Simple explicit formulae for calculating limit dimensions to avoid undercutting in the rotor of a Cycloid rotor pump

A new and simple method is used to derive the formulae for the tooth profile of the small rotor in a Cycloid rotor pump. Undercutting is avoided by calculating the maximum radius of curvature of the small rotor tooth profile on the convex section. It is found that undercutting can be avoided so long as the maximum value is not larger than zero. The derivation of the formula for the radius of curvature is based not on the tooth profile formulae of the small rotor, but on those of the locus of the centre of the circular tooth of the large rotor relative to a coordinate system fixed to the small rotor. This simplified method yields explicit formulae for calculating limit dimensions of the large rotor to avoid undercutting on the tooth profile of the small rotor.