[math-fun] ~s gears
John McCarthy collects inventions that came too late to do much good, e.g., the non-pulsating candle wick. In this era of numerical machi- ning, we ought to be able to make interesting gears to solve mechanical problems of yesteryear. As a minor (and probably unoriginal) example, to minimize stripping, a smaller gear ought to have broader teeth and narrower notches than the larger gear it meshes with. This must be geometrically possible, at least sometimes, since you could delete alternate teeth from a(n even-toothed) larger gear and fill in the corresponding notches of the smaller one. However, if we view this as a deformation of gears with half as many teeth, we have lost something like half the tooth amplitude (proper term?), so there may be little advantage in desymmetrizing. We might get certain exotic ratios with differential planetaries where the ring and central gears differ by an odd number of teeth. This might be possible if those gears are in slightly different planes, slightly beveled, with slightly tilted planets spanning the gap. The planets or ring might have a hollow shaft coaxial with the central's, both driven (at different speeds) by one adjoining shaft bearing two gears. This would require "continuous" scalability of one gear and its mate on one of the coaxial shafts. I'd like to animate gears with improbably small numbers of teeth (3??, 4?). Can anyone save me the trouble of deriving the involute curves that avoid sliding friction? --rwg PS, apologies for my churlish Mahalingam ouburst. A few minutes of Google, or consulting with any Subcontinental would have taught me that it is a proud old name of long standing. E.g., Welcome to Shankar Mahalingam's homepage. Professor and Chair Department of Mechanical Engineering University of California, Riverside ... This gentleman has *absolutely no connection* with the villain in the up-and-coming Goldmember sequel. And all this is dinky by comparison with former African head-of-state Houphouet Boigny, which in his own language means "Pit of Excrement". "Oh Miss Rice, here's some xylo- caine in case you need to bite your cheeks during the introductions." SUBNARCOTIC OBSCURANTIC BUCCINATORS (You bet your mahalingam.)
Who is collecting inventions that were ahead of their time -- e.g., Greek/Roman gear trains, DaVinci war machines, etc. ? I'm particularly interested in why the Roman civilization never invented powered machines -- they obviously had excellent technology in civil engineering and naval engineering. I have a pretty good idea why the Greeks didn't -- they were way too fixated on theory rather than practise, but that didn't seem to be a Roman problem. Perhaps the inward-looking spiritual outlook of the Christian era diverted attention from mechanical progress. At 10:57 AM 2/7/2005, R. William Gosper wrote:
John McCarthy collects inventions that came too late to do much good, e.g., the non-pulsating candle wick.
The Greeks may have been just as practical as the Romans. One is less likely to find documentation. Heron of Alexandria is usually credited with the invention of the turbine. R. On Wed, 9 Feb 2005, Henry Baker wrote:
Who is collecting inventions that were ahead of their time -- e.g., Greek/Roman gear trains, DaVinci war machines, etc. ?
I'm particularly interested in why the Roman civilization never invented powered machines -- they obviously had excellent technology in civil engineering and naval engineering.
I have a pretty good idea why the Greeks didn't -- they were way too fixated on theory rather than practise, but that didn't seem to be a Roman problem.
Perhaps the inward-looking spiritual outlook of the Christian era diverted attention from mechanical progress.
At 10:57 AM 2/7/2005, R. William Gosper wrote:
John McCarthy collects inventions that came too late to do much good, e.g., the non-pulsating candle wick.
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Henry Baker wrote:
I'm particularly interested in why the Roman civilization never invented powered machines -- they obviously had excellent technology in civil engineering and naval engineering.
The one that baffles me is how they managed to miss the overhead water wheel. They had aquaducts, they had water wheels that went into rivers, and it's *so* much more efficient to pour the water in on top... --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.
participants (5)
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Henry Baker -
Marc LeBrun -
Michael Kleber -
R. William Gosper -
Richard Guy