View Full Version : Summary: Estimating Joint Torques

Marcia K. O'malley
01-04-2002, 09:18 AM
Thanks to all for your responses. The initial posting asked if there
was a way to estimate the torques realized in each joint of the arm if
you know the force at the hand (for example, if you push on a solid
surface with a known force, how much torque is seen at each degree of
freedom of the arm?). The desired application was for force reflection
to a human via an arm exoskeleton. Normally you can calculate all the
joint torques if you know the jacobian of the exoskeleton and the force
to be displayed (from torque = transpose of the jacobian times your
force vector). However, this calculation gets cumbersome and can slow
down your sampling times as your degrees of freedom increase. I was
seeking a simpler method for estimating the torques at each joint based
on a known force vector. A summary of responses is included below.
-- M. O'Malley

>From Edward Morra (ed@orl-inc.com)
You can develop a simple model to calculate joint torques as a function
of hand load and joint angles, just work out a 2D free body diagram of
the arm and develop the static equilibrium equations from it. Examples
can be found in most biomechanics text books. If you have an equal
amount of equations as unknowns you can readily solve the problem. If
you have more unknowns than equations than you have to rely on some
optimization algorithm to get your answer. Most spreadsheet software and
certainly MatLab are effective tools in developing quasi-static
approximations in both cases.

>From Germano Gomes (G.T.Gomes@ncl.ac.uk)
If you want to use some freely available routines I recommend the
robotics toolbox for Matlab. It was developed by Peter Cork and is
available at:
In particular, the function RNE (it uses a recursive Newton Euler
approach) should give you exactly what you want if you describe the
kinematics of the limb in terms of a D-H matrix (standard or modified).
Another package to consider is Spacelib developed by Legnani and
available in Matlab and C language from the ISB Technical Group on
Computer Simulation at:
http://www.isbweb.org/~tgcs/ Good luck

>From At Hof (a.l.hof@meg.rug.nl)
Some ideas might be got from my paper
A.L. Hof An explicit expression for the moment in multibody systems
J. Biomechanics 25: 1209-1211 (1992)
I hope this is what you need.


Marcia K. O'Malley
Assistant Professor
Mechanical Engineering and Materials Science - MS 321
Rice University
6100 Main Street
Houston, TX 77005-1892

Tel: 713.348.3545
Fax: 713.348.5423


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