Despite the [hopefully] interesting assertion that I to linked yesterday: One of the advantages of cycloidal gearing for clocks is that its tooth depth is non-critical … The wheel centre distances are optimised when the train is planted.
Small MOD values, HPC give 2.4 times MOD for 0.25 – 1 MOD and 2.25 x MOD for 1.25 – 8 MOD
In that case no – I don't see why the total tooth depth equation should vary with MOD value? Surely different MOD values are simply scaled versions of one another.