The design of rehabilitation devices for patients experiencing musculoskeletal disorders (MSDs) requires a great deal of attention. This paper aims to develop a comprehensive model of the upper limb complex to guide the design of robotic rehabilitation devices that prioritize patient safety, while targeting effective rehabilitative treatment. A 9 degree-of-freedom kinematic model of the upper limb complex is derived to assess the workspace of a constrained arm as an evaluation method of such devices. Through a novel differential inverse kinematic method accounting for constraints on all joints, the model determines the workspaces in which a patient is able to perform rehabilitative tasks and those regions where the patient needs assistance due to joint range limitations resulting from an MSD. Constraints are imposed on each joint by mapping the joint angles to saturation functions, whose joint-space derivative near the physical limitation angles approaches zero. The model Jacobian is reevaluated based on the nonlinearly mapped joint angles, providing a means of compensating for redundancy while guaranteeing feasible inverse kinematic solutions. The method is validated in three scenarios with different constraints on the elbow and palm orientations. By measuring the lengths of arm segments and the range of motion for each joint, the total workspace of a patient experiencing an upper-limb MSD can be compared to a pre-injured state. This method determines the locations in which a rehabilitation device must provide assistance to facilitate movement within reachable space that is limited by any joint restrictions resulting from MSDs.