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This problem was contributed by Jon Stingel at Stanford University.

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(a) Q


(b) QWe 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

Mathinline
body--uriencoded--\ell%5e%7B\mathrm%7BS%7D%7D = \ell_%7B\mathrm%7Bo%7D%7D%5e%7B\mathrm%7BS%7D%7D = 2.7~\text%7Bμm%7D
).

(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 (

Mathinline
body--uriencoded--\ell_%7B\mathrm%7Bo%7D%7D%5e%7B\mathrm%7BM%7D%7D
). What is the joint displacement (
Mathinline
body\Delta \theta
) beyond which the muscle will generate zero active force? Assume the muscle has the linear force–length relationship shown here:

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S6.7 Micro-muscle design
S6.7 Micro-muscle design

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