Functional electrical stimulation (FES) is the application of electrical current across muscle fibers to elicit muscle contractions with the goal of achieving some function outcome (e.g. walking, cycling). FES-cycling has become a very popular rehabilitative strategy over the years as it has proven to yield numerous health benefits for individuals suffering from neurological conditions. In this paper the idea of FES-cycling is extended to the upper limbs and a new arm-cycling testbed is introduced. A dynamic model for the arm-cycle-rider system is presented and a robust sliding-mode controller is developed for the nonlinear, autonomous, state-dependent, switched system. The controller is designed with the goal of tracking a specified crank velocity by switching between muscle stimulation and an electric motor. Despite the uncertainties and nonlinearities associated with the system, global exponential tracking of the desired crank trajectory is proven with a Lyapunov-based stability analysis. Preliminary experiments are performed with an able-bodied subject to characterize the performance of the designed controller. The results of the experiment are presented to illustrate stable tracking of the designed control system.