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Young Hui Chang
07-27-1995, 12:51 AM
Many thanks to everyone who responded to my queries (dated 7/25/95). I am
amazed at what a resource this list is to me. My posting went something
like this:
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"I asked for (1) approximate levels of moments PRODUCED ON THE GROUND BY
THE FOOT in the vertical axis. I would only like this information in order
to have something by which to compare my own data.

"However, I am doing kinetics of a different sort than is conventionally
done. My 6 degree-of-freedom transducer was mounted ABOVE the animal (on
the "ceiling) and was used to measure animals that arm-swung beneath it
(grabbing on to it at a defined handhold).

"Thus, relative to my second question, the animal is able to grab on to its
superstrate (something not commonly seen in terrestrial locomotion). True,
a pure moment about the cranio-caudal (or vertical axis) shouldn't alter
the translational path of the center of mass. However, the issue of moments
applied about the horizontal plane of the transducer is very real in
brachiation (arm-swinging locomotion) whereas this is not the case in
terrestrial locomotion.

"So my 2nd question was about (2) the EFFECT OF PURE MOMENTS (produced by a
hand gripping onto an overhead "branch") UPON THE MOVEMENT OF THE ANIMAL'S
CENTER OF MASS which is presumably some distance beneath the application of
the torques."
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THESE WERE THE RESPONSES (I have taken the liberty of some minor editing):
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(thanks to: Paolo de Leva, Ton van den Bogert, Brian L.Davis, Gideon Ariel,
Michael Rowling, Bruce Knoth, Michael Orendurff, John P. Holden, Bill
Sellers, Neil Messenger, & Jim Patton).

There were many references to the following:
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J.P. Holden, P.R. Cavanagh (1991). The free moment of ground reaction in
distance running and its changes with pronation. Journal of Biomechanics,
24, 10, 887-898.

Bogert, A.J. van den and B.M. Nigg, `Three dimensional stress
analysis of the tibia during running,' Proceedings 14th ISB
Congress, pp. 1384-1385, Paris, France, 1993.

Messenger N, Bowker P (1987) Foot-ground reaction torque as an indicator
of sub-talar and foot function. Proceedings of " gait analysis and
medical photogrametry" April 1987. Oxford Orthopaedic Engineering Centre
and the Biological Engineering Society (UK)

Messenger N (1988) The clinical value of the objective measurement of
gait. PhD thesis. University of Salford. (UK)

Schoenhaus H D et al. (1979) a preliminary report of computerised
analysis of gait. J Am Podiatry Association. 69:2-10

Whittle M W (1991) Gait analysis: an introduction. Oxford:Butterworth
Heinemann

SOUTAS-LITTLE, R. W. (1990) CENTER OF PRESSURE PLOTS
FOR CLINICAL USES, BIOMECHANICS OF NORMAL AND PROSTHETIC
GAIT, WINTER ANNUAL MEETING OF ASME, BOSTON.

http://www.arielnet.com/~ariel/


THESE WERE THE COMMENTS:
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Paolo de Leva writes:

...Just remember that pure torques (couple of forces), whatever is
the axis about which they are exerted, NEVER PRODUCE any acceleration of
the CM of the system to which they are applied. This is stated by Newton's
1st law (in short: when sum of forces is zero, there's no acceleration of
the system CM)

However, the horizontal torque you described (which is a pure
torque, and can exist because the hand can apply both upward and downward
forces in this case...) would cause a rotation (angular accelaration) of
the body about the CM. In turn, this would cause a linear acceleration of
the hand, IF the hand WERE NOT FIXED. Since the hand IS fixed, horizontal
forces are produced by the apparatus ON THE HAND, to prevent hand motion.
THESE HORIZONTAL FORCES are responsible for the linear acceleration of
the body CM.

Consider that these horizontal forces, which are produced as a
"secondary effect" of the pure torque, are already taken into account
by your force plate. I mean that your data INCLUDES these horizontal
forces, so you don't have to worry. If you are only interested in
linear acceleration (and first or second integral of acceleration data),
what you get from the force plate is enough.

Paolo

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Ton van den Bogert writes:

You're right that your kinetics are done differently. With force
plate work, the Mx and My are never reported, but transformed
into an equivalent point of application. Because foot-ground
pressures can only be compressive (pointing downward on the
ground), this point of application always lies within the contour
of the foot. In your case, the forces can have any direction (up
or down) and if you do the same thing, you will often get a
'point of application' outside the hand. So in your case, a
representation in terms of a force vector and a moment vector
with 3 components each is more appropriate.

>So my 2nd question is about (2) the EFFECT OF PURE MOMENTS (produced by a
>hand gripping onto an overhead "branch") UPON THE MOVEMENT OF THE ANIMAL'S
>CENTER OF MASS which is presumably some distance beneath the application of
>the torques.

I think you still don't need the moment. Changes in horizontal
velocity will be accompanied by horizontal reaction forces in
your transducer. Any 3-D calculation of joint moments should also take this
moment into account. It may be small, but significant.

You are probably familiar with the force plate work by Merkens et
al. on horses. If not, contact Henk Schamhardt
who developed the methods of
analysis for that project. I don't remember if they ever
reported the moments. That work was published in Equine Vet. J.
between 1985 and 1990.

>We often use integration of the animal's accelerations (from force data) to
>get velocity and position data. However, this is (again) neglecting torques
>produced by the animal.

You don't need the moment for that purpose. The Mz moment is
related to changes in angular momentum about the vertical axis.
Changes in velocity are only related to the force, not to the
moment.

>what is the integral of a moment?

t2
/
J(t2) - J(t1) = | M.dt
/
t1

J is the total angular momentum vector of the body, M is the
moment vector with respect to the center of mass.

Ton van den Bogert

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Bruce Knoth writes:

..Certainly, an animal holding a
handhold can apply couples to the platform. Also, there will be
moments-of-force due to the inertial forces of the animal's body and the
distance of the handle from the dynamic-center of the platform. (The
dynamic center is the point where a horizontal force won't produce any Mx
or My terms when applied to the force plate; it is approximately half the
height of the plate.)

The dynamics in the case of a swinging chimp are more complex than for a
foot step. You do know the exact point that the moments and forces are
applied to the platform, so you can measure the shear forces, calculate
the moment-of-force, subtract that from the measured torques, and get the
couples applied to the platform. I know this has been a bit vague, so
let me know if you have questions.

Bruce Knoth Software and System
Manager AMTI 176 Waltham Street

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Michael Orendurff writes:

We used to have a system here in our gait lab which included torque
measurements (in the horizontal plane) and the values in gait were
often less than 1% of body weight, but there was a definite pattern to the
graph. We have since abandoned the system (Helen Hayes Hosp developed
it so maybe they have some information for you) for more commercial
software (Vicon). I hope this helps in some way.

Michael Orendurff
Shriners Hospital
Portland Oregon

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Neil Messenger writes:

For my PhD I was particularly interested in the Mz torque (about the
vertical axis) trace in barefoot walking. There is considerable inter
subject variability in this data and quite a bit of intra subject
variability but you can expect to see peak values between 250 and 500
%bwt.mm (i.e. using force data presented in terms of % of body weight) and
in some cases values in excess of 1000%bwt.mm may be observed
particularly during the propulsive phase.

It as been suggested ( Schoenhaus et al 1979) that Mz data may be related
to subtalar function, this appears to be supported by my findings
(Messenger and Bowker 1987). However Whittle (1991) suggests that this is
not the case saying that the data can be fully explained as a result of
gross uperbody movements. Whilst this is probably true after heel lift
and mid-stance (when the Subtalar joint is supinated and therefore the
foot is behaving rigidly) I believe it can not explain the differences
observed between individuals prior to mid stance.

Dr Neil Messenger

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Bill Sellers writes:

The reason you don't see people talking about moments from force plate
data is that by and large, they haven't got the information! The way
most force plates are set up with force transducers at each corner
means that you can only get the moment around the vertical axis -
moments about the other two axes are lost because the information is
used to calculate the centre of application of the force. If you know
the actual centre of application of the force recorded by the
forceplate, and it differs from the one calculated by the forceplate
then you can calculate the torque applied. I feel sure it's quite
important. It certainly was when I was modelling leaping in prosimians
- they, like your brachiators, grip the substrate, and certainly apply
a torque. (Actually, they resist a torque - it works out to be mostly
negative). I'm pretty sure that any form of horizontal jump will
involve appreciable torques applied to the ground, and we really ought
to measure them.

As to the effect, a torque applied to a body won't produce a linear
acceleration of the centre of mass, but it will produce an angular
acceleration. It all falls out as normal when you do a free body
analysis - just treat the ground contact as another joint.

If you want to measure brachiation torques, attach a rigid bar to your
inverted forceplate. That way, you know where your animal is applying
it's force. The see where the forceplate software thinks it's applying
a force and do your moment calculations to find the torque. (I think
that should work - it's what I wanted to do with my prosimian leapers).
Or, create a forcepole that specifically measures torque. That should
definitely work.

Have fun

Bill Sellers
Centre for Human Biology, Leeds University.

PS. The latest and greatest modern forceplates probably have extra
sensors so they can give you all the torque information as well as
position of contact...

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Jim Patton writes:

REGARDING THE FORCE PLATE MOMENTS, I THINK YOU ARE SPEAKING OF A PLANAR
ANALYSIS OF MOTION. IN THE THREE DIMENSIONAL WORLD, THERE ARE OF COURSE
MOMENTS APPLIED TO THE FLOOR, PARTICULARLY IN GAIT. THESE ARE THE SO-CALLED
"TWISTING" MOMENTS, OR MOMENTS ABOUT THE VERTICAL AXIS, WHICH VANISH IN
SAGITTAL ANALYSIS. AS FAR AS ARM-SWINGING KINETICS, THE TWIST WOULD
DEFINITELY BE A SIGNIFICANT FACTOR. SOME ALSO BELIEVE THAT SOME OTHER (OFTEN
NEGLIGIBLE) COMPONENTS OF THE MOMENT EXIST AS WELL.

I FEEL THAT THE TRUE WAY TO UNDERSTAND THIS ISSUE IS TO UNDERSTAND HOW A
FORCE PLATE COMES UP WITH THE INFORMATION (THE COP CALCULATION). FOR AN
ALTERNATIVE APPROACH TO THE CALCULATION THAT DOES ASSUME MORE THAN MERELY A
VERTICAL TWIST COMPONENT.

Good luck,
Jim Patton
Northwestern U.
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(end of summary)


Young Hui

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Young Hui Chang
Department of Anatomy phone: 607-253-3551
College of Veterinary Medicine fax: 607-253-3541
Ithaca, NY 14853-6401 e-mail: (yhc3@cornell.edu)

"If you can't hear me, it's because I'm in parentheses." -Steven Wright
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