Ian Stokes

06-10-1991, 08:31 AM

Dear Biomch-l Readers,

The Joint moment - center/axis of rotation (C of R) debate is, I

believe, most important to the fields of Biomechanics and Human Motion

science. Therefore, I am glad that the discussion initiated by Fabio Catani

which I joined lately has provoked so much discussion and debate. My own

contribution, in which I argued that the C of R is *not* an appropriate

reference point for consideration of joint moments has stimulated a number of

further contributions which have been most helpful. Some of these postings

have invited me to respond, but as fast as I have tried to collect my

thoughts, new ideas and opinions have been posted! I should add that other

contributors have more experience of this kind of biomechanics in practice,

but perhaps I have something to offer at least from a theoretical point of

view. As of today I believe I understand the following:

1. Force and moment equilibrium about joints is a common tool in biomechanics.

Many text books and many courses in biomechanics teach that the C of R is the

reference point about which we consider moment equilibrium, because the joint

force passes through it. The literature in the Journal of Biomechanics (and

elsewhere) is not consistent about this reference point - centers of curva-

ture, contact and rotation are used singly and in combination. Theoretical

considerations support all of these (with certain conditions such as neg-

ligible friction and surface compliance). We can prove this by analyzing

geometry, statics and/or virtual work.

2. Practical considerations depend on the purpose of the study/analysis.

Biomechanics studies can be divided into:

- Quasi-static vs. dynamic analyses and

- Studies of internal forces vs. studies of joints as actuators

(actuators transmit torques and generate power).

Considering dynamic analyses, use of the C of R is simpler, because relative

motion has fewer degrees of freedom about the center/axis of motion.

Therefore, the inertial terms are easier to deal with. However, the practical

problems of finding the C of R are great, so in some joints and some situa-

tions it would be better to look at the anatomy and constraints, and use other

information (fixed center of rotation, or knowledge of joint contact or center

of curvature).

Considering 'joints as actuators' (net moments) vs. 'internal forces', the

important question to ask is 'does it matter?' The objective in both cases is

to have an expression for joint moment which includes the effects of muscles,

in equilibrium with external and inertial forces. The joint force should be

excluded by considering moments about a point on its line of action.

(Ligament forces, and joints with two condyles complicate this.) It seems

that the net moment on each side of this equilibrium is sensitive to the point

about which moments are calculated, except that if the muscles forces are

nearly parallel to the joint force, as probably is often true, the sensitivity

could be small compared to other sources of errors. Certainly, in 'net

moment' measurement and reporting for any particular joint, standardization in

the biomechanics field would be very helpful.

3. As biomechanicians and teachers the most important thing we must remember

is to be critical and to be sure of the assumptions on which we base our

analyses. This is especially important in multi-disciplinary cases in which

studies/analyses may be done by one person and interpreted or applied by

another. This happens often in the clinical field where scientific findings

from studies of a few people in a controlled research situation may be applied

to a larger population. Also, sophisticated equipment, designed with known

limitations can be adapted to turn-key operation for people not necessarily

trained in all aspects of its interpretation. In anything as complex as human

joint function there are no simple answers, but the basic principles must be

clear to us before we get into the complexities. This debate certainly has

helped me.

Ian Stokes

The Joint moment - center/axis of rotation (C of R) debate is, I

believe, most important to the fields of Biomechanics and Human Motion

science. Therefore, I am glad that the discussion initiated by Fabio Catani

which I joined lately has provoked so much discussion and debate. My own

contribution, in which I argued that the C of R is *not* an appropriate

reference point for consideration of joint moments has stimulated a number of

further contributions which have been most helpful. Some of these postings

have invited me to respond, but as fast as I have tried to collect my

thoughts, new ideas and opinions have been posted! I should add that other

contributors have more experience of this kind of biomechanics in practice,

but perhaps I have something to offer at least from a theoretical point of

view. As of today I believe I understand the following:

1. Force and moment equilibrium about joints is a common tool in biomechanics.

Many text books and many courses in biomechanics teach that the C of R is the

reference point about which we consider moment equilibrium, because the joint

force passes through it. The literature in the Journal of Biomechanics (and

elsewhere) is not consistent about this reference point - centers of curva-

ture, contact and rotation are used singly and in combination. Theoretical

considerations support all of these (with certain conditions such as neg-

ligible friction and surface compliance). We can prove this by analyzing

geometry, statics and/or virtual work.

2. Practical considerations depend on the purpose of the study/analysis.

Biomechanics studies can be divided into:

- Quasi-static vs. dynamic analyses and

- Studies of internal forces vs. studies of joints as actuators

(actuators transmit torques and generate power).

Considering dynamic analyses, use of the C of R is simpler, because relative

motion has fewer degrees of freedom about the center/axis of motion.

Therefore, the inertial terms are easier to deal with. However, the practical

problems of finding the C of R are great, so in some joints and some situa-

tions it would be better to look at the anatomy and constraints, and use other

information (fixed center of rotation, or knowledge of joint contact or center

of curvature).

Considering 'joints as actuators' (net moments) vs. 'internal forces', the

important question to ask is 'does it matter?' The objective in both cases is

to have an expression for joint moment which includes the effects of muscles,

in equilibrium with external and inertial forces. The joint force should be

excluded by considering moments about a point on its line of action.

(Ligament forces, and joints with two condyles complicate this.) It seems

that the net moment on each side of this equilibrium is sensitive to the point

about which moments are calculated, except that if the muscles forces are

nearly parallel to the joint force, as probably is often true, the sensitivity

could be small compared to other sources of errors. Certainly, in 'net

moment' measurement and reporting for any particular joint, standardization in

the biomechanics field would be very helpful.

3. As biomechanicians and teachers the most important thing we must remember

is to be critical and to be sure of the assumptions on which we base our

analyses. This is especially important in multi-disciplinary cases in which

studies/analyses may be done by one person and interpreted or applied by

another. This happens often in the clinical field where scientific findings

from studies of a few people in a controlled research situation may be applied

to a larger population. Also, sophisticated equipment, designed with known

limitations can be adapted to turn-key operation for people not necessarily

trained in all aspects of its interpretation. In anything as complex as human

joint function there are no simple answers, but the basic principles must be

clear to us before we get into the complexities. This debate certainly has

helped me.

Ian Stokes