The　upper-limb　rehabilitation　exoskeleton　is　a　critical　equipment　for　stroke　patients　with　the　motor　function　disorder.　The　exoskeleton　devices　are　used　to　make　up　deficiencies　of　the　manual　rehabilitation　training　and　reduce　the　workload　of　rehabilitation　physicians.　The　configuration　synthesis　of　the　exoskeleton　is　conducted　using　the　advanced　mechanisms　theory.　Besides,　the　mobilization　of　the　glenohumeral　joint　(GH)　is　taken　into　account.　Several　configuration　combination　of　the　shoulder　chain　Θs　and　the　elbow-forearm　chain　Θef　are　obtained.　According　to　optimum　principles　of　configuration　a　configuration　with　preferable　human-machine　compatibility　is　selected.　Then,　the　compatible　exoskeleton　(Co-Exos)　for　the　upper-limb　rehabilitation　is　designed　and　developed.　A　gravity　balance　system　and　elastic　components　are　introduced　into　Co-Exos　for　improving　the　uncertainty　and　motion　cooperativity.　The　human-machine　compatibility　model　of　the　shoulder　chain　Θs　is　established　based　on　the　kinematic　model　of　GH.　Meanwhile,　an　approach　is　proposed　to　compensate　the　vertical　displacements　of　GH.　The　Co-Exos　and　the　upper　arm　can　be　simplified　as　a　guide-bar　mechanism.　The　kinematic　models　of　passive　joints　are　deduced.　Furthermore,　the　human-machine　compatibility　platform　is　constructed　to　measure　the　displacements　of　passive　joints.　Though　comparing　measured　displacements　with　theoretical　displacements,　it　can　be　found　that　the　shoulder　chain　Θs　and　the　compatible　human-machine　chain　can　can　compensate　the　position　changes　of　GH　mostly,　especially　the　vertical　displacements.　Hence　Co-Exos　has　good　human-machine　compatibility　for　GH.　©　2018　Journal　of　Mechanical　Engineering.