For the existing adaptive constrained robotic control algorithms, the demanding ``feasibility conditions'' on virtual controller is normally inevitable and the extra limits on constraining functions have to be imposed, making the corresponding approaches more demanding and less user friendly in control development. Here, we develop a new neuroadaptive constrained control strategy for uncertain robotic manipulators in the presence of position and velocity constraints. First, a novel unified mapping function (UMF) is constructed so that the restriction on constraining boundaries is removed and more kinds of constraining forms can be handled. Second, by integrating the UMF-based coordinate transformation with the ``universal'' approximation characteristic of neural networks over some compact set, the developed neuroadaptive control completely obviates the complicated yet undesired ``feasibility conditions.'' Furthermore, it is proven that all closed-loop signals are semiglobally bounded and the constraints are not violated. The effectiveness of the proposed control is validated via a two-link rigid robotic manipulator.