The Inverse Kinematics (IK) problem of manipulators can be divided into two distinct steps: (1) Problem formulation, where the problem is developed into a form which can then be solved using various methods. (2) Problem solution, where the IK problem is actually solved by producing the values of different joint space variables (joint angles, joint velocities or joint accelerations). The main focus of this paper is concentrated on the discussion of the IK problem of redundant manipulators, formulated as a quadratic programming optimization problem solved by different kinds of recurrent neural networks.