In this article a radial basis function network (RBFN) approach for fast inverse kinematics computation and effective geometrically bounded singularities prevention of redundant manipulators is presented. The approach is based on establishing some characterizing matrices, representing some bounded geometrical concepts, in order to yield a simple performance index and a null space vector for singularities avoidance/prevention and safe path generation. Here, this null space vector is computed using a properly trained RBFN and included in the computation of the inverse kinematics being performed also by another properly trained RBFN.