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Sliding mode control is often used for systems with parametric uncertainties due to its desirable robustness and stability, but this approach carries undesirable chattering. Similarly, joint elasticity is a common phenomenon induced by transmission systems in robots, but it presents additional complexity in robot dynamics that could lead to robot vibrations or even instability. Coupling these two phenomena presents further compounded challenges, particularly when faced with the human interface's added uncertainties. Here, a stable voltage-based adaptive fuzzy strategy to sliding mode control is proposed for an elastic joint robot arm that uses a human's upper limb electromyogram (EMG) signals to direct its movement. The concurrent use of EMG with the elastic joint arm provides a suitable framework for human-robot interaction. EMG signals represent human's 'intention' on motion, i.e., they move between 50-100 ms before the mechanical motion begins. Hence this strategy potentially builds better synchronization between the robot and human intention. Furthermore, the adaptive fuzzy strategy eliminates the system chattering while also providing robustness against parametric uncertainties and time delay. Lyapunov analysis also shows bounded-input bounded-output stability of the closed-loop system. Finally, the proposed approach is experimentally implemented in the Sport Science Research Institute. Comparisons with a competing strategy, as well as a torque mode controller, shows that the proposed approach leads to a computationally faster and more accurate controller.