[ATM] Off Topic: Pits and Pendulums and Cable Cars

["Richard Schwartz" <richard1941@gmail.com>]

I remember something from geometry that if you fix too ends of a loose
string, a pencil pressing against tha string traces out an ellipse.

I remember something from calculus that a sufficiently small portion of any
smoothe curve (like an ellipse, for example) is close to a parabola.

Put these ideas together, and you have... The cable car over the pit!   The
grinder rides on a cable, suspended on a pulley, and cuts an elliptical
channel into the blank.  The distance between the ends of the cable is
somewhat outboard the edge of the glass so that the turned up edge effect is
cut to an acceptable level. (And this is a prolate ellipse, the wrong side
of a circle for our needs.)   Rotate the blank on the turntable, and do it
again.  Eventually you have hogged out your approximate curve.

This provides the ability to generate curves whose radius might reach beyond
your ceiling.

A variation for DEEP parabolas would be to have a very high suspension point
for one end of the cable, and a suspension point near the focal point for
the other end.  Then the suspended grinder traces out the curve of a long
narrow ellipse that is very close to a parabola.   In fact, you could get an
exact parabola if you could hang the upper end of the cable from a
frictionless slider riding on a straight horizonta rail.   Alas, Home Depot
not carry frictionless sliders.

I have never done it; it's just a dumb idea.   Anybody know a similar way to
do a hyperbola?

Finally, for convex surfaces, you could hang the workpiece from three cable
cars and have a fixed grinder underneath.
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