Many people with motor disabilities are unable to complete activities of daily living (ADLs) without assistance. This paper describes a complete robotic system developed to provide mobile grasping assistance for ADLs. The system is comprised of a robot arm from a Rethink Robotics Baxter robot mounted to an assistive mobility device, a control system for that arm, and a user interface with a variety of access methods for selecting desired objects. The system uses grasp detection to allow previously unseen objects to be picked up by the system. The grasp detection algorithms also allow for objects to be grasped in cluttered environments. We evaluate our system in a number of experiments on a large variety of objects. Overall, we achieve an object selection success rate of 88% and a grasp detection success rate of 90% in a non-mobile scenario, and success rates of 89% and 72% in a mobile scenario.