The point of tangency of the tip circle of the male rotor and the root circle of the female rotor is used as a starting point in generating the series of curves defining the male and female conjugate rotor profiles. The present invention provides: reduced viscous drag through the use of a departure angle; strengthened female lobes by controlling thickness along the pitch circle; opened root of male rotor to enhance manufacturability and tool life; a tortuous leakage path for gas traveling from a high pressure thread to a low pressure thread; better control of root diameter; and control of the pressure angle independently of the other variables.