The Beall Clock Forum

General => Wheels and pinions => Topic started by: Mark Main on July 02, 2014, 05:07:33 PM

Title: Even/Uniform Wooden Clock Gear Wear using Relatively Prime/Coprime Tooth Counts
Post by: Mark Main on July 02, 2014, 05:07:33 PM
I've not found information on the Internet that explains how to get an even/uniform gear using gear proper tooth counts in a wooden clock design. It's really quite easy once you know the answer. Uniform gear wear is achieved by ensuring the tooth counts of the two gears meshing together are Relatively Prime (also called Coprime) to each other; this occurs when the Greatest Common Divisor (GCD) of each gear tooth count equals 1, e.g. GCD(16,25)=1

Any other result other than 1 will have a repeating pattern that does not allow every tooth to mesh with each other. E.g. a 15 tooth pinion meshing with a 25 tooth drive gear. GCD(15,25)=5  and so 15/5=3 and 25/5=5; this means that the same 3 pinion teeth will mesh with the same 5 drive gear teeth, they will not have uniform wear.
Title: Re: Even/Uniform Wooden Clock Gear Wear using Relatively Prime/Coprime Tooth Counts
Post by: jasc15 on July 03, 2014, 01:26:01 PM
Its a common practice in geared devices to choose prime number tooth count for the reasons you mentioned.  However, this applies where the exact gear ratio is not so critical, such as in a car's transmission.  The problem with using this in clocks is that the ratio of 2 prime numbers cannot be an integer.

However, you only really need integer ratios for gearing the hands together, while the rest of the power train can be of prime toothed gears.
Title: Re: Even/Uniform Wooden Clock Gear Wear using Relatively Prime/Coprime Tooth Counts
Post by: steve323 on July 16, 2014, 11:18:50 AM
It seems like all the gears before the minute hand could take advantage of this feature.  It may require an escape wheel with a prime number of teeth and a pendulum with a slightly different period.  Eventually, the minute hand needs to rotate exactly once per hour.

The gears between the minute hand and hour hand are really slow moving, so don't really have an issue with wear.

Steve
Title: Re: Even/Uniform Wooden Clock Gear Wear using Relatively Prime/Coprime Tooth Counts
Post by: emmajost on December 29, 2014, 03:38:24 AM

Ee is read to gain knowledge as much as I am. Permission for others to have a dip in reading this story I do not like it.