This　paper　describes　a　dynamic　mathematical　model　of　a　new　type　two-stage　nutation　drive　system　with　double　circular-arc　bevel　gears.　The　dynamic　displacement-vibration　coupling　model　takes　into　account　the　gyro　torque　and　side　clearance　of　the　nutating　gear.　A　numerical　analysis　geometric　model　of　the　nutation　drive　system　is　developed.　The　geometric　model　considers　the　time-varying　and　contact　deformation　of　nutation　gear　meshing.　Subsequently,　the　model　is　analyzed　using　the　ANSYS/LS-DYNA　software,　and　the　dynamic　contact　characteristics　of　the　nutation　gear　are　calculated.　The　simulation　results　revealed　that　the　nutation　transmission　of　the　double　circular-arc　spiral　bevel　gear　is　reliable.　Moreover,　the　mathematical　verification　showed　that　the　simulation　is　feasible　and　accurate.　The　research　has　important　significance　for　improving　the　tooth　load　capacity　and　transmission　stability　of　nutation　drives.