This　article,　for　the　first　time,　presents　the　generation　of　Roots　rotor　tooth　profiles　based　on　an　Assur-group-associated　virtual　linkage　method.　Taking　the　original　Roots　rotor　as　an　example,　structure　and　geometry　of　the　Roots　rotor　are　introduced,　and　based　on　the　principle　of　inversion,　an　equivalent　virtual　linkage　is　identified　for　generating　dedendum　tooth　profile　of　the　rotor.　Using　linkage　decomposition　associated　with　elemental　Assur　groups,　algorithm　for　computing　the　tooth　curve　is　constructed　leading　to　the　explicit　expression　of　rotor　profile　and　the　corresponding　numerical　simulation,　verifying　the　validity　of　the　proposed　approach.　For　demonstration　purpose,　the　virtual　linkage　method　is　then　extended　to　the　generation　of　tooth　profiles　for　the　variants　of　Roots　rotors　with　arc-cycloidal　curves　and　arc-involute　curves.　Integrated　with　computer-aided　design,　computer-aided　engineering　and　computer-aided　manufacturing　software　platforms,　as　well　as　the　three-dimensional　printing　technology,　this　article　provides　an　efficient　and　intuitive　approach　for　Roots　rotor　system　design,　analysis　and　development.