Rotary　vector　reducer　(RV　reducer)　serves　as　a　crucial　drive　train　component　in　industrial　robots,　and　its　time　varying　torsional　stiffness　significantly　impacts　the　dynamic　characteristics,　vibration　and　transmission　accuracy.　Existing　methods　for　calculating　the　torsional　stiffness　suffer　from　two　limitations:　(1)　considering　only　the　time　varying　meshing　stiffness　of　the　gear　pair　or　the　time　varying　radial　stiffness　of　the　bearings　as　a　single　factor,　and　(2)　the　calculated　results　according　to　the　traditional　initial　meshing　clearance　formula　of　the　cycloid　pin　gear　do　not　align　with　the　definition　of　tooth　side　clearance.　To　comprehensively　and　accurately　analyze　the　time　varying　torsional　stiffness,　this　study　proposes　a　method　for　the　reducer,　taking　into　full　consideration　the　time　varying　characteristics　of　gear　meshing　stiffness　and　radial　stiffness　of　bearings.　To　analyze　the　time　varying　meshing　stiffness　of　the　cycloid　pin　gear　pair,　a　novel　initial　meshing　clearance　formula　is　derived.　Firstly,　a　new　calculation　model　was　constructed　to　accurately　obtain　the　initial　meshing　clearance　of　cycloid　pin　gear　single　tooth　pair　in　the　low-speed　stage.　The　time　varying　meshing　stiffness　of　the　cycloid　pin　gear　was　calculated　by　determining　the　number　of　teeth　engaging　in　meshing　simultaneously.　Secondly,　the　time　varying　meshing　stiffness　of　the　involute　modified　gear　in　the　high-speed　stage　was　simulated　employing　the　weber　energy　method.　Then,　time　varying　radial　stiffness　of　the　crankshaft,　arm　bearings,　and　supporting　bearings　was　analyzed　utilizing　finite　element　method.　Finally,　by　equivalating　the　time　varying　meshing　stiffness　of　the　two-stage　gear　mechanism　and　the　time　varying　radial　stiffness　of　bearings　to　the　output　end,　the　time　varying　torsional　stiffness　of　the　reducer　was　calculated.　The　experimental　results　of　the　torsional　stiffness　have　only　a　3.81%　difference　compared　to　the　simulated　value,　which　validates　the　accuracy　of　this　method.