The　measurement　of　planar　double-enveloping　hourglass　worms　has　always　been　a　technical　problem　in　the　field　of　gear　metrology.　To　solve　this　problem,　we　propose　a　new　method　and　develop　a　measuring　machine　to　inspect　each　deviation　of　the　worms.　In　a　cylindrical-coordinate　system,　the　measuring　principle　adopts　electronic　generative　metrology.　The　mathematical　model　of　the　worms　is　established　according　to　the　forming　process　of　the　worms.　Based　on　the　definitions　of　error　items　to　be　measured,　the　model　of　each　deviation　will　be　determined.　The　model　could　be　transformed　to　the　control　path　that　leads　the　probe　by　controlling　the　movements　of　X　axis,　Y　axis　and　Theta　axis.　In　this　process,　probe　radius　compensation　is　necessary　to　correct　the　control　path.　At　last,　the　helix　deviations,　the　tooth　profile　deviations　and　the　topologic　deviations　of　a　worm　are　inspected.　It　is　the　first　time　that　the　topologic　deviation　of　this　kind　of　worm　is　measured.　The　analysis　shows　that　the　deviations　of　the　worm　could　be　a　reference　to　adjust　the　processing　of　the　worms.　The　measuring　machine　could　inspect　the　hourglass　hobs,　the　cylindrical　worms　and　the　hobs　as　well.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.