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We present kinematics, workspace analysis and detailed design of ASSISTON-SE, a novel powered exoskeleton for robot-assisted rehabilitation that allows for movements of the shoulder girdle as well as shoulder rotations. ASSISTON-SE can both actively and passively enable translational movements of the center of glenohumeral joint, thus can adjust its joint axes corresponding to shoulder rotations, providing an ideal match between human joint axes and the exoskeleton axes. Thanks to this feature, ASSISTON-SE not only guarantees ergonomy and comfort throughout the therapy, but also extends the usable range of motion for the shoulder joint. Adjustability feature also significantly shortens the setup time required to attach the patient to the exoskeleton. In addition to typical shoulder rotation exercises, ASSISTON-SE can deliver glenohumeral mobilization (scapular elevation/depression and protraction/retraction) and scapular stabilization exercises, extending the type of therapies that can be administered using upper-arm exoskeletons.