6.7 Micro-muscle design

This problem was contributed by Jon Stingel at Stanford University.

We wish to construct a micro-muscle using sarcomeres from human skeletal muscle. The micro-muscle must satisfy the performance requirements described below. For this problem, assume that a sarcomere produces a maximum active force of 1 pN at optimal length (i.e., when ).

(a) Suppose the micro-muscle must have an optimal fiber length of 54 μm and must generate 5 pN of peak active force. What configuration of sarcomeres will achieve this objective and how many sarcomeres will be required in total?

(b) We will now select a moment arm for the micro-muscle designed in part (a). The muscle must generate a peak active moment of at least 0.14 pN·mm. What is the smallest moment arm that will achieve this objective?

(c) Suppose the micro-muscle spans an ideal pin joint and the muscle has the moment arm computed in part (b) when at its optimal length (). What is the joint displacement () beyond which the muscle will generate zero active force? Assume the muscle has the linear force–length relationship shown here:

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