Rehabilitation robots have become important tools in stroke rehabilitation. Compared to manual arm training, robot-supported training can be more intensive, of longer duration and more repetitive. Therefore, robots have the potential to improve the rehabilitation process in stroke patients. Whereas a majority of previous work in upper limb rehabilitation robotics has focused on end-effector-based robots, a shift towards exoskeleton robots is taking place because they offer a better guidance of the human arm, especially for movements with a large range of motion. However, the implementation of an exoskeleton device introduces the challenge of reproducing the motion of the human shoulder, which is one of the most complex joints of the body. Thus, this paper starts with describing a simplified model of the human shoulder. On the basis of that model, a new ergonomic shoulder actuation principle that provides motion of the humerus head is proposed, and its implementation in the ARMin III arm therapy robot is described. The focus lies on the mechanics and actuation principle. The ARMin III robot provides three actuated degrees of freedom for the shoulder and one for the elbow joint. An additional module provides actuated lower arm pro/supination and wrist flexion/extension. Five ARMin III devices have been manufactured and they are currently undergoing clinical evaluation in hospitals in Switzerland and in the United States.