A　key　approach　for　reducing　motor　impairment　and　regaining　independence　after　spinal　cord　injuries　or　strokes　is　frequent　and　repetitive　functional　training.　A　compatible　exoskeleton　(Co-Exos　II)　is　proposed　for　the　upper-limb　rehabilitation.　A　compatible　configuration　was　selected　according　to　optimum　configuration　principles.　Four　passive　translational　joints　were　introduced　into　the　connecting　interfaces　to　adapt　the　glenohumeral　joint　(GH)　movements　and　improve　the　compatibility　of　the　exoskeleton.　This　configuration　of　the　passive　joints　could　reduce　the　influence　of　gravity　of　the　exoskeleton　device　and　the　upper　extremities.　A　Co-Exos　II　prototype　was　developed　and　still　owned　a　compact　volume.　A　new　approach　was　presented　to　compensate　the　vertical　GH　movements.　The　shoulder　closed-loop　was　simplified　as　a　guide-bar　mechanism.　The　compatible　models　of　this　loop　were　established　based　on　the　kinematic　model　of　GH.　The　compatible　experiments　were　completed　to　verify　the　kinematic　models　and　analyze　the　human-machine　compatibility　of　Co-Exos　II.　The　theoretical　displacements　of　the　translational　joints　were　calculated　by　the　kinematic　model　of　the　shoulder　loop.　The　passive　joints　exhibited　good　compensations　for　the　GH　movements　through　comparing　the　theoretical　and　measured　results,　especially　vertical　GH　movements.　Co-Exos　II　showed　good　human-machine　compatibility　for　upper　limbs.　©　2019　IEEE.