This article develops a new output feedback tracking control scheme for uncertain robot manipulators with only position measurements. Unlike the conventional sliding mode controller, a quasi-continuous second-order sliding mode controller (QC2C) is first designed. Although the QC2C produces continuous control and less chattering than conventional sliding mode and other high-order sliding mode controllers, chattering exists when the sliding manifold is defined by the equation s = ⋅ = 0. To alleviate the chattering, an adaptive fuzzy QC2C (FQC2C) is designed, in which the fuzzy system is used to adaptively tune the sliding mode controller gain. Furthermore, in order to eliminate chattering and achieve higher tracking accuracy, quasi-continuous third-order sliding mode controller (QC3C) and fuzzy QC3C (FQC3C) are investigated. These controllers incorporate a super-twisting second-order sliding mode observer for estimating the joint velocities, and a robust exact differentiator to estimate the sliding manifold derivative; therefore, the velocity measurement is not required. Finally, computer simulation results for a PUMA560 industrial robot are also shown to verify the effectiveness of the proposed strategy.