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 12:10:58 GMT
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Viewed:
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731 times
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In lugnet.cad.dev, Philippe Hurbain writes:
> Hi Kevin,
>
> I think common tangent to circles is too restrictive, since rubber belts
> tolerate quite a lot of misalignment.
> (http://www.lego.com/constructopedia/entry.asp?letter=P&id=1)
>
> So the problem should be reformulated as:
> Two circles in 3D space define two cylinders orthogonnally extruded from
> them. Among tangents common to these cylinders, find the ones for which
> tangency points are located on the circles.
>
> Ouch ! I need some Aspinin now ;o)
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.
Have you recovered? If so, do you a mathematical solution to your new
problem? :-)
Thanks,
Kevin
>
> Philo
> www.philohome.com
>
> >
> > In 3D space you can have circles that are tangent along one line. Imagine a
> > vertical bar that has a circle attached tangentially, but can turn around
> > the bar, and slide up and down the bar. Attach another circle to the bar
> > with the same capabilities. You can hold one circle fixed, and place the
> > other circle an infinite number of places and orientations and still be
> > tangent to the line.
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Message has 1 Reply:
 | | Re: Tangent between two circles in 3D space?
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| (...) More or less... there are 4 tangents to the 2 cylinders that happen to be on the circles. (...) 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 (...) (21 years ago, 22-Jan-03, to lugnet.cad.dev)
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Message is in Reply To:
| | Re: Tangent between two circles in 3D space?
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| Hi Kevin, I think common tangent to circles is too restrictive, since rubber belts tolerate quite a lot of misalignment. ((URL) the problem should be reformulated as: Two circles in 3D space define two cylinders orthogonnally extruded from them. (...) (21 years ago, 22-Jan-03, to lugnet.cad.dev)
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