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    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
    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 :
    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:
    Select the Geoffrey Dyson Award and you will find the paper.

    I hope it helps, good luck


    ************************************************** ******
    * Dr.Christian Peham
    * email:
    * 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
    ************************************************** ******
    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

    A A S S MM MM I
    A A SS M M M I
    A A S S M M I
    ************************************************** *******
    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:
    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 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, 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 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
    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

    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 ( 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)
    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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