This　paper　proposes　a　novel　three-lobe　helical　rotor　with　the　cross　section　as　a　combination　of　concave　and　convex　arcs　and　cycloidal　curves　for　the　Roots　blower.　Based　on　the　geometric　analysis,　the　mathematical　model　of　this　new　tooth　profile　is　presented,　leading　to　a　presentation　of　a　helical　tooth　profile　and　a　comparative　study　between　the　three-lobe　helical　tooth　and　a　conventional　straight　tooth.　The　study　reveals　the　advantage　of　the　new　tooth　design　that　creates　greater　air　flow　and　reduces　the　peak　of　the　blower　pressure.　The　geometric　study　leads　to　the　investigation　of　machining　the　profile　of　the　new　tooth.　The　cutter　trajectory　is　revealed　and　the　contact　characteristics　between　the　cutter　and　the　work　piece　are　identified.　By　identifying　the　cutter　distance　and　the　cutter　mounting　angle,　the　paper　characterizes　the　relationship　between　these　machining　parameters　that　governs　the　machining　of　the　novel　tooth.　The　simulation　and　tooth　machining　are　provided　in　the　end　of　the　paper.　(c)　2005　Elsevier　B.V.　All　rights　reserved.