The influence of component errors on the final error is a key point of error modeling of computer numerical control (CNC) machine tool. Nevertheless, the mechanism by which the errors in mechanical parts accumulate to result in the component errors and then impact the final error of CNC machine tool has not been identified; the identification of this mechanism is highly relevant to precision design of CNC machine. In this study, the error modeling based on the Jacobian-torsor theory is applied to determine how the fundamental errors in mechanical parts influence and accumulate to the comprehensive error of single-axis assembly. First, a brief introduction of the Jacobian-torsor theory is provided. Next, the Jacobian-torsor model is applied to the error modeling of a single-axis assembly in a three-axis machine center. Furthermore, the comprehensive errors of the single-axis assembly are evaluated by Monte Carlo simulation based on the synthesized error model. The accuracy and efficiency of the Jacobian-torsor model are verified through a comparison between the simulation results and the measured data from a batch of similar vertical machine centers. Based on the Jacobian-torsor model, the application of quantitative sensitivity analysis of single-axis assembly is investigated, along with the analysis of key error sources to the synthetical error ranges of the single-axis assembly. This model provides a comprehensive method to identify the key error source of the single-axis assembly and has the potential to enhance the tolerance/error allocation of the single axis and the whole machine tool.

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