For　circular　arced　rotors　in　Roots　blower,　there　are　three　different　kinds　of　profile　of　the　transverse　section.　The　equations　of　the　profiles　of　these　three　kinds　of　three-lobe　circular　arced　rotor　are　derived　in　details　in　this　article.　The　explicit　expression　of　the　radius　of　curvature　of　the　profile　and　the　maximum　ratio　of　r(a)/a　are　derived.　The　characteristics　of　these　three　different　kinds　of　circular　arced　rotors　are　discussed　and　compared.　The　equations　of　the　helicoids　of　the　helical　rotor　and　the　axial　section　of　the　milling　cutter　are　derived.　The　cutting　parameters　and　interference　problem　during　cutting　are　discussed　deeply.