The gears
used in all of my clocks have geometry based on the standard gear profile
formulae with some adjustment to the tooth profile to thin them down a little to
make it a bit less sensitive to the inaccuracies inherent when using hand
cutting methods to produce them.

When
designing clock gears I generally use the metric system to define the teeth but
both metric and imperial can be used interchangeably. The chart shown below
shows the formulae I use for gear calculation.

For the teeth
to engage with each other they must both be calculated using either the same
Diametral Pitch (DP) or the same Module these two terms relate to the way the
teeth are spaced around the Pitch Circle Diameter (PCD). Once you have decided
on the DP or Module you are going to use that to calculate all the other features
using the formulae in the chart above.

There are two
main gear trains in a clock, the minutes train that requires a total ratio of
60:1 this runs between the shaft carrying the minute hand and the escapement
wheel. The escape wheel normally turns once a minute and it connects through
the train with the shaft holding the minute hand, which turns once an hour,
hence the 60:1 ratio.

The second
train runs between the minute hand and the hour hand which requires 12: reduction. This ratio normally has to 2
sets of gears with ratio's of 3:1 and 4:1 and the centre distance of each are
normally the same as the gears are mounted on the same pairs of shafts, I
always use a 8 teeth and 32 teeth pair along with a 10 teeth and 30 teeth pair,
as it allows the shafts to be shared.

With the 60:1
ratio there are many more options open to you and will to a large extent depend
on the design you are trying to achieve, so I must leave that up to you to
decide. Having said that a simple set of 3 gears using 3 pair sets with ratio's
of 3:1 4;1 and 5:1 works quite well as when multiplied together they will give
you a 60:1 ratio.

Having
decided on the gear arrangement I
normally try to determine the Module value I am going to use and that relates
to the size of the gears I want. To determine that I would normally work out on
CAD or on paper what size I want the largest gear to be, so in my case this is
usually a 60 tooth gear. As an example I have decided the gear needs to be
about 125mm (5ins) diameter so from the chart above I can work out a value for
the module.

Module =
Outside Diameter mm / ( Number of teeth +2)

This gives a
value for the Module of 2.016 so round that down to 2.0 and you can now use
that value to calculate the sizes for all of your gears.

If you are an
organised person you would use a spread sheet to enter all your values to work
out the relevant gear sizes, I never got round to doing this so finish up
working them out on a calculator.

The chart
below shows a typical gear pairing for a 3:1 gear ratio and a Module of 2 using
a 60 tooth and a 20 tooth gears. The tooth thickness is slightly less than the
normal 50% of the CP value I have used between 44% and 48% of that value
depending on what looks to work best in the CAD simulations.

Thanks for this write up! Just what I was looking for.

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