Rene Ferdinands
07-01-1998, 09:18 AM
Hello! My name is Rene' Ferdinands, and I am currently doing my Masters in
Biomechanical Engineering at the University of Waikato in New Zealand. I
presently hold a Bach. of Electrical Engineering Degree from
R.M.I.T,Australia. My research centres upon optimising the cricket bowling
actionin terms of various biomechanical parameters. Mathematical modelling,
3DVideo and EMG will be used to achieve this end.

At present, I am attempting to model the human body a system of 14 coupled
segments using Lagrangian dynamics. The method used is based on David
A.Winter's technique outlined in 'Biomechanics and Motor Control of Human
Movement (2nd ed.)'and a paper by Onyshko, S. & Winter, D.A. 1980. 'A
Mathematical Model for the Dynamics of Human Locomotion', Journal of
Biomechanics, 13, 361 - 368. So far I have only modelled two segments,which
represent the upper and lower arm as they traverse an orbit about the
shoulder joint, as an attempt to simulate the action of the bowling arm in
cricket. I use numerical techniques to obtain solutions. At this stage, I
am finding difficulty in obtaining practical solutions. The Langrangian
equations are very lengthy, especially when they are converted to a system
of first order D.E's to enable numerical integration.

So I am posing the following for anyone who can help, so that I can review
the approaches of others before me:

(i) Is there any published work that has already modelled the movement of
the human body as a dynamic set of Lagangian equations.
(ii) Alternatively, are there complete models using Newtonian mechanics
iii) It would be useful to have an email address for David A. Winter.
(iv) Could I have some references for other types of
mathematical/mechanical models of the human body.
(v) It would be of use to have complete mathematical/mechanical models of
JAVELIN/THROWING/BASEBALL PITCHING because this can be most suitably
adapted to the cricket bowling action.
(vi) If anyone has personal experience in this area, and can offer some
useful suggestions, please feel free to do so.

Your help is most welcome, and appreciated.




From: Derek Kamper

I have used the dynamics package Working Model
to simulate a mulit-segment biomechanical model.
It has a GUI and will compute the dynamics for
you (Newtonian mechanics).
In robotics, Newton-Euler equations are typically
used to solve for forward and inverse dynamics. The
algorithms lend themselves nicely to numerical
solution by computer.
Ex. JJ Craig, Introduction to Robotics. Algorithms
by Luh, Walker,Paul. Good luck.

derek kamper

From: Steve Onyshko


Your e-mail message was forwarded to me. I shall make a few
comments regarding your questions. First, I should say that I worked on
the problem of modeling of human locomotion when I was on sabattical leave
in 1977-78 in Dr.D.A. Winter's locomotion lab at the University of
Waterloo, Waterloo, Onatario, Canada. This resulted in the paper which
appeared in 1980 which you cited in you e-mail. Dr. Winter in now retired,
however, I believe, he is still doing some research at the University of
As you must be aware, the model I came up with was a seven segment
model in a 2-D plane, ie, there were seven second order DE's or
equivalently, 14 first order DE's.
The problem you're talking about, conceptially, is striaght
forward. However, its extremely messy to work out all the details.
To comment specifically on your points:

(i) Its not clear what you mean by Lagangian equations in that the final
result will be a set of equations of motion which will the same whether you
use the Lagangian approach or Newton's second law.
(ii) There must be, but I haven't been looking into this for a long time now.
(iii) I don't have David A. Winter's e-mail, but you should be able to
get it easily enough by contacting the University of Waterloo.
(iv) I haven't been looking into this lately.
(v) I have no such information.
(vi) This involves very much messy work. Doing it manually is tough
because of the large volume of work you will always make a few errors which
are hard to locate. Using software to manipulate the algebra and calculus
will result in many thousands of lines of code and you will easily get lost
in it.

Goog luck

Steve Onyshko

I work for a company that makes rigid body dynamics software for
design engineering applications. You may want to consider using such
a code for your application. When I did my Ph.D. in biomechanics several
years ago, I derived all my dynamical equations myself using a symbolic
maniputator. While there are some advantages to being able to get your
hands on the actual equations, if you don't need to do this, then a
variety of commercial packages will let you get the job done much
more quickly. Also, these packages usually provide a complete
for numerially integrating the equations, visualizing the motion of the
model, and plotting the results. Some products even have built in
optimization. In any case, for any complex dynamical model, I certainly
would not try to derive the equations by hand, since the chances of
getting the correct equations in the end is pretty low.

Here are some suggestions on commercial products you may want to

Autolev - a symbolic manipulator for deriving dynamical equations using
Kane's method.
Pros: Relatively easy to derive the equations, equations can be output
to a C or Fortran program which is ready to be numerically
The most recent version also has some plotting and visualization
Cons: You need to know Kane's method,and you need to create input text
files to derive the equations.
SD-Fast - a symbolic manipulator for automatically generating equations
of motion from a system description.
Pros: Very easy to derive the equations, an infrastructure is provided
for numerically integrating the equations, and little knowledge of
dynamics is required (you just create an input text file providing a
description of the tree structure of the system and the applied
Cons: No visualization or plotting capabilities.
Mechanica Motion - commercial grade dynamics package providing a
simulation and optimization environment.
Pros: Little knowledge of dynamics required, you create models with
graphical user interface rather than input text files, an implicit
and explicit numerical integrator are built in, optimization is
in, and graphing and visualization are provided.
Cons: You can't get your hands on the actual symbolic form of the
(if you need this, e.g., for an analysis you are developing), and
problems (e.g., a planar knee joint where the translations are a
prescribed function of the rotation) cannot be handled.

Hope this information is helpful.

B.J. Fregly

Benjamin J. Fregly, Ph.D.
Research and Development Engineer
Pro/MECHANICA MOTION Analysis Technology
Parametric Technology Corporation
2590 North First Street, Suite 200
San Jose, CA 95131
Tel: 408/953-8650
E-mail: bj@sj.ptc.com
Dear Rene,
I know from my own experience that dealing with the Lagrangian formulation
may turn out to be a nightmare even for planar systems with low degrees of
freedom (DOF) if you don't know how to approach the problem. If the
system's DOF is high, as it is in your case, manual derivation of the
equations will be useless. You will definitely make small errors like
inappropriate use of +/- signs etc. What I would suggest to you is using a
software that can handle symbolic manupulations such as Mathematica. You
should formulate the kinetic and potential energy terms manually which are
much easier compared to the whole equations of motion. Taking derivatives
and simplifications of the terms are automatically performed by the
symbolic manipulator. Moreover you can save the final equations in text
form and transfer them to your own code by a simple cut and paste
operation. So you don't have to write the final equations again for your
own code.
Using Lagrangian or Newtonian approach depends on what you are looking for.
If you are interested in the forces and moments transmitted through the
joints than Newtonian mechanics will be the best choice (it is also
possible to compute joint forces using Lagrangian mechanics but it is doing
the same job twice). If you decide to use Newtonian mechanics I would
suggest to employ the recursive Newton-Euler formulation which is a
standart application in robotics. If your aim is to make simulations and
you are interested in the simulated joint motions due to applied joint
forces and/or moments then Lagrangian formulation will be appropriate.
If you have further questions I will be glad to answer them.

================================================== =
H. Cenk Guler
Middle East Technical University
Department of Mechanical Engineering
06531 Ankara, Turkey

Tel. : (90) 312 210 5256
Fax : (90) 312 210 1266

E-mail : b092065@orca.cc.metu.edu.tr
From: "Paolo de Leva - Sport Biomechanics, Rome, IT"
Dear Rene,

I would suggest you to read, for instance, a paper by Feltner and
Dapena on the mechanics of baseball pitching on the Journal of
biomechanics (I don't have now the exact reference, but you can fin it

In my personal opinion, you should avoid using Lagrangian mechanics.
I am not familiar with it, but I believe that Newtonian mechanics is
suited for your purpose, as well as Lagrangian mechanics. The advantage
is that the first can be understood by all readers, whilst Lagrangian
mechanics cannot (I'm sure about that; many high level researchers don't
know it, and readers are not supposed to be high level researchers).
If you try and publish your work on a reviewed journal, you might be
asked (I would do it) by the reviewer to show that Newtonian mechanics
was not suited for your purpose, and I bet it would be quite difficult.
This is a basic matter, which is not always considered,
unfortunately: when you have two or more methods to do exactly the same
thing, you shoud use the simplest and most widely known one.
Moreover, Newtonian mechanics is by far simpler and clearer and more
widely known than anything else (including, e.g., Dalembert's approach
based on non-inertial frames and virtual inertial forces/torques, which
is abused in research but rarely taught in undergrad classes).

From: Ian Fisher

Hi Rene,

This sounds like a very interesting project. One chapter I found very
useful for the sort of thing you're talking about is:

'Euler's & Lagrange's Equations for Linked Rigid Body Models of
Three-Dimesional Human Motion' James G Andrews, p.145 et seq.

in 'Three Dimensional Analysis of Human Movement' Allard, Stokes & Blanchi
Human Kinetics Publishers 1995.

(for more info, look up

, I think it's more or less what you are after. A lot of the other
chapters are very good too.

I would have thought a Newtonian approach would be easier - are you
including muscle actions ?

>(v) It would be of use to have complete mathematical/mechanical models of
>JAVELIN/THROWING/BASEBALL PITCHING because this can be most suitably
>adapted to the cricket bowling action.

(especially if the bowler is a certain Sri Lankan!!)

Have you seen 'Biomechanics of Baseball Pitching' at


>(vi) If anyone has personal experience in this area, and can offer some
>useful suggestions, please feel free to do so.

I don't have any experience of working with cricket biomechanics, but I am
interested in cricket & biomechanics and a couple of things occur to me.

(1) I'm sure a lot of insight or valuable model validation could be gained
by looking at which structures normally get injured while bowling and
attempting to draw conclusions (there shouldn't be a shortage of injuries
to study !).

(2) I'm curious as to whether you're planning on modelling the wrist &
finger actions required to spin the ball . One of my mates asked me
whether or not there is any biomechanical reason why you can't bowl fast
with a lot of spin when we were watching a game. I'm pretty sure that the
most important factor is that the action of the entire body is different in
both cases, but we weren't sure whether or not the muscle's force-velocity
relationships would significantly hamper fast hand movements while the arm
is moving quickly.

I'm English, so I know the following is very important in bowling:

(3) Don't be English.
(2) If you are on no account play for the national side.
(1) Don't be Andy Caddick.

Of course, point 3 does not apply if you're Melvyn Betts.

Hope some of the above is useful,
Dear Rene',
contact Prof. Hatze
University of Vienna, Austria.
Professor of Biomechanics and Head of the Department
He describes his modell in a paper which is on the net.
ISBS '98: http://www.isbs98.uni-konstanz.de/
Select the Geoffrey Dyson Award and you will find the paper.

I hope it helps, good luck


************************************************** ******
* Dr.Christian Peham
* email: Christian.Peham@vu-wien.ac.at
* Clinic for Orthopaedics in Ungulates
* Locomotion Research Group
* University of Veterinary Medicine Vienna
* Phone: +43-1-250 77/5506; Fax: +43-1-250 77/5590
* Josef Baumanngasse 1; A-1210 Wien
* http://www.vu-wien.ac.at/i111
************************************************** ******
You may wnat to seek out the Biomechanics researchers at the Univ of
California, Davis. Many published articles on Baseball and Javolin.

Let me know how I can further help

Motion Analysis Corporation
Daniel India, Vice President
3617 Westwind Blvd
Santa Rosa, CA 95403 USA
HQ Tel: 707-579-6500 Direct 847-945-1411
HQ Fax 707-526-0629 Direct 847-945-1442
From: "Glenn Fleisig"
Dear Rene',
While we have not yet looked at the cricket throwing motion, we have
studied baseball, American football, and softball throwing kinematics
and kinetics. Some of the equations are in a few of our articles in the
"Journal of Applied Biomechanics" (Fleisig et al., 1996; Escamilla et
al., 1998; Barrentine et al., 1998). We also wrote a review article in
"Sports Medicine" (Fleisig et al., 1996) that compared and discussed
many different throws, but not cricket.

I hope this is helpful. Feel free to contact me if I can be of further

- Glenn

************************************************** *******
Glenn S. Fleisig, Ph.D.
work phone: 205-918-2138
work fax: 205-918-0800
address: American Sports Medicine Institute
1313 13th Street South
Birmingham, Alabama 35205
web site: http://www.asmi.org
From: Rod Whiteley
On 24-Jun-98, Rene Ferdinands wrote:
>Hello! My name is Rene' Ferdinands
G'Day Rene'

>(v) It would be of use to have complete mathematical/mechanical models of
>JAVELIN/THROWING/BASEBALL PITCHING because this can be most suitably
>adapted to the cricket bowling action.
>(vi) If anyone has personal experience in this area, and can offer some
>useful suggestions, please feel free to do so.

With regard your last two points; I've been interested for a long time in the
mechanics of the throw as they relate to pathology. Being an Australian,
cricket is the summer sport of choice over my beloved baseball, so I've always
been attempting to extrapolate from the well studied and documented act of
baseball pitching to cricket bowling. (Note that there is very little in the
literature on the throws of fielders.) My gut feelinig is that these are very
different activities. The only evidence I can give you for this is a clinical
piece. Throwers with demonstrable shoulder anterior instability are unable to
throw or pitch, but can usually happily bowl. I'd love to stay informed of
your work, and if I can help (with mechanics of pitching references I guess)
let me know.
Rod Whiteley

Mitchell & Whiteley Physiotherapy.
Find attached to this mail a couple of pitcing mechanics references. Once
you've got these, if you chase their reference lists, you'll be well on your
way to the bulk of the throwing literature.
Keep me informed as to your progress regarding bowling, I'd love to be of any
help I can. As I said, I've been thinking about these things for a long time
nw, and may have some ideas of use to you.
Mitchell & Whiteley Physiotherapy.

Elliot B., Grove R. Gibson B., Thurston B. A three dimensional
cinematographic analysis of the
fastball and
curveball pitches in baseball. International journal of sport biomechanics
1986 2:20-28
Feltner M., Dapena J. Dynamics of the shoulder and elbow joints of the
throwing arm during a
pitch. International journal of sport biomechanics 1986 2:235-259
Fleisig G Andrews J Dillman C Escamilla R Kinetics of baseball pitching
with implications about
mechanisms American Journal of Sports Medicine 23 3 1995
Joris, H.J.J., Edwards van Muyen A.J., Van Ingen Schenau J.G., et al Force,
velocity, and energy
flow during
the overarm throw in female handball players. Journal of Biomechanics, 1985
Pappas A.M., Zawacki R.M., Sullivan T.J. Biomechanics of baseball pitching
A preliminary report
American Journal of Sports Medicine 13:4, 216-222

From: BASTIEN Richard
Hi René

Take a look at http://www.ceit.es/english. They're in Spain near the
french border and have developed a manikin which can simulate movement
based on a motion capture system. The calculation gives you torques,
acceleration etc.
You can also take a look at http://www.transom.com, they're retailing
JackTM software which has been developed by Norm Badler (Univ of
Pennsylvania, Philly), this manikin has a inverse kinematic engine that
might give you some ideas.
You can also take a look at
http://www.adams.com/mdi/product/modules/android.htm. They've got a
manikin that is used by some R&D lab in sports. They have a good
background in sport simulation, even if this isn't written in their web
site. I have the name of the development manager in LA if you're

Hope this helps

From: Wolfgang Pagani
Reply-To: pagani@writeme.com
Dear Rene Ferdinands,

if you want to do any 3D modeling try a software that is called SIMI Motion or
SIMI Motion Capture. With those two packages you are able to digitize any kind
of motion and make your own virtuell charackters move like real ones. Or you
just want to analyze motion e.g. velocity(left foot right foot)
angles(hip-knee-ankle).... 3D view...
For more information go to http://www.simi.net

Yours sincerely

Wolfgang Pagani
From: Dwight Meglan
Subject: Dynamics of movement

Hi Rene,

It wasn't clear to me if you are doing inverse or forward dynamics, i.e.
analyzing the forces/torques at the joints based on captured data or if you
are synthesizing motions from prescribed forces/torques. For Inverse
dynamics there a number commercial packages around (check the biomechanics
website) and there is a public domain package that I wrote a number of
years ago (also at the website). For forward dyanmic simulations, there are
also a number commercial packages, such as ADAMS/Android (Mechanical
Dynamics) and SIMM/Dynamics Pipeline (MusculoGraphics) which are just for
human figure simulation. In addition, I did my own forward dynamics package
for for my PhD years ago-- I wouldn't use though, too many unfinished
pieces and a fuzzy mind on my part relative to support ;-) There have been
a number of research works on figure simulation in recent years, e.g.
Michael McKenna of MIT. Also, I know at least one free package for
multibody dynamics called dynamechs out of the naval postgraduate school --
don't have the web address but I am sure you can dig it up. Lastly, I
recently saw a demo from a company called Katrix which had a dynamic
simulation of a human figure. It was a 2.5D simulation (partial right-left
balance) with maybe 12-17 DOF but it ran at 30 Hz on a PC -- they are
working on this to add better motion to characters in games and dismounted
infantry for military simulations. Boston Dynamics also sells a product for
dismounted infantry, DI/Guy.

Do some digging on the web you'll find all kinds of stuff -- have fun ;-)
From: Tom Buchanan


I suggest you look at the software being developed by Ali Seireg at U
Wisconsin (http://www.engr.wisc.edu/me/faculty/seireg_ali.html). It models
many, many body segments. It is scheduled to be released very soon, along
with a series of textbooks describing how to use it.

From: "Harald Böhm"
Organization: Deutsche Sporthochschule Köln
X-Mailer: Mozilla 4.03 [de] (WinNT; I)
To: redf1@waikato.ac.nz
Subject: Re: Lagrange Mechanics

Hallo Rene

> (i) Is there any published work that has already modelled the movement of
> the human body as a dynamic set of Lagangian equations.

In the book: E.J. haug: 'Computer -Aided Kinematics and Dynamics of mechanical
Systems'Allyn and Bacon Boston,
They describe how to write the Equations of motion with the help of Lagrange
It is not directly for the human Body but they explain Joints and everything
you need to build
a human Body.

> (ii) Alternatively, are there complete models using Newtonian mechanics
> (force-mass-acceleration-torque).
> (iii) It would be useful to have an email address for David A. Winter.
> (iv) Could I have some references for other types of
> mathematical/mechanical models of the human body.
> (v) It would be of use to have complete mathematical/mechanical models of
> JAVELIN/THROWING/BASEBALL PITCHING because this can be most suitably
> adapted to the cricket bowling action.
> (vi) If anyone has personal experience in this area, and can offer some
> useful suggestions, please feel free to do so.

I have some experience in modeling Human Multibody Systems but I've formulated
the equation of motion only for 2D. by myself. In 3D. the Equations are too
long and too much so that I am using a multibody software such as ALASKA,
DADS, SIMPACK... (This software is quite expensive.)

In the software DADS they are using Euler Parameters for describing the
rotations to avoid singularities in their matrices. maybe this could help you
to obtain better solutions.


Maybe this Information helps a little

So long



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