Abstract Through analysis of the basic transformation of the typical body, the error transformation of the position vector and the displacement vector between two adjacent bodies are proposed. By means of the lower numbered body array, which is constructed by the topological construction of a system, a complicated model including thermal errors is presented for four axes machining centers based on the Multi-body System Theory. The spindle thermal errors are measured by normal five points method. The structure thermal errors of machining centers are determined by using a RBF neural network method, which are related with five temperature sensors All the thermal errors are integrated in a model. Meanwhile, a special work piece including many dummy clubs is designed for the error compensation experiment, which is carried out in Makino four-axes machining center. Compared with four points in different dummy clubs on the conditions of the theoretical result , with and without compensation results , the positioning errors are decreased 60%, the accuracy of the work piece is improved obviously.