Abstract: Number of lobe of rotor in rotating pump may be two or three. For cycloid rotor, the ratio k(k＝d2/R)of the distance d2 (from rotating center of the rotor to the center of the circular addendum) to the radius R of pitch circle is a very important parameter. The larger the ratio is, the thinner the rotor will be, the larger the volume coefficient of the cavum will be, and the larger the flux will be. However, if this ratio exceeds an extremum, then the profile of the rotor will intersect itself. There will be large backlash between rotors after cutting. Thus the flux and pressure will decline sharply. A simple formula to calculate radius of curvature of the cycloid valley of the rotor and an explicit expression to calculate extremum of the ratio k(k＝d2/R) are derived. Exact values of the extremum of the ratio are calculated. This work sets a theoretical base for the design of the rotor in this kind of rotating pump.

Key words: Curvature, Cycloid rotor, Extremum, Profile