This　paper　presents　an　inner-type　of　magnetic　gears　for　non-contact　driving,　based　on　the　nutation　gearing　principle.　An　improved　three-dimensional　analytical　model,　based　on　the　magnetic　vector　potential　of　rectangular　permanent　magnets,　via　the　equivalent　current,　is　deduced　for　the　proposed　nutation　magnetic　gears.　The　transformation　of　coordinates　is　applied　for　a　global　field　solution.　The　analytical　model　and　the　finite　element　model　have　analyzed　the　output　torque　of　the　nutation　magnetic　drive,　respectively.　The　results　show　that　the　values　calculated　by　the　two　models　are　consistent.　The　proposed　analytical　model　can　provide　a　reference　for　the　design　and　optimization　of　nutation　magnetic　gears　and　other　permanent　magnetic　mechanisms　with　rectangular　magnets.　©　2020　by　the　authors.　Licensee　MDPI,　Basel,　Switzerland.　This　article　is　an　open　access　article　distributed　under　the　terms　and　conditions　of　the　Creative　Commons　Attribution　(CC　BY)　license　(http://creativecommons.org/licenses/by/4.0/).