As　the　core　components　of　nutation　drive,　the　internal　meshing　pair　of　bevel　gear　must　be　delicately　designed　to　achieve　desirable　operational　performances　for　the　transmission　device.　For　this　purpose,　this　paper　designs　a　face-hobbed　internal　meshing　pair　of　cycloidal　bevel　gears　with　double　circular-arc　profile　(DCAP).　First,　a　cutter　head　with　DCAP　cutting　edges　is　designed　to　generate　the　tooth　surface　of　internal　gear　pair.　Then,　the　tooth　geometry　of　the　external　and　internal　bevel　gears　are　derived　according　to　the　meshing　theory.　Finally,　a　finite　element　model　is　developed　to　simulate　the　meshing　characteristics　of　the　gear　pair.　The　simulation　results　reveal　that　the　proposed　face-hobbed　cycloidal　bevel　gear　pair　with　DCAP　has　higher　contact/bending　strength,　better　load　sharing　and　smaller　transmission　error　compared　with　the　logarithmic　spiral　bevel　gear　pair　with　DCAP.　The　effects　of　four　typical　manufacturing　errors　on　meshing　characteristics　of　the　proposed　bevel　gear　pair　are　investigated　to　provide　fundamental　references　for　the　tolerance　design　of　cycloidal　bevel　gears.　©　2022　Elsevier　Ltd