This article centers around investigating the event-triggered nonsingular fixed-time tracking issue for an n -link rigid robot manipulator with full-state constraints, external disturbances, and model uncertainties. We propose the definition of the constrainedly practically fixed-time stability (CPFTS) and provide a sufficient condition for CPFTS. A novel auxiliary function is developed to address the singularity issue caused by repeated differentiation in achieving the fixed-time tracking control. The uncertain parameters are approximated using the radial basis function neural network (RBFNN). This study proposes the model-based and the neutral network-based tracking control approaches, designed using the scaling function technique and the barrier Lyapunov function, respectively, to ensure that the tracking error systems are CPFTS and the full-state constraints comply. Moreover, the communication transmission load is reduced using the relative threshold event-triggered control strategy. Simulation results demonstrate the effectiveness of the proposed tracking control algorithms.