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.