Minimum tooth difference in internal-external involute gear pair

The transmission ratio increases with the decrease in gear ratio of internal-external gear pair in 'two-gear epicyclic drive' such as plano-centric, harmonic drives, etc. For an involute tooth the gear ratio, or in other words, the difference between the gear teeth and pinion teeth numbers, cannot be lower than a certain limit because of the tooth tip interference. In the present work an attempt has been made to examine the possibility of lowering the difference as much as possible in the internal-external involute gear pair with the help of simple gear corrections. It is found that by addendum modification the tooth difference can be reduced, though not to unity, from their value with full depth gears. By introducing center distance modification, although this number cannot be reduced further for practical purposes (avoiding tip interference) the contact ratio improves. A mathematical relation has also been established to investigate the conditions of avoiding tip interference when the pinion rim is deflected as in the case of harmonic drives. These analyses enable one in selecting a suitable involute gear pair for its application in two gear epicyclic drive units.