 | | Tangent between two circles in 3D space? —Kevin Clague
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| | | Anyone know how to find out the tangent between two cicles in 3D space? Kevin (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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| | | | | Re: Tangent between two circles in 3D space? —Steven Combs
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| | | | | (...) 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? Steven (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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| | | | | | | Re: Tangent between two circles in 3D space? —Kevin Clague
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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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| | | | | | | | | Re: Tangent between two circles in 3D space? —Don Heyse
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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 (...) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | | Re: Tangent between two circles in 3D space? —Kevin Clague
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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 (...) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | | Re: Tangent between two circles in 3D space? —Don Heyse
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| | | | | | | | | | (...) Ah Ha! Apparently there were TWO other pulleys you weren't telling us about. (URL) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | | | Re: Tangent between two circles in 3D space? —Kevin Clague
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| | | | | | | | | | I have a child in fourth grade, and like many his age, he is a natural born lawyer looking for loopholes, so 'm well versed in the tactic because it is hard to resist.... If you notice my original post, I didn't even mention pulleys, I just asked (...) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | | | Re: Tangent between two circles in 3D space? —Paul Easter
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| | | | | | | | | | (...) What you really need is to find a way to find just one side of the "rubber band". Say, pulley A to pulley B, "Side one". Then you could use the same function to determine pulley B to C, side one or two, and so on... Right? Paul (22 years ago, 24-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | | | Re: Tangent between two circles in 3D space? —Kevin Clague
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| | | | | | | | | | <snip> (...) Yes. lsynth only deals with 1 peice of stretched rubber band at a time, which is why I was keeping those other three pulleys a secret from Don. Kevin (...) (22 years ago, 24-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | Re: Tangent between two circles in 3D space? —Anders Isaksson
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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 (...) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | | Re: Tangent between two circles in 3D space? —Kevin Clague
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| | | | | | | | | | (...) This looks great! This is what I was trying say the other day during my ah,hah! moment, but not so tersely. Now I just need to know how to calculate the intersection of the line and each circle and I'll be all set I think. I'll do some (...) (22 years ago, 22-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | | | Re: Tangent between two circles in 3D space? —Steven Combs
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| | | | | | | | | | | Kevin, I have been watching this thread with great interest and it is really fun to watch the community pitch in and assist you. Would you do me a favor. When you finally have the solution, could you summarize in a post? I plan on using this as a (...) (22 years ago, 23-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | | | Re: Tangent between two circles in 3D space? —Anders Isaksson
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| | | | | | | | | | "Kevin Clague" <kevin_clague@yahoo.com> skrev i meddelandet news:H94xC1.11z@lugnet.com... (...) calculate (...) If the condition above (Dist(...) etc.) holds, then it's just a matter of projecting the circle centers onto the line, ie. solve for a (...) (22 years ago, 23-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | Re: Tangent between two circles in 3D space? —Ross Crawford
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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 (...) (22 years ago, 22-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | | Re: Tangent between two circles in 3D space? —Ross Crawford
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| | | | | | | | | | (...) Well, I'll start 8?) Step 6 - thats radius Step 7 - should be sin T = L / R ROSCO (22 years ago, 22-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | Re: Tangent between two circles in 3D space? —Philippe Hurbain
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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. (...) (22 years ago, 22-Jan-03, to lugnet.cad.dev)
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| | | | | | | | | | Re: Tangent between two circles in 3D space? —Kevin Clague
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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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| | | | | | | | | | Re: Tangent between two circles in 3D space? —Philippe Hurbain
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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 (...) (22 years ago, 22-Jan-03, to lugnet.cad.dev)
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| | | | | | | Re: Tangent between two circles in 3D space? —Don Heyse
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| | | | | | (...) I'm sure you're probably looking for a solution with x,y,z coords, but just in case, the 2D solution is on page 7 of Graphics Gems, and also here: (URL) think you should be able to transform your circles into the x,y plane with one center at (...) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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| | | | | | | | Re: Tangent between two circles in 3D space? —Kevin Clague
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| | | | | | (...) Don, this is what I do for planar rubber bands and it works great if the two pulleys are in the same plane. But I can imagine a four pulley configuration where the first pulley is parallel to the YZ plane, the second pulley is parallel to the (...) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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| | | | | Re: Tangent between two circles in 3D space? —Erik Olson
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| | | | (...) What have you tried so far? And which tangent? Think about it, there's an infinite number of solutions. Even on a plane there are multiple solutions. Recommendation: start with the book _Computational Geometry in C_ by Joseph O'Rourke. -Erik (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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