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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 For this problem, assume that a sarcomere produces a maximum active force of 1 pN at optimal length (i.e., when
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| 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 |
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; at its minimum length, each sarcomere has a length of | Mathinline |
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body | --uriencoded--0.5 \ell_%7B\mathrm%7Bo%7D%7D%5e%7B\mathrm%7BS%7D%7D. 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 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 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?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 (
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| body | --uriencoded--\ell_%7B\mathrm%7Bo%7D%7D%5e%7B\mathrm%7BM%7D%7D |
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). 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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| title | Solution (only visible by instructors; please contact us to request access) |
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| S6.7 Micro-muscle design |
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| S6.7 Micro-muscle design |
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