In　this　paper,　follow-up　grinding　of　crankshaft　is　studied　and　the　mathematical　model　of　follow-up　grinding　motion　is　established.　Taking　the　double　grinding　wheel　crankshaft　follow-up　grinder　as　the　research　object,　the　motion　errors　of　the　machine　tool　are　obtained　by　analyzing　the　motion　relations　among　the　moving　bodies.　Based　on　the　kinematics　theory　of　multi-body　system,　the　kinematics　model　of　the　whole　machine　tool　is　established.　The　position　matrix　of　any　cutting　point　is　described　according　to　the　kinematic　chain　of　＇bed-workpiece＇　and　＇bed-tool＇,　and　the　precise　machining　model　of　double　grinding　wheel　follow-up　grinding　machine　tool　is　established　by　using　the　coincidence　principle　of　tool　actual　trajectory　and　tool　path.　The　coordinate　system　of　each　moving　body　is　established,　the　transformation　matrix　between　moving　bodies　is　obtained,　and　the　precision　machining　model　of　double　grinding　wheel　follow-up　crankshaft　CNC　grinding　machine　is　solved,　which　lays　a　foundation　for　error　compensation　of　the　machine.　©　Published　under　licence　by　IOP　Publishing　Ltd.