Majority of wheelchair users experience upper-body muscular weakness, resulting from neuromuscular diseases, which limit their ability to perform common activities of daily living. A Wheelchair Mounted Robotic Arm (WMRA) will assist these individuals to eat, drink, and move objects as needed. This paper presents the design of a new WMRA as well as the analysis of its function. The design is side-mounted onto either a normal or power wheelchair, and incorporates a slim profile to allow ease of passage through doorways and be otherwise unobtrusive. The arm is easily removable, with assistance, for storage or travel. The mechanical design utilizes a belt and pulley system for remote actuation of each joint, driven by DC Gearmotors located in the base of the arm. This helps to shift the weight closer to the wheelchair and to maintain the required speed, torque and inertia while actively driving each joint of the robot. The end effector is a unique design, intended to have the adaptability to securely lift a large variety of objects. Grasping simulations were performed on several standard objects which might be encountered daily. Structural, kinematic and workspace analyses are conducted, and results confirm that the designed WMRA is rated to lift a 4 kg payload, while also having a reach of 1.3 meters long radius.