NOTE: I've been losing mail from phys-l, and
possibly other mail. Of the first 8 messages
in the Segway thread, I only received 7. I
did not receive my own "KE elephant" message.
-- I don't know whether this is related to
the fact that the listserv machine was offline
for a few hours on saturday.
-- I don't know whether any of the above is
related to the SQL Slammer worm currently
rampaging around the net.......
Anyway............
Bob Sciamanda wrote:
| It is the RATIO which is to be non-integer, not the number of teeth.
| EG: Teeth numbers of 24 and 12 have an integer ratio: 24/12 = 2.
| OTOH teeth numbers of 24 and 13 have a non-integer ratio:
Please look at the Segway statement in context.
I continue to assert that relative primeness is
the necessary and sufficient condition for what
they say they are trying to achieve, namely:
"This means that the teeth will mesh in a
different location each revolution, maximizing
the life of the gearbox."
By way of example, consider the gear ratio 90/60.
That comes out to 1.5 which is not an integer.
It's about as far from being an integer as anything
could possibly be. But the tooth-counts are rather
spectacularly not relatively prime. A given tooth
on the big gear will visit only two of the 60 teeth
on the small gear.
Changing the ratio to something relatively prime, e.g.
91/60 or 89/60, would be advantageous for prolonging
the life of the gearbox.
There are plenty of references that get this wrong,
referring to non-integer when they mean relatively
prime. But they're wrong nevertheless.