Both the English and the Swiss have standards for cycloidal gear
profiles, mostly for their (now almost vanished) horological industries.
However, if you examine them, you will find that they actually specify an
approximation to the true cycloidal curve; this consists of an ogival arch
(like a church window) constructed of segments of circular curves, with the
radii specified in a table. And even at that, most users modified the form
beyond recognition- at the Waltham Watch Co., for example, after
experimenting with the cycloidal form for years, they finally threw it out
and used a form of their own invention. The problems of constructing a
cycloid curve in metal are not easy to solve, nor are they new.
In addition, there is the problem of center distances Ed Huntress
mentioned. What he didn't say is that the form of the gear tooth also
depends on the tooth count of its mating pinion. So, to cut a true
cycloidal form with form cutters, one needs a set of cutters, for each tooth
size, which includes a range of forms for the range of gear tooth counts
(just as for involute) but for each pinion count as well. By the end of the
19thC, Brown and Sharp had gotten it down to only 64 cutters for each pitch
size, vs. 8 for involute (though they offered sets of 32 for non-critical
work.) You can see why involute took over.
Another reason might be that involute is better suited to gearing
down (e.g. the speed of a gasoline engine to the speed of a tire, or an
electric motor to a loom) while cycloidal is better suited to gearing up
(e.g. the once/day rotation of a grandfather clock winding barrel to the
once per minute of the escape wheel).
So you need to ask yourself, not only, do you really need to
reproduce cycloidal teeth, but also, are the old teeth really cycloidal?
Most guys think they can tell at a glance, but they're not looking at the
curve- they're looking at the whole tooth. Though clock wheel teeth are
usually sharp-pointed, and slenderer than regular gear teeth, those features
have nothing to do with the actual curve. In other words, cycloidal teeth
can be stout and truncated, and involute teeth slender and pointed. These
features have more to do with the overall wheel design (e.g., how deep the
mating wheel is gashed, or the ratio of tooth width to intertooth space, or
the required tooth strength) than with the mathematical curve the tooth
profile follows. And of course, the tooth root being rounded or square is
completely inconsequential to this. And don't forget, most horologists, let
alone gearheads, have never seen a true cycloidal tooth, or even an image of
one (as opposed to what I call an ogival tooth, i.e. what the English &
Swiss standards define as "cycloidal".)
On top of al this, I'd like to point out that the involute form
occupies the middle ground, or boundary, between the epicycloidal and
hypocycloidal curves. That's why any involute gear will mate with any other
of the same tooth size and pressure angle, whereas an epicycloidal wheel
will only mate with a hypocycloidal pinion.
But if you're still hell-bent on cycloidal, the book you need is
Willis's 19thC "Treatise on the Teeth of Wheels". It contains a handy
cardboard calculator he calls the "Odontograph" for generating cycloidal
teeth. There's really nothing practical on cycloidal tooth generation in
any of the 20thC books on gears (at least that I've seen, and that's a lot),
except that the textbook for the Swiss watchmakers training course (given
free to selected candidates in the U.S., but whose German acronym I can't
seem to extrude from my tired brain) has the Swiss "cycloidal" standard.
Good luck!


"Tom Miller" wrote in message
...

"Chuck Sherwood"
wrote in message
...
They're not restoring this to use for road
building, they're
restoring it for a museum. It should be as
close to the
original as possible, or else why not just use
photos and
paper mache models?

In thg original post it was stated that the wear
was not
discovered until the gear covers were removed.
This makes
me ask will the public even see the gears? If
they are
not visiable and its a static display why spend
the time
and money doing anything to them?

Actually it was discovered when the covers were
removed. The machine will be a working machine and
not a static display. I hope to drive it at a
rally later this year.

Tom Miller