A large number of patients suffer from severe disabilities resulting from strokes, and many upper body functions are severely affected. Robotic devices have the potential to play an important role as rehabilitation tools during therapy and also as assistive devices to improve the quality of life for this population. We are designing a robotic exoskeleton for assisting with upper body movements of subjects with severe disabilities. Our goal is to design a device that can support weight of the upper body and provide assistive force for patients so that they can achieve the intended motions and follow the guided movement passively during therapy. We are focusing on the design of an upper-body exoskeleton mechanism that provides unconstrained mobility to all the joints. A well-organized exoskeleton mechanism functions as a force transmission system from the actuators to the human body, and it can also protect the human joints from undesirable external forces.