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.