differenc to the outcome)

Normalised by weight and limb length = 5.25 V's 5.25 V's 5.25 (weight or
limb length do not alter the outcome value but on its own what does 5.25

So that it is likely that if the limb length is proportional to the height
within a population then the fully normalised value will be the same for the
same rate of CoM acceleration regardless of weight of the subject. Just to
check that, suppose the tall man weighs in at 120kg.

120*10.5 /2=630N/0.5=315N/(120*0.5) = 5.25

Does that make sense Susan? I hope so. All the best Dave Smith

----- Original Message -----
From: "Susan K M Wilson"
Sent: Thursday, February 01, 2007 2:59 PM
Subject: [BIOMCH-L] Normalisation of joint torques

> Dear all,
> My research has involved investigating the effect of chair biomechanics on
> the ability of older adults to stand up with and without the use of their
> arms. I am mainly focusing on the peak moments created at the upper and
> lower limb joints. My query is with regard to the normalisation of joint
> torques for comparison between subjects. I have reviewed a number of
> papers
> that have normalised their data to Body mass and have thus been able to
> compare between groups and test conditions. I have however read a few
> papers that normalise their data to body height as well as body mass.
> I am keen to get a better understanding of why you would normalise your
> data
> to body height (and body mass) as surely the height of the subject/ body
> segment has already been taken into account during initial calculations.
> Thanks in advance for your time and help on this matter,
> Susan
> Susan Wilson
> PhD student,
> Bioengineering Unit,
> University of Strathclyde,
> Wolfson Building,
> 106 Rottenrow,
> Glasgow,
> G4 0NW,
> Scotland, UK
> Email: s.k.m.wilson@strath.ac.uk
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