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 16:19:37 GMT
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Viewed:
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727 times
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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.
Kevin
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Message has 4 Replies:
 | | 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 (...) (21 years ago, 21-Jan-03, to lugnet.cad.dev)
| | | Re: Tangent between two circles in 3D space?
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| "Kevin Clague" <kevin_clague@yahoo.com> skrev i meddelandet news:H92o0p.CGB@lugnet.com... (...) a (...) Line = Intersect(C1.Plane, C2.Plane) if (Dist(C1.Center, Line) = C1.Radius) and (Dist(C2.Center, Line) = C2.Radius) ... (Or have I (...) (21 years ago, 21-Jan-03, to lugnet.cad.dev)
| | | Re: Tangent between two circles in 3D space?
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| (...) 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 (...) (21 years ago, 22-Jan-03, to lugnet.cad.dev)
| | | 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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