The　goal　of　this　article　is　to　present　a　number　synthesis　method　for　the　self-adapting　upper-limb　rehabilitation　exoskeletons.　The　human　joint　kinematics　and　the　variability　of　joint　axes　around　their　supposed　locations　were　analyzed;　the　axes　misalignments　caused　by　the　wearing　error　and　the　movement　coupling　between　joint　rotations　and　axes　motions　in　human　joints　were　taken　into　account,　and　the　kinematic　incompatibility　of　upper-limb　exoskeletons　was　investigated　from　an　over-actuation　perspective.　Then,　a　number　synthesis　method　of　the　self-adapting　upper-limb　exoskeletons　was　proposed　by　using　the　traditional　degrees　of　freedom　analysis　approach　of　spatial　multiloop　chains.　Applying　this　method,　the　basic　chains　of　the　self-adapting　four-degrees　of　freedom　shoulder-elbow　and　five-degrees　of　freedom　shoulder-elbow-forearm　exoskeletons　were　synthesized　and　classified　into　three　and　two　groups,　respectively.　Finally,　the　feasible　simplified　chains　of　the　self-adapting　upper-limb　exoskeletons　were　investigated　with　the　consideration　of　the　quasi-anthropopathic　feature　and　structure　simplicity,　and　several　examples　were　enumerated.　The　proposed　simplified　chains　could　be　used　as　the　candidates　for　further　studies　on　the　performance　analysis,　the　chain　compare　and　selection,　and　structure　design　of　the　self-adapting　upper-limb　exoskeletons.