View Full Version : summary: inverse dynamics and muscular forces

Gabriele Paolini
11-13-2001, 12:04 AM
Hi everyone,
this is a summery of the responses to my posting dated thu 8th Nov:

My message was:

Hello everyone,

I am working on biomechanics of the upper limb during tennis serve.
I captured the motion using a Vicon system (8 cameras, 120 Hz) and now I am
facing the well known problem of inverse dynamics to determine the resultant
of forces and moments acting on the joints.
The goal I'd like to reach is to predict single muscle forces and I was
wondering if someone of you knows about good articles I could read.
I read Cote and Hubbard (ISCSB 2001) and I saw a lot of reference to
Yamaguchi et al. (J of Biomechanics, 1995) but I did not read it yet.
I am especially looking for a specific algorithm validated with experimental
data (if it does exist in literature...) and specifically directed to the
analysis of the upper limb redundant problem.

I will need to integrate the equations of motion as well,so i would like to
know if there is some good software package (i.e. ADAMS) and if I can find
some free trial version on the internet.

For those who are interested, I will make a summery of the responses and
post it.

Look forward to hear from all of you...



Dear Ms. Gabriele Paolini,

Perhaps some of these programs can be useful:

- Visual Nastran 4d




about the capacities of this software you can consult the Dr. Scott L.

http://www.stanford.edu/group/biomech/faculty/delp.html ).

Best Regards,

Wagner de Godoy

Gait Laboratory



ICQ: 121658600

AACD - Associação de Assistência à Criança Deficiente

Disabled Children Care Association




Hi Gabriele Paolini,

I used to be a Ph.D. student working with Gary Yamaguchi, and

I think the best reference for Gary's methodology is in his book:

Yamaguchi, G.T., 2001.

Dynamic Modeling of Musculoskeletal Motion.

Kluwer Academic Publishers, Norwell, MA, USA.

You can find this book through amazon.com.

In his class, we used the software package "AUTOLEV" to integrate the

equations. You can find the info for this package at the ISB web site.

Unfortunately this package is not free, however, the price is pretty cheap

compared to ADAMS.

Good luck with your project,



Gabriele, We have two articles that may be interested to you:

G. Li et al. "Prediction of muscle recruitment and its effect on joint

reaction forces during knee exercises", Annals of Biomedical Eng., Vol. 26.

pp725-733, 1988.

G. Li et al. "Prediction of antagonistic muscle forces using inverse dynamic

optimization during flexion/extension of the knee", J Biomechanical Eng.

Vol. 121, pp316-322, 1999.

Hope they will help.

Guoan Li

Orthopaedic Biomechanics Lab

Harvard Medical School

Boston, MA



I just completed my master's thesis on a related theme - volleyball spiking.

As far a individual muscle forces, that one is difficult. It is relatively

easy to calculate the joint reaction forces and moments, but translating

those into muscle forces is beyond my current understanding.

If you are even minimally proficient in C (or Visual Basic, or Fortran,

etc.) you can write your own code to analyze the motion trials. Instead of

relying on a specific package, I wrote my own code in C to import the raw

data from a (tab delimited) text file (that our motion analysis system

created), filter the positional data with a fourth order Butterworth digital

filter, and calculate the joint reation forces and moments, as well as the

angular velocities of each of the segments of the striking arm. This gave me

a better understanding of the inverse dynamics process, as well as how to

calculate the joint reaction forces and moments.

A good place to start is with Vaughan's Dynamics of Human Gait. He provides

all the equations necessary to develop joint reaction forces and moments

from force plate inputs. Of course, for the upper limb, you'll need to

derive the reaction force from the accelerations of the ball and racquet.

Additional resources (specific to the upper limb) include:

Feltner & Nelson, 1996, Three dimensional kinematics of the throwing arm

during the penalty throw in water polo. Journal of Applied Biomechanics, Vol

12, pp. 359-382.

Feltner & Taylor, 1997, Three dimensional kinetics of the shoulder, elbow

and wrist during a penalty throw in water polo. Journal of Applied

Biomechanics, Vol 13, pp. 347-372.

Feltner & Dapena, 1986, Dynamics of the shoulder and elbow joints of the

throwing arm during a baseball pitch. International Journal of Sport

Biomehanics, Vol 2, pp. 235-259.

Sakurai, et al, 1993, A three dimensional cinematographic analysis of upper

limb movement during fastbal and curveball baseball pitches. Journal of

Applied Biomechanics, Vol 9, pp 47-65.

Springings,1994, A three-dimensional kinematic method for determining the

effectiveness of arm segment rotations in producing racquet-head speed.

Journal of Biomechanics, Vol 27, pp. 245-254.

Hope this helps.

Gary Christopher

Oregon State University


Dear Gabriele,

It is difficult to validate muscle muscle distribution algorithms because

the muscle forces are difficult to measure. So it is much a question of

faith which algorithm you favor. You should be looking for algorithms with

the following properties:

- synergistic muscles should collaborate

- antgonistic muscle actions should be predicted for cases where they are

known to occur

- muscles should not be loaded above their physiological strength when the

load increases.

This rules out the sum of muscle forces as a valid criterion, but many other

criteria will work fine and are in fact mathematically equivalent. You might

want to read:

Rasmussen, J., Damsgaard, M. & Voigt, M. (2001): Muscle recruitment by the

min/max criterion - a comparative numerical study. Journal of Biomechanics,

vol. 34, no. 3, pp. 409-415.

for further explanation.

We are developing the AnyBody (http://anybody.auc.dk) system based on these

ideas. We hope to be able to distribute this system for testing in the

scientific community some time in the near future. If you want to be kept

up to date with the development, you can sign up for the project's interest

group on the home page.

When you distribute forces between muscles in forward dynamics, you are

essentially assuming that the organism is capable of actvating the muscles

as quickly as the recruitment criterion predicts, and you are disregarding

wobbly masses. This means that there is a limit to how fast motions can be

simulated reasonable by inverse dynamics. I don't know where the limit is,

but we have good indications that a squat jump is modeled reasonable by the

inverse dynamics method we are using, so perhaps a tennis serve would also

be feasible.

I hope this helps and look forward to seeing what other feedback you get.

Best regards and good luck,


John Rasmussen, Assoc. Prof., PhD, http://www.ime.auc.dk/~jr.


The AnyBody Group,


Institute of Mechanical Engineering Aalborg University,



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