Robot-assisted physical therapy has been shown to aid in the rehabilitation process following neurological injuries. As a therapeutic or training tool, the robot provides a means to implement and evaluate assistance cues to the operator's arm in addition to displaying the forces arising from the dynamics of the virtual environment. Furthermore, training in virtual environments also provides increased repeatability, scalability, safety and a greater control on the experimental setup over training in natural environments. This thesis presents the analysis of various design constraints that apply to the design of such devices. In this context, the author also presents the design of a five degree-of-freedom haptic arm exoskeleton designed for training and rehabilitation in virtual environments. The device has high structural stiffness, minimal backlash, low friction and absence of mechanical singularities in the workspace, which are some of the properties that characterize high quality haptic interfaces. A scheme for the force control of the robot, using a novel joint-based methodology is also presented.