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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 the following range of lengths: at its maximum fiber length, each sarcomere will be at its 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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; at its minimum fiber length, each sarcomere will have a length of | Mathinline |
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. For this problem, assume that a sarcomere produces a maximum active force of 1 μN at | Mathinline |
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(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 it has the moment arm computed in part (b) when it is at its optimal length. What is the joint displacement (
) beyond which the micro-muscle will generate zero active force? Assume 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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