As a machinist I love you guys but have to throw in my 2 cents for early on and say I’d roll the cylinder first and cut the hole in the side.
What is this AutoCAD of which you speak? 
Amen. Hallelujah. End of discussion. If one has a mill at their disposal.
I was a little too quick in my reply. You wouldn’t need a mill… How about a (deep throat) hole saw, a drill motor , and a vice? Easy-peasy.
When done, flatten out the slug from the hole saw, and you’d have a souvenir template.
Well really, if you’re going to do practical hands-on solutions; get a big wood cylinder same size, bore a hole into it, the wrap around it with paper to get the pattern of the hole to transfer to sheet metal. No worries about sheet metal cylinder deforming under the pressure of power tools, etc. Or do it the other way, take a wood cylinder the size of the smaller intersecting pipe and cut it with a circular cut radius size to mimic the intersection. Transfer that to paper. it occurs to me a concave and convex cut would of course have the same outline pattern.
Acquiring “big wood cylinder”(s) in applicable pipe or duct ODs might prove to be problematic for you. Think (perhaps) telephone pole size dowels. Home Depot would not be your friend there.
FWIW: A couple of strap clamps around either side of the point of intersection of a hole saw into thin sheet metal duct will make it as ridgid as a wedding dick, if in fact we are talking about duct work (yet to be established).
Bolding mine.
Huh? What? How? Now we’re getting back to the math/drafting conundrum, and I don’t think that is settled.:smack:
“Well really”:rolleyes:… Keep working on your tech solution. Leave the "practical hands-on" to other folks… They probably have already moved on.
I puzzled on that awhile too. I’m *pretty sure *what he meant was as follows:
- Get a dowel the diameter of the small pipe & chuck it up in a vise.
- Get a hole saw the diameter of the large pipe.
- Use the hole saw to cut off the end of the dowel at the appropriate angle (typically 90 degrees to the dowel long axis) and large/small axis offset (typically zero).
- The cut end of the remaining dowel simulates the edge we’re seeking.
His solution is not analytical at all. He’s simply doing the real work on (supposedly) easier to obtain and easier to work with materials at 100% scale. Then tracing the result onto the real materials.
Which for many problems and materials (e.g. stonecutters) was/is how it’s been done for dozens of centuries now.
And the point was: This was the least practical hands on solution offered.
That was understood. The issue is the overall “practicality” of the matter. Initially, math was hoped to provide the magic bullet, and that never panned out. Then, drafting (be it old school, or CAD) was the next candidate until it proved to be overly complex and perhaps an expensive solution (that would derive merely an approximation) as would other, simpler methods already offered. Then it was back to math again… Then it wasn’t.:smack:
Now, after the fact, a proponent of the previously mentioned (and less than stellar) technical solutions begins to lecture about a “practical” solution with, let’s face it… Goofy notions. Notions that while* technically feasible*, are far more impractical than the ideas previously offered… A little tough to swallow, hence the "Huh? What? and How?’
Gotcha. Sorry if I tweaked your nose there.
So I finally got bored enough to work out some equations.
Suppose we have cylinders x[sup]2[/sup] + y[sup]2[/sup] = R[sup]2[/sup] and y[sup]2[/sup] + z[sup]2[/sup] = r[sup]2[/sup] where r <=R. If we further restrict the second cylinder to non-negative values of x the intersection of the two cylinders will be a one dimensional loop embedded in 3-space.
This gives us the following parametric equations:
(Sqrt(R[sup]2[/sup] - r[sup]2[/sup] Cos[sup]2[/sup]t), r Cos t, r Sin t) for 0 <= t < 2π
The above is very similar to the formula given in post 11. The difference is that I chose a different orientation.
Now we would like flatten out the first cylinder to a plane. We need a map that preserves distances which I will provide without deriving. I don’t think it’s too difficult to work this out and I will be happy to go into more detail upon request.
Here’s the map…
(x, y, z) -> (R Tan[sup]-1[/sup] (y/x), z)
Now we just have to compose the original parametric equations with the map…
(R Tan[sup]-1[/sup] (r Cos t / Sqrt(R[sup]2[/sup] - r[sup]2[/sup] Cos[sup]2[/sup]t)), r Sin t) for 0 <= t < 2π
Now let’s look at the special case r = R = 1. We get…
(Tan[sup]-1[/sup] (Cot t), Sin t) for 0 <= t < 2π
Now resist the urge to simplify Tan[sup]-1[/sup] (Cot t) to a line. We actually want the sawtooth form Tan[sup]-1[/sup] (Cot t). However, it’s not too hard to see that we could reparameterize this last equation to the more elegant…
(t, ± Cos t) for -π/2 <= t < π/2
Which is quite nice indeed.
Note that Fusion 360 is free for enthusiasts if that fits the bill.
I would also note that if the dimensions are critical it will really depend on the materials and the forming techniques.
While the light method above would work, for those who need a quick solution but have access to a cylinder of appropriate diameter I would use one of the many free tube and pipe notching calculators to produce the notched tube template and then simply trace around on the paper.
But if the OP could mention how critical the dimensions are the useful answer on how to calculate it may be a lot simpler. Unless the material is very thin the forming process would cause issues.
I took drafting back when schools had “a” CAD machine and on paper, if I was going to program this or draw it I would use parallel line development by starting with the height of the cross section of the intersecting tube section.
I can’t remember the right terms for it but I did find this video that will cover some of the concepts.
I was trying to remember the hack for G02/3 to abuse the arc movement but can’t remember it or find it and I doubt the OP will want to write raw gcode.
Note this is only a suggestion due to my own limited knowledge and will not be perfect or suitable for any critical dimensions.
It’s tax time, I’m easily provoked.
In most cases this solution would be close enough, I could add more lines if I wanted to for more accuracy. This is one of those things that I run into now and then when making things and I finally decided that I was tired of just figuring it out on the spot and grinding and shaping to fit.
I was trying to use a drafting method but I wasn’t able to visualize the problem correctly until after I actually saw it done on a video.