To　solve　the　rehabilitation　problem　of　hand　dysfunction　caused　by　stroke　and　other　accidental　injuries,　an　underactuated　four-finger　three-joint　hand　rehabilitation　mechanism　with　good　physical　human-robot　interaction　performance　was　designed.　The　configuration　design　and　operation　principle　of　the　mechanism　were　introduced　at　first.　At　the　same　time,　the　statics　analysis　and　kinematics　simulation　of　the　mechanism　were　carried　out.　Finally,　the　prototype　was　developed　to　complete　the　performance　test　and　operation　reliability　experiment.　The　robot　innovatively　designs　a　power　transmission　system　using　only　connecting　rod　mechanism.　Compared　with　the　traditional　gear　drive　or　hybrid　drive　ones,　it　has　a　simple　structure　and　can　realize　synchronous　movement　of　three　joints　driven　by　a　motor.　The　experimental　results　of　the　prototype　show　that　the　mechanism　can　meet　the　needs　of　human　finger　rehabilitation　and　effectively　improve　the　physical　human-robot　interaction　performance.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.　2023.