derive functions for generating projections for the interpenetration of two cylinders for making fittings

Question

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I want to make custom fittings for constructing large molecular models using copper tubing.

I will need to cut a hole in one piece of tubing that will closely fit around another inserted piece. I thought about cutting a pattern on a flat piece of sheet metal. I would wrap this around the tubing where it would serve as a guide for a cutting tool.

I have viewed this video that describes the interpenetration of two perpendicular cylinders. I am lost as to how to handle cylinders joined at an angle, let alone generate a projection that I can use for the pattern.

Can someone tell me how to begin deriving the functions to do this?

Answer 1

OnShape is a useful free (if ou make your designs public) 3D CAD program. There's an introductory tutorial showing some of the techniques to create sheet metal cylinder on YouTube TechProductDesign channel.

Figure 1. The pipe with hole extruded from angled plane. Note the gap at the rear to allow the sheet metal flattening.

Figure 2. The flattened sheet metal pattern.

Figure 3. Intersecting pipe and cylinder. Note that Plane 1 is defined by the construction line at the bottom right and the point visible above the pipe intersection.

Expect to put some effort into learning how to do this. It's not difficult but will take some time so do some simple exercises before you attempt your real project.