Abstract: The tracking error of tool center point, which is generated by the coupling of each uniaxial feed system based on the relationship of spatial structure and motion, has a great significance for the machining precision. In order to perform the coupling characteristics of tracking error for multi-axis motion system, three tracking error models for three kinds of topology structures are constructed, which are uncoupling, two-axis coupling and three-axis coupling, respectively. Taking three-dimensional linear tracking error of three-axis motion system as the research object, the mathematical expression of the tracking errors of three models are deduced considering there are three tracking error components for the high-speed feed system in the working process. Based on the spatial structure of three-axis motion systems from a typical machine tool, the influence of the coupling characteristics of the structure on the tracking error is quantified. Meanwhile, the sensitivity analysis is carried out by Sobol method. The analysis results show that the three-dimensional linear tracking error of the feed system is coupled to the tracking error of the tool center point with the coupling relationship of the spatial structure. Furthermore, the magnitude of the tracking error of the feed system is proportional to the influence of the coupling characteristics on the tracking error of the tool center point. The tangential and normal components of the tracking error of the feed drive system are equivalent to the sensitivity of the axial components. So, special attention should be paid to the research for high speed and high precision machine tools.