This paper investigates adaptive neural control methods for robotic manipulators, subject to uncertain plant dynamics and constraints on the joint position. The barrier Lyapunov function is employed to guarantee that the joint constraints are not violated, in which the Moore-Penrose pseudo-inverse term is used in the control design. To handle the unmodeled dynamics, the neural network (NN) is adopted to approximate the uncertain dynamics. The NN control based on full-state feedback for robots is proposed when all states of the closed loop are known. Subsequently, only the robot joint is measurable in practice; output feedback control is designed with a high-gain observer to estimate unmeasurable states. Through the Lyapunov stability analysis, system stability is achieved with the proposed control, and the system output achieves convergence without violation of the joint constraints. Simulation is conducted to approve the feasibility and superiority of the proposed NN control.