8/ is there a process (maybe involving perfect planes, or three threads interoperating, or something) that can bootstrap mathematical truth
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Replying to @MorlockP
9/ into the real world, and deliver a perfect thread, where thread pitch is invariant over the length of the thread (i.e. if pitch angle is
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Replying to @MorlockP
10/ 60° at one end of the screw, it's the same in the middle, and at the far end, etc. Not worried about thread profile, which comes from
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Replying to @MorlockP
11/ the shape of the cutter. American Unified Thread standard has 60° profile (IIRC), and that is easily derived though simple geometric
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Replying to @MorlockP
12/ construction with a straightedge and a compass. I've got a vague memory that the first high precision thread was hand made near perfect
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Replying to @MorlockP
13/ along a 1" or 2" length and then this was used as a lead screw in a lathe, thus allowing it to self replicate along length of workpiece
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Replying to @MorlockP
14/ but I can imagine the existence of other techniques. For example, the surveyor's transit is simple, but amazingly cool.
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Replying to @MorlockP
15/ Picture a tripod with a flat platen on top, engraved with degree markings. Then a telescope pivots atop that. Scope has indicator arrow
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Replying to @MorlockP
16/ Naively, I aim scope at church steeple #1, note degrees, then aim at steeple #2, note degrees, subtract, find angle.
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Replying to @MorlockP
17/ Problem is that precision is gated by the crispness of the incised angle marks on the platen. Not even talking accuracy in layout!
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18/ Just noting that on a 1' dia circle, the width of the chisel incised layout ticks is very noticeable. 1/2 ° or more!
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Replying to @MorlockP
19/ I ran into exactly this when tramming in Bridgeport's head: head has angle markings. Setting it at 0° is just the start of the process
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Replying to @MorlockP
20/ So how does a surveyor's transit do its magic? The platen can rotate and there is a second indicator. Hand wavingly, you lock scope
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