3/ ...because there IS an analagous process to generate a perfectly flat surface! You take three stones and rub them, A vs B, B vs C ...
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Replying to @MorlockP
4/ A vs B does not work. There are an infinite number of solutions to "f() is the inverse of g()". A develops a spherical shape...
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Replying to @MorlockP
5/ and there are an infinite number of spheres (varying r) and matching g() (concave matching shape).
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Replying to @MorlockP
6/ but why matching A vs B vs C you create a simultaneous equation where f() inverse g(), g() inverse h(), h() inverse f(), and there is >
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Replying to @MorlockP
7/ only one solution to that: f() = g() = h(), where all describe sphere w r = ∞ (i.e. perfect plane). So my question re threads is:
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Replying to @MorlockP
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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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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