This　paper　investigates　the　geometric　properties　of　the　toroidal　drive,　reveals　the　meshing　characteristics,　and　develops　analytical　models　of　both　axial　section　and　normal　section　of　the　toroidal　tooth　profile.　Based　on　coordinate　transformation,　the　meshing　function　is　obtained　and　leads　to　the　necessary　condition　of　existence　of　the　enveloping　surface.　The　helix　and　helix　lead　angle　are　then　proposed　for　meshing　between　the　sun-worm　and　planet　worm-gears　and　both　undercutting　curve　and　meshing　limit　curve　are　introduced.　This　further　leads　to　the　induced　normal　curvature　for　evaluating　gearing　properties　and　the　selection　of　the　best　suitable　meshing　parameters.　The　geometric　analysis　and　analytical　modeling　present　a　tool　for　design,　leading　to　three　tables　of　numerical　results　and　design　parameters.　This　is　then　demonstrated　in　a　three-dimensional　modeling　of　both　helical　sun-worm　and　stationary　internal　gear　of　the　toroidal　drive.　Copyright　©　2005　by　ASME.