Specifications

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From the time the passive force sets in, the tendon starts to elongate a little bit.
The total origin-insertion length of the muscle-tendon unit is the tendon length plus the muscle length, i.e.
Lm + Lt. When Lt is stretched, the effect is that the muscle fibers stretch that much less, and since the
muscle's strength depends on the momentary length of the contractile element, the strain in the tendon can
influence the strength of the muscle. The figure above shows that the tendon stretch is rather limited and
we might therefore expect that the influence on the muscle strength is also limited. However, some muscles
in the human body (for instance m. soleus) have the property of relatively short fibers and a long tendon,
and in this case the effect can be significant.
The three-element muscle model attempts to take this into account in the computation of muscle activity,
coping with the fact that this is a catch 22 type of problem in inverse dynamics:
• We cannot compute the elongation of the tendon until we know the force in the muscle.
• We do not know the force in the muscle until we have solved the muscle recruitment problem.
• To solve the muscle recruitment we need the momentary strength of each muscle.
• The momentary strength depends on the elongation of the tendon.
We seem to be faced with a circular dependency between the muscle properties. The three-element model
copes with this through a one-time correction: It recruits the muscle without taking the tendon elongation
into account. Then it computes the tendon elongation. Finally, it computes the influence of the elongation on
the muscle's strength and corrects the muscle activity to the level that provides the necessary force with the
modified strength. This is only an approximative solution because the change of muscle strength may
theoretically alter the distribution of force between the muscles, and this alteration is not done by the
system; the correction is local to each muscle.
So much for passive properties. It is more instructive to investigate a muscle model with active force. The
easiest way to do so is to enable our hand force again and change it to point directly upward. This causes
the previously inactive Muscle2 to become active:
// Define one simple segment
AnySeg Arm = {
r = {0.500000, 0.000000, 0.000000};
Mass = 1.000000;
Jii = {0.100000, 1.000000, 1.000000}*0.1;
AnyRefNode Jnt = {
sRel = {-0.5, 0.0, 0};