5.4 Muscle–tendon equilibrium

This problem was contributed by Carmichael Ong at Stanford University.

An experiment is performed in which a muscle–tendon unit is fixed at some (unknown) length, the muscle is activated to a predetermined level, and the tendon force is measured once the muscle and tendon have reached equilibrium (steady state). The muscle has the following active and passive force–length relationships:

The tendon has the following force–strain relationship:

The muscle and tendon parameters are , , , and pennation .

For each of the following experimental conditions (specified activation and measured tendon force), calculate the length of the muscle and the length of the tendon .

(a) ,

(b) ,

(c) ,

(d) ,

Solution (only visible by instructors; please contact us to request access)

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