This problem was contributed by Jon Stingel at Stanford University.

Suppose a muscle–tendon unit has the following properties:

and it is exerting force between two bones in the following scenario:

activation
pennation angle

(a) Assume the tendon is rigid, the muscle is contracting isometrically, and the muscle and tendon are in equilibrium. Calculate the length of the muscle () and the force in the muscle ().

(b) Now assume that the tendon is compliant with stiffness . Further assume that both the muscle and tendon have linear force–length relationships (see figures below). Design an algorithm (using pseudocode or a flowchart) to solve for the muscle force (), starting from an initial guess for muscle length () and iterating until a stopping condition is met. Just describe the algorithm (do not try to solve for ).

(c) Complete one iteration of the algorithm you designed in part (b) using the properties and scenario described above. Use the initial guess . Based on your calculations, how should you change your guess to get closer to the point where the muscle and tendon are in equilibrium?

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

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