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 00:29:26 GMT
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Viewed:
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774 times
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In lugnet.cad.dev, Kevin Clague writes:
> In lugnet.cad.dev, Steven Combs writes:
> > In lugnet.cad.dev, Kevin Clague writes:
> > > Anyone know how to find out the tangent between two cicles in 3D space?
> >
> > Wouldn't they have to be on the same plane in order to find the tangency? Or
> > did you mean the tangency of two spheres?
>
> With two circles in the same plane you can have four possible tangent lines.
> LSynthcp uses this to calculate straight line segments of rubber bands
> around pulleys.
>
> 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.
>
> So, given two pulleys in a rubber band synthesis specification, I need to be
> able to tell if there is a common tangent between the two of them in 3D
> space, and if so, what the parameters for the line are. This will allow me
> to synthesize non-planar rubber bands.
>
> I barely made it through planar rubber bands, but non-planar is next, so I
> thought I'd ask for help.
OK. Here's my rather convoluted analysis:
1. Find the plane of pulley A
2. Find the plane of pulley B
3. If they dont intersect, no tangent so stop here
4. Find the angle between them, call it T
5. Find the normal to plane A that passes through centre of pulley B, call it L
6. Call readius of pulley B R
7. If sin T = R / L then pulley b is tangent to plane of A so possible
tangent, otherwise abort
8. Do the same, reversing pulley A & B; if both are tangents to the plane of
the other, then the line of intersection of their planes is the required
tangent. I think.
I haven't included the math, as I can't remember it, but I'm pretty sure you
can do all these calculations....
Anyone wanna tear this apart?
ROSCO
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Message has 1 Reply:
Message is in Reply To:
 | | Re: Tangent between two circles in 3D space?
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| (...) With two circles in the same plane you can have four possible tangent lines. LSynthcp uses this to calculate straight line segments of rubber bands around pulleys. In 3D space you can have circles that are tangent along one line. Imagine a (...) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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