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Inverse kinematics computation using an artificial neural network that learns the inverse kinematics of a robot arm has been employed by many researchers. However, the inverse kinematics system of typical robot arms with joint limits is a multivalued and discontinuous function. Since it is difficult for a well-known multilayer neural network to approximate such a function, a correct inverse kinematics model cannot be obtained by using a single neural network. In order to overcome the discontinuity of the inverse kinematics function, we proposed a novel modular neural network system that consists of a number of expert neural networks. Each expert approximates the continuous part of the inverse kinematics function. The proposed system uses the forward kinematics model for selection of experts. When the number of the experts increases, the computation time for calculating the inverse kinematics solution also increases without using the parallel computing system. In order to reduce the computation time, we propose a novel expert selection by using the performance prediction networks which directly calculate the performances of the experts.