Subject:
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Re: Tangent between two circles in 3D space?
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Newsgroups:
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lugnet.cad.dev
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Date:
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Wed, 22 Jan 2003 13:28:07 GMT
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Viewed:
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829 times
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>
> Yes. This *is* the ultimate (and probably universal) solution, although we
> probably need to be able to find one of four cylinders between any two
> circles in 3D space.
>
> You are thinking in terms of pulleys always on the outside of the band.
> With rubber bands that cross over themselves, or bands with pulleys on the
> outside of the band pushing in, we need a second pair of tangents.
More or less... there are 4 tangents to the 2 cylinders that happen to be on
the circles.
>
> Have you recovered? If so, do you a mathematical solution to your new
> problem? :-)
Some thoughts that could perhaps (with [lots of] work) lead to an iterative
solution:
- Select one of the circles, then choose one radius of this circle.
- This radius defines a plane, orthogonal to the radius and tangent to the
circle.
- Now, study the intersection between this plane and the second circle. When
there is an intersection, look at the radii at the intersection points. If
one of these radii is orthogonal to the plane, you have one solution...
As I guess, in the general case you should find 4 radii/planes that are
solutions to the problem... But additionnal checks should probably be
performed to assure that the resulting rubber band is mechanically usable...
Good luck with that ! (You did stock a lot of Aspirin, didn't you ???)
Philo
www.philohome.com
PS: I'm not quite sure that what I say above is mathematically correct...
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Message is in Reply To:
 | | Re: Tangent between two circles in 3D space?
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| (...) Yes. This *is* the ultimate (and probably universal) solution, although we probably need to be able to find one of four cylinders between any two circles in 3D space. You are thinking in terms of pulleys always on the outside of the band. With (...) (22 years ago, 22-Jan-03, to lugnet.cad.dev)
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