Robotic rehabilitation is an effective platform for sensorimotor training after neurological injuries. In this paper, an adaptive controller is developed and implemented for the RiceWrist, a serial-in-parallel robot mechanism for upper extremity robotic rehabilitation. The model-based adaptive controller implementation requires a closed form dynamic model, valid for a restricted domain of generalized coordinates. We have used an existing method to define this domain and verify that the domain is widely within the range of admissible tasks required for the considered application (movements-based wrist and forearm rehabilitation). Simulation and experimental results that compare the performance of the adaptive controller to a proportional-derivative controller show that the trajectory tracking performance of the adaptive controller is better compared to the performance of a PD controller using the same values of feed-back gains. Further, comparable absolute error performance is obtained with the adaptive controller for feedback gains nearly one third that required for the PD controller. With the lower gains used in the adaptive controller, good tracking performance is achieved with a more compliant controller that will allow the subject to indicate their ability to independently initiate and maintain movement during a rehabilitation session.