There　are　many　kinds　of　characteristic　curves　that　characterize　involute　helical　gears.　The　most　well-known　are　involute　and　helix　with　clear　geometrical　definition.　In　fact,　there　are　other　characteristic　curves　with　outstanding　engineering　value　such　as　profile　of　path　of　contact　and　contact　line　on　the　tooth　surface.　However,　the　addition　of　characteristic　lines　brings　two　problems.　One　is　that　the　complex　equations　of　the　characteristic　curves　are　not　related　to　each　other　and　lack　mathematical　unity.　The　other　is　that　except　for　involute　and　helix,　other　characteristic　curves　have　no　measuring　method,　which　results　in　a　lack　of　measurability.　According　to　the　characteristics　of　involute　gear　transmission,　the　characteristic　curves　on　the　tooth　surface　are　mapped　to　the　meshing　plane.　It　is　found　that　each　characteristic　curves　on　the　tooth　surface　has　its　corresponding　2-D　straight　line　in　the　meshing　plane.　Based　on　this,　a　straight-line　model　is　established　to　uniformly　express　various　characteristic　curves　on　the　tooth　surface.　On　basis　of　the　3-D　deviation　measurement　data　of　the　gear　and　the　unified　model　of　the　characteristic　curves,　the　extraction　method　of　the　deviations　of　various　characteristic　curves　is　proposed,　which　is　applied　to　the　measurement　practice.　By　comparing　with　the　profile　deviation　and　helix　deviation　measured　by　the　general　gear　measuring　instrument,　the　effectiveness　and　practicability　of　the　unified　model　of　the　characteristic　curves　and　the　extraction　method　of　the　deviations　of　the　characteristic　curves　are　proved,　and　the　measurability　of　the　complex　characteristic　curves　on　the　tooth　surface　is　solved.　Meanwhile,　the　unified　model　of　the　gear　characteristic　curves　also　has　important　application　value　in　the　traceability　of　gear　process　error　and　the　prediction　of　transmission　performance.　©　2022　Editorial　Office　of　Chinese　Journal　of　Mechanical　Engineering.　All　rights　reserved.