This study proposes using an Artificial Neural Network (ANN) to train a 6-DOF serial manipulator with a non-spherical wrist to solve the inverse kinematics problem. In this approach, an ANN has been trained to determine the configuration parameters of a serial manipulator that correspond to the position and pose of its end effector. The network was modeled after the AUBO-i5 robot arm, and the experimental results have shown the ability to achieve millimeter accuracy in tool space position with significantly reduced computational time relative to an iterative kinematic solution when applied to a subset of the workspace. Furthermore, a separate investigation was conducted to quantify the relationship between training example density, training set error, and test set error. Testing indicates that, for a given network, sufficient example point density may be approximated by comparing the training set error with test set error. The neural network training was performed using the MATLAB Neural Network Toolbox.