Wheelchair mounted upper limb exoskeletons offer an alternative way to support disabled individuals in their activities of daily living (ADL). Key challenges in exoskeleton technology include innovative mechanical design and implementation of a control method that can assure a safe and comfortable interaction between the human upper limb and exoskeleton. In this article, we present a mechanical design of a four degrees of freedom (DOF) wheelchair mounted upper limb exoskeleton. The design takes advantage of non-backdrivable mechanism that can hold the output position without energy consumption and provide assistance to the completely paralyzed users. Moreover, a PD-based trajectory tracking control is implemented to enhance the performance of human exoskeleton system for two different tasks. Preliminary results are provided to show the effectiveness and reliability of using the proposed design for physically disabled people.