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. The micro-muscle will operate over a range of fiber lengths: at its maximum length, each sarcomere is at the optimal sarcomere length (i.e., ); at its minimum length, each sarcomere has a length of . For this problem, assume that a sarcomere produces a maximum active force of 1 μN at its optimal length.

(a) Suppose the micro-muscle must have an optimal fiber length of 54 μm and must generate 5 μN 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 micro-muscle must generate a peak active moment of at least 128 μN·m. Furthermore, when starting from its optimal fiber length, the micro-muscle must be able to generate active force when the joint that it crosses displaces by up to 60°. What is the range of moment arms that will satisfy these two conditions?

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