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Upper Limb Rehabilitation Robots (ULRR) for the patient having shoulder and elbow joint movement disorders, requires further study for development. One aspect that must be fulfilled by such robots, is the need to handle uncertainties due to biomechanical variation of different patients, without significantly degrading performance. Currently, rehabilitation robots require re-tuning of controller gain for each individual. This is time consuming process and requires expert training. To overcome this problem, we propose robust sliding mode control algorithm, which uses very basic information of subject like weight, height, age and gender to handle these model uncertainties. For analysis, we have compared our proposed algorithm with Robust Computed Torque Control (RCTC) and Boundary Augmented Sliding Mode Control (BASMC) algorithms with diverse subjects. Results describe the superiority of the proposed algorithm in handling uncertain parameters human arm and robot without degrading the performance.