32/ generates the three dimensional revolution of it, i.e. straight edge -> cylinder or cone), we can wrap straight edge onto the cylinder
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Replying to @MorlockP
33/ and it's an elementary geometric proof that the angle that the edge makes vs circumference A is the same angle it makes vs circumf B
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Replying to @MorlockP
34/ bc the circumference at point A is a parallel line to the circumference at point B (non Euclidean space, obviously!)
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Replying to @MorlockP
35/ to whit, the old "a line that intersects paralllel lines creates corresponding angles" proof (not axiom?) http://www.mathnstuff.com/math/spoken/here/2class/260/trans.htm …
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Replying to @MorlockP
36/ which still holds in the simple non Euclidean space we're talking about.
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Replying to @MorlockP
37/ So we can create the thread pitch we want with simple compass work (bisection is legal, trisection is not), but we can also get 60°
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Replying to @MorlockP
38/ and we can then align a straightedge along this angle and wrap it, and then we get a constant thread. Now it's a "simple" matter of
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Replying to @MorlockP
39/ building some sort of pantograph machine which can take these angles and straight edges off references and apply to spinning workpiece
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Replying to @MorlockP
40/ which is actually a tricky bit of design and machining, and will add inherent errors to output...but it is, in principle, doiable
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Replying to @MorlockP
Once you make two threads, you can average them to make the third higher precision. IIRC Da Vinci designed a machine for that.
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so averaging is a powerful technique. I was reading up on Whippletrees the other night in bed https://en.wikipedia.org/wiki/Whippletree_(mechanism) … bc I had a thought
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re some firewood sheds I want to build. Don't want to do the work of putting in footings (also, don't want to pay taxes on permanent struct
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had just watched a video where a guy built a platform for his machine room granite surface plate that was supported at 4 - but kinda 3 - pts
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