View Full Version : Re: about definition of moment

David Smith
02-24-2007, 12:38 AM
Dear Sae Yong Lee

I can see why you can get confused with all the terminology and many papers
don't state whether they are presenting external or internal moments and in
what terms.
I will assume you are working in a 2D frame.

This is my explanation:

1) Moments are the result of a minimum of two opposing offset forces that
have lever arm about a point of interest acting on a body, known as a force
couple, and cause a tendency for that body to rotate. (This would be a lot
easier if we could post diagrams) So usually in the human body the applied
forces cause rotation at the joints. This as a result of the force couple
between Joint force (bone and soft tissue) and internal or external forces
E.G. muscle or GRF.

So a moment is (Force * lever arm) but only if there is an equal and
opposite (force * lever arm) (lever arm also known as moment arm)

It seems simple but is very useful to remember that all forces are equal and
opposite and the sum of all forces is zero and this is is true for moments.
F-m*a=0 applied forces or moments - resisting forces or moments = 0. The
forces and moments in any mechanical system, dynamic or static, are always
in eqilibrium.
Therefore when speaking of the magnitude of forces and moments it is
necessary to define when we mean applied or resisting since the sum of the
two is always zero and the product of each are always equal..

Applied force: That force acting on the body of interest
Resisting force: That force resisting the applied force

External force: In terms of biomechanics is usually the force applied by GRF
or some force extrinsic to or outside the body EG the weight of a kettle
held in a hand or the force of a boxing glove applied against a boxers head.
This can also be thought of as an external moment.
Internal force: Is usually the force that resists the external force and is
exerted by forces intrinsic or inside the body EG muscles, inertia,
ligaments, bone.
This could also be thought of as an internal moment.

Clockwise moment: Is a way of defining the rotation or tendency to rotate
of the moment (force * lever arm) in a 2D plane.
Anticlockwise moment: (Anticlockwise and clockwise moments can also be
thought of as positive and negative moments as can the forces but stick with
the former for now)

You may be able to see from the above descriptions that a moment in a given
direction (say anticlockwise) about a joint of interest may be the sum of
external and internal forces.This may be where you get confused since
External forces * lever arm + Internal forces * lever arm = internal and
external moments acting in the same direction, when intuitively you might
imagine they would be in opposite direction.

The easiest way to imagine and summate the moments is to find all the forces
* lever arms causing an anticlockwise rotation minus the forces * lever
arms causing a clockwise rotation about the joint of interest. This negates
(cancells the importance of) the fact of whether they are internal or
external. Can you see that Internal and external are not absolute terms but
more a comparative term. So therefore in terms of the body as a whole a
given force or moment of interest may be internal or intrinsic but in terms
of a given joint of interest the same force or moment may be external or
extrinsic to that joint.

Nett: That sum remaining after all deductions from the gross or grand total.
Gross sum: = total sum of everything
Nett sum: = the gross sum less a certain individual sum of interest.
Therefore it could be said that the individual sum is the nett sum. EG Gross
of all stock value of a shop = 117.50 - Gross sum net of Value Added Tax at
17.5% = 100 - Nett sum of VAT = 17.50

Joint moment: is the sum of moments acting about the joint of interest,
which is ZERO. The NET sum of joint anticlockwise moments = X and the NET
sum of joint clockwise moments = Y (X - Y = 0)

2) So you may now see that although all moments within the mechanical
system must be in equilibrium we cannot easily directly measure the internal
moments and forces of the muscles and joints and bones etc. We can however
measure the external forces (external and internal in terms of the whole
body) of GRF for instance.
Then by using the laws of Newton to caculate the external moments about a
joint of interest we can, by knowing that moments are equal and opposite,
calculate the forces required from the internal structures for equlibrium of
moments to be established. This is known as inverse dynamics using linked
segment models. It is inverse because the action is reversed whereas in real
life (some would say) muscles are the initiating or driving force and not
GRF for instance. (For me the two are inseperable as the muscles could not
move the body without the opposite action of external forces).

3) There are two basic systems for studying Human movement, a) Kinetics
=forces and b) Kinematics = motion, Vicon or Motion monitor systems
characterise the kinematics (motion) of the joint and limb. Therefore they
do not measure related forces, which are Kinetics, which can be measured
using a force plate for instance, moments can then be calculated. It is
possible to calculate the forces and moments from the kinematics by finding
the product of the accelerations of a limb and its body parameters. This is
known as the Forward solution or Forward Dynamics.
This brings the Anthropometry into the picture and Anthropometry is the
knowledge of the body parameters such as Dimensions, Mass, CoM and Radius of
Gyration of a segment and the location of its joint centres. These are
necessary for both forward and inverse dynamic calculations.
A good reference for this is Biomechanics and Motor Control of Human
Movement, David Winter, Wiley interscience NY.isbn 0-471-50908-6

Does this help? all the best Dave Smith.

----- Original Message -----
From: "Sae Yong Lee"
Sent: Friday, February 23, 2007 4:07 PM
Subject: [BIOMCH-L] about definition of moment

> Dear Biomch-L subscriber
> My name is Sae Yong Lee. I am doctorate student studying at University of
> Virginia in Kinesiology program.
> I have question related to moment. Are there anyone help me to clarify the
> definition of moment related termiology?
> 1. Difference between joint moment, net joint moment, external moment,
> muscle moment, and internal moment. I'll write down my understanding of
> those terms.
> Joint moment: The moment acting at the joint to overcome external moment.
> net joint moment: Sum of all moment acting at the joint including internal
> (active (muscle) + passive (ligament, joint capsule...), external moment.
> muscle moment: Moment produced by the muscle (different to quantify using
> motion analysis system).
> Internal moment: Moment produced by active (muscle) + passive (ligament,
> joint capsule...). part of joint moment.
> external moment: Moment produced by external forces such as ground
> reaction force.
> Please give me some comments whether or not my understanding is right.
> 2. What is general Newtonian inverse dynamics calculating? I have been
> believed that it is internal moment which is moment produced by passive
> and active structures crossing the joint. But I got confused these days
> while I was reading articles. It seems like quite a lot of articles
> alternatively use all those terms I mentioned. Even though the several
> articles use same system to calculate Moment, one said it is external
> moment and the other said internal moment. Is it joint moment, net joint
> moment, external moment, muscle moment, or internal moment.
> 3. If anyone use Vicon system or Motion monitor system, what kind of
> moment does this system calculating? Are there any reference article that
> mention about the calculation of moment of these systems?
> Thanks
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