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Homework7960 - TAM 7960 Legged Locomotion of Robots and...

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TAM 7960 Legged Locomotion of Robots and Animals (Terrestrial Locomotion) Spring 2010 Updated March 5, 2010 Homework Each homework assignment will start on a fresh page. This document will grow in length as the semester progresses. HW due Tuesday Feb 2 1. A natural measure of energy use is ”The specific energetic cost of transport”, Energy used weight distance Note that weight is a force (mass times ) so is a dimensionless number. Estimate, using whatever numbers you know or look up, the for at least 3 of these things. a person walking a person biking a car (full weight) a car (only counting weight of passengers) a freight truck a freight train a passenger train (only counting weight of passengers) some other animal of your choice, walking, running or flying. Make your assumptions clear and clearly identify (so I can check) any sources you use. Best if you have two different estimates, based on different types of data. 2. What would be a good measure of locomotion speed for comparing different animals or robots? Justify your answer as best you can. If you have more than one candidate, compare them. I am not looking for a quote from some paper or other, but your own thoughts. 1
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HW due Thursday Feb 11 1. An ideal passive transmission conserves energy. One example of a transmission is a screw- drive or ‘worm drive’ (read about such in, say, wikipedia). A model for the basic mechanics of a worm drive (left) is the wedge (right). A B F A F B F A F B F A N A N B F B F F A B ˆ ı ˆ j θ θ θ (a) (b) (c) (a) For simplicity, assume that all sliding is frictionless and that the parts have no mass or weight. Think of A as the input and B as the output. i. Find in terms of and . ii. From geometry (kinematics), find the sideways motion of B in terms of and the motion of A. iii. Note that the results above are consistent with energy conservation. iv. Simplify all of the expressions above using a small angle approximation ( sin etc. (b) Now include friction, but just on the surface AB. Assume a friction coefficient or friction angle with tan . Assume that the friction against the walls is still zero. For the worm drive this is like assuming that the shafts have good bearings but that all the friction is on the screw surface. Assume the wedge is going down.
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