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-Exoskeleton)　with　four　passive　translational　joints　is　proposed　for　the　upper-limb　rehabilitation.　There　are　only　three　passive　translational　joints　to　track　and　assist　movements　of　the　glenohumeral　joint　(GH),　where　two　joints　are　installed　horizontally　at　the　front　section　and　another　one　at　the　connecting　interface　of　the　upper　arm.　This　type　of　configuration　can　lower　the　influences　of　gravities　of　the　exoskeleton　device　and　upper　extremity.　The　kinematic　models　of　GH　and　the　corresponding　human-machine　system　are　established　using　the　analytical　method.　A　numerical　simulation　of　the　kinematic　models　is　implemented　with　MATLAB　to　emphatically　analyze　the　kinematic　characteristics　of　passive　joints　and　the　center　of　Co-Exoskeleton.　The　translational　displacements　of　passive　joints　in　four　elevation　planes　are　obtained　during　the　elevating　process.　The　results　of　the　kinematic　analysis　show　that　the　passive　joints　have　similar　motion　characteristics　under　different　elevation　planes.　Additionally,　the　position　changes　of　GH　in　three　directions　can　be　tracked　and　compensated　approximately.　Co-Exoskeleton　has　an　especially　good　compensation　effect　for　the　vertical　movement　of　GH.　The　compensation　effect　and　kinematic　models　are　verified　by　using　the　elevating　experiments.　This　research　provides　theoretical　and　methodological　guidance　for　the　ergonomic　design　and　kinematic　analysis　of　the　rehabilitation　exoskeleton.