Purpose　Upper-limb　joint　kinematics　are　highly　complex　and　the　kinematics　of　rehabilitation　exoskeletons　fail　to　reproduce　them,　resulting　in　hyperstaticity　and　human-machine　incompatibility.　The　purpose　of　this　paper　is　to　design　and　develop　a　compatible　exoskeleton　robot　(Co-Exos　II)　to　address　these　problems.　Design/methodology/approach　The　configuration　synthesis　of　Co-Exos　II　is　completed　using　advanced　mechanism　theory.　A　compatible　configuration　is　selected　and　four　passive　joints　are　introduced　into　the　connecting　interfaces　based　on　optimal　configuration　principles.　A　Co-Exos　II　prototype　with　nine　degrees　of　freedom　(DOFs)　is　developed　and　still　owns　a　compact　structure　and　volume.　A　new　approach　is　presented　to　compensate　the　vertical　glenohumeral　(GH)　movements.　Co-Exos　II　and　the　upper　arm　are　simplified　as　a　guide-bar　mechanism　at　the　elevating　plane.　The　theoretical　displacements　of　passive　joints　are　calculated　by　the　kinematic　model　of　the　shoulder　loop.　The　compatible　experiments　are　completed　to　measure　the　kinematics　of　passive　joints.　Findings　The　compatible　configuration　of　the　passive　joints　can　effectively　reduce　the　gravity　influences　of　the　exoskeleton　device　and　the　upper　extremities.　The　passive　joints　exhibit　excellent　compensation　effect　for　the　GH　joint　movements　by　comparing　the　theoretical　and　measured　results.　Passive　joints　can　compensate　for　most　GH　movements,　especially　vertical　movements.　Originality/value　Co-Exos　II　possesses　good　human-machine　compatibility　and　wearable　comfort　for　the　affected　upper　limbs.　The　proposed　compensation　method　is　convenient　to　therapists　and　stroke　patients　during　the　rehabilitation　trainings.