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A new method of solving inverse kinematics of 6R welding robot based on radial basis function（RBF） neural networks was presented to improve the precision of the position and orientation and the accuracy of welding trajectory for the 6R welding robot. The inverse kinematics solution prediction model of the 6R welding robot was established based on RBF neural networks because the inverse kinematics equations were high-dimensionally nonlinear and solving these equations was complex. The work space in which 6R welding robot position and orientation sample parameters were situated was divided based on scale-space theory. After that the training sample set was selected optimally based on uniform design and the cluster theory. The parameters were transformed and normalized according to the Z-Y-Z coordinate conversion principle. The problem of solving the inverse kinematics equations was transformed into six inputs and six outputs prediction system based on RBF neural network. Complex movement trajectory of 6R robot was simulated and the spot welding experiments were done by means of this prediction system. The results of the prediction and welding track accuracy were compared with the inverse kinematics solution based on combinatorial optimization iteration algorithm and back propagation (BP) neural networks. The results showed that the RBF prediction model of solving 6R welding robot inverse kinematics equations was simpler, more accurate and easier to do trajectory planning, and it was proved to be feasible and effective.