This　paper　investigates　the　toroidal　tooth　profile　of　an　epicyclic　gear　train　based　on　the　analysis　of　the　integrated　motion　from　both　sun-worm　and　planet　worm-gears　and　develops　a　mathematical　model　based　on　the　coordinate　transformation　between　the　coordinate　system　of　the　stationary　internal　gear　and　that　of　the　planet　worm-gear.　The　model　is　derived　from　the　geometrical　analysis　of　the　meshing　system　and　is　used　to　model　the　meshing　surface　which　is　produced　as　a　result　from　the　enveloping　surface.　This　is　further　extended　to　model　the　internal　toroidal　tooth　profile　in　the　stationary　gear,　the　normal　tooth　profile　and　the　helix　trajectory.　Based　on　these　models,　the　shape　of　normal　tooth　section　of　the　stationary　toroidal　tooth　profile　is　obtained　and　the　three-dimensional　modelling　of　this　tooth　profile　is　completed.　The　paper　further　examines　the　case　of　manufacturing　by　developing　a　fly-blade　for　the　machining　process　and　develops　a　manufacturing　procedure　which　successfully　produced　a　stationary　internal　toroidal　tooth　profile　manufactured　by　a　fly-blade　on　a　hob　machine.　©　IMechE　2004.