An exoskeletal rehabilitation device supports a hand, a lower arm portion, and an upper arm portion of a user relative to a supporting surface for rehabilitating the arm. The device has a shoulder frame that pivots about a first shoulder axis relative to a base frame fixed onto the supporting surface. An upper arm frame alongside the upper arm portion pivots on the shoulder frame about a second shoulder axis transverse to the first. A lower arm frame alongside the lower arm portion pivots on the upper arm frame about an upright elbow axis. A wrist frame supports a handle frame that receives the hand relative to the lower arm frame. The wrist frame pivots on the lower arm frame about a longitudinal axis longitudinal of the lower arm portion, while the handle frame pivots on the wrist frame about a wrist axis for flexion and extension of the hand.