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This paper explains why neural oscillators can enable synchronization and assist effect of a robot for rhythmic power assist. Synchronization gain is introduced in this study to adjust the synchronization level. Larger gain enables the neural oscillator synchronize its oscillation frequency with the input oscillation frequency, but the oscillation amplitude of the neural oscillator is getting larger along with the increase of the gain. The synchronized outputs of neural oscillator can be used as either joint toque or desired angle of a robot for different assist purpose. To realize synchronization, in this paper we proposed using human joint torque as input to the neural oscillator, and the output of neural oscillator as robot joint torque. This approach is referred to as the synchronization-based power assist in this study. We conducted a series of simulations and experiments to explain the mechanism of how significant assist effect and synchronization action was obtained, and we verified the validity of our proposal using neural oscillator for rhythmic power assist.