For those interested in learning how to make gears of all types, spur gears
(what we think of as gears normally),
herringbone, worm, bevel, etc, and the theory behind their mesh, creation,
and movement, best book I can
recommend for simplest presentation is *Gears & Gear Cutting: Workshop
Practice Series 17 *by Ivan Law.
If you want to learn specifically about horological gearing (ie: clock and
watch gears)- best book I can recommend
is *Wheel & Pinion Cutting In Horology* by J. Malcolm Wild, FBHI.
*Watchmaking* by George Daniels is another great book for that, but covers
how to make every part of a watch,
including escapements. He covers gearing well too, and how to make gear
cutters for timepieces, but above
book specializes in just that only.
Thing is- timepiece gearing is not the same gearing in everything else,
like your bicycles, cars, machinery, etc.
Timepiece, or horological gearing, uses a different style of tooth, a form
called cycloidal gearing.
Pretty much everything else in the world, save special instances of exotic
forms, uses involute gearing.
They are not interchangable. They work differently in design. If you want
to make gears from scratch for a clock
or watch, you have to learn the difference is all.
Here's a quick primer of a website that covers the most basic stuff in a
quick view: Designing Cycloidal Gears
<http://www.csparks.com/watchmaking/CycloidalGears/>
Hope that helps anyone interested. I possess the books mentioned above,
anyone is welcome to borrow them
if interested.
-Andrew
On Thu, Feb 25, 2016 at 4:59 PM, Andrew C. <soshumasamune@xxxxxxxxx> wrote:
Joachim,
See here, about 1/2 page down.
<https://en.wikipedia.org/wiki/Sidereal_time>
"Greenwich Mean Sidereal Time (GMST) and UT1
<https://en.wikipedia.org/wiki/UT1> differ from each other in rate, with
the second of sidereal time a little shorter than that of UT1,
so that (as at 2000 January 1 noon) 1.002 737 909 350 795 second of mean
sidereal time was equal to 1 second of Universal Time (UT1).
The ratio varies slightly with time, reaching 1.002 737 909 409 795 after
a century.[3] <https://en.wikipedia.org/wiki/Sidereal_time#cite_note-3>"
What I need for the timepiece is a way of not only generating a
non-standard gear ratio, in this case, 1:1.002737909350795, but something
that
also modifies that gear ratio over time to the latter value, and beyond,
to account for the celestial drift errors over centuries. Much like the
Clock of the Long Now Foundation does this with their equation of time
cam for 10,000 years drift variation calculated in stack
<http://demonstrations.wolfram.com/VariationOfTheEquationOfTimeWithThePrecessionOfTheEquinoxes/>
.
Now that I see it is possible to make a non-standard gear ratio with
helical spur gears, that can help, but I can't make a set that will fit in
a watch-
maybe a large clock. It also isn't continuous, there is no way to keep it
running in the same direction when it reaches the end of it's gear spiral.
The ratio was going to be approximated to as many places as possible for
normal gearing- it has been done out 6 or so places with only a few gears
by G. Daniels. That was why I wanted to learn Python- that program I
started was a gear calculation program to calculate that ratio out as many
places as possible. That was directly for a geartrain in a watch that
showed sidereal time derived from a solar (mean) time gear train, as
accurately
as possible to theory ratios with as few gears as possible. The python
program I have also showed the deviation from that ratio and calculated
the error in time difference over centuries for a given set of gears.
I have no idea if it is possible to modify a gear ratio in running over
time. I know there are progressive lead screws, where pitch gradually
varies,
but I've never seen a progressive geared mechanism that gradually changes
gearing ratio a specific amount over time. Most people would never
need such a thing mechanically. I do.
Not sure if it's possible, but learning python would help more...
-Andrew
