The　new　internal　S-gear　and　its　contact　characteristics　were　studied.　Based　on　the　S-shaped　tooth　profile　cutter　and　relationship　of　machining　motion,　the　teeth　surface　equations　of　the　new　internal　S-gear　were　deduced,　and　the　interference　check　of　internal　S-gear　pair　was　derived.　The　modified　tooth　surface　was　constructed　by　superimposing　the　modified　surface　onto　the　standard　tooth　surface.On　this　basis,　Matlab　programming　was　used　to　calculate　the　coordinate　of　the　three-dimensional　grid　node　of　the　modified　gear.The　geometric　contact　characteristics　and　loaded　contact　characteristics　of　internal　S-gear　pair　under　different　modifications　and　errors　were　studied　by　using　tooth　contact　analysis　(TCA)　and　loaded　tooth　contact　analysis　(LTCA).　The　calculation　example　was　given,　and　the　results　show　that　the　newly　designed　internal　S-gear　does　not　produce　root　cutting　or　interference,　and　the　working　teeth　surface　contact　performance　is　good,　and　the　correct　meshing　transmission　can　be　achieved.　After　teeth　surface　modification,　load　distribution　of　internal　S-gears　teeth　surface　is　improved　effectively　and　its　error　sensitivity　is　reduced.　©　2023　Huazhong　University　of　Science　and　Technology.　All　rights　reserved.