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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Tue, 21 Jan 2003 16:51:43 GMT
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Viewed:
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3001 times
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Don,
I'm assuming four pulleys in this case. Two are parallel to each other
where the rubber band bends to be non-planar, and two others that pull the
band around the two parallel pulleys.
Kevin
In lugnet.cad.dev, Don Heyse writes:
> 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.
>
> It sounds like you want the intersection point of the 2nd circle with
> the plane of the first circle. I guess that should be exactly one point
> unless they're in the same plane. However, I don't see how the rubber
> band gets back to the first circle without violating your rules. Is
> there another pulley/circle you're not telling us about?
>
> Don
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Message is in Reply To:
 | | Re: Tangent between two circles in 3D space?
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| (...) It sounds like you want the intersection point of the 2nd circle with the plane of the first circle. I guess that should be exactly one point unless they're in the same plane. However, I don't see how the rubber band gets back to the first (...) (24 years ago, 21-Jan-03, to lugnet.cad.dev)
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