<p>Positioning error is the critical indicator for evaluating the feed accuracy of the linear axis of machine tools. The objective of this research is to analyze the degree-of-freedom constraints of the joint surfaces between linear axis components through the meta-action theory and then to trace and model the propagation of positioning errors. First, the meta-action units of the linear axis components are analyzed and the propagation paths of positioning errors are determined. Secondly, the error source parameters are introduced and the propagation model of the positioning error is established. Thirdly, the effect of linear axis positioning errors on the machining errors is simulated. Finally, measurement and compensation experiments of positioning errors were performed on three-axis machine tools, and the changes in the machining accuracy of the machines were verified by machining workpieces. The results indicate that the propagation model of the positioning error improves the efficiency of path analysis and identification and provides an effective guidance for scientifically optimizing the manufacturing and assembly of the linear axis.</p>