View Full Version : Passive moments at elbow joint

Panagiotis Artemiadis
09-12-2004, 06:23 PM
Dear Sirs,

I am working on my PhD on the Control System Laboratory
of the Mechanical Engineering Department of the National
Technical Universoty of Athens, Greece.

I am working on a dynamic model of the
human forearm-arm, concerning the flexion-extension of
the elbow joint.

As I have seen on a paper I should include passive moment
for the elbow joint, which is calculated by the following

M(q) = Ko*q + bo*q_dot + k1*(exp(K2*q) -1)

where q = angle of joint
q_dot = velocity (=dq/dt)

I wonder if it is critical to be added, and where
can I fing those parameters: Ko, K1, K2, bo

This formula is presented in the following paper:

Winters, J. M. and Stark, L. (1985) Analysis of fundamental human movements patterns
through the use of in-depth antagonistic muscle models. IEEE Trans. biomed. Engng 32,

I would be very gratefull if anyone can send me this paper
in pdf format, or advice me of this passive moment, and the
significance of its existance in a dynamic model.

The equation of the model that I have already developed is just
the following, without any friction parts:

(I+m*d^2)*q_ddot + m*g*d*cos(q) = M

where I : moment of inertia with respect to elbow joint
d : the distance between the joint and the center of mass
of the forearm+hand
q : the angle of joint
q_ddot : second derivative of angle q
m : mass of forearm+hand
g : gravity
M : torque produced by the muscle force

Thank you in advance for your replies,

Panagiotis Artemiadis

Panagiotis K. Artemiadis
PhD Candidate
Control Systems Laboratory
Mechanical Eng. Dept
National Technical University of Athens
9 Heroon Polytechniou Str.,
Zografou Athens 15700, Greece
Phone : ++30 - 210 - 7723656

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