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 Post subject: Mechanism design challenge: The Flipping Axes Cuboid
PostPosted: Tue Sep 03, 2013 7:39 am 
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Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
In going over possible 3x3x3 cuboids (of which there are, ahem, a lot), there's one which I find particularly interesting and would like to present as a challenge for mechanism designers.

First, the doctrinaire description: Make a 3x3x3 cuboid which can't move on the U and D axes and only allows greater than deep cuts on the F, B, R and L axes. To make things more interesting, the mechanism should also allow slice moves, in fact as long as you're moving, say R and L, you should be able to rotate both of them completely independently without an internal mechanism ever getting stuck.

A possibly more intuitive way of understanding the puzzle is to think of it as a regular shallow cut 3x3x3 cuboid, with four axes which can turn and the curious property that whenever you rotate a face then the four axes which aren't opposite that one flip which ones can rotate and which ones can't. The slicing property still applies, so as long as you're moving just R and L they should rotate completely independently without any internal mechanism catching. Thinking about the puzzle this way makes the way the slicing property works out seem much more magical.

Epicyclic gearing may be helpful in designing this one, although I honestly am not sure how to do it even using that, so I present it as a mechanism design challenge for all you inventors out there.


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