A Geometry-Aware Method for Analyzing Contour Error in Three-Axis CNC Machine Tools Through Planning–Execution Decomposition

Contour error in CNC machine tools results from both trajectory generation and servo execution, yet the final error magnitude alone cannot explain how changes in control parameters alter the underlying formation process. This study proposes a geometry-aware planning–execution analysis framework that maps the nominal G-code trajectory, CNC target trajectory, and actual trajectory to a common geometric reference. The framework separately quantifies deviations introduced during trajectory planning and servo execution and attributes parameter-induced error increments to planning, servo execution, and their directional interaction. The framework was evaluated on a three-axis translational CNC platform using LinuxCNC/EtherCAT under eight control configurations, with four independent repetitions per configuration. The results reveal substantial variation in the global error-formation structure across control backgrounds, with the dominant contribution shifting between trajectory planning and servo execution. The propagation pathways associated with different parameter perturbations also exhibit different sensitivities to the control background. Local trajectory geometry further redistributes the induced error increments. Under feed-rate perturbations, servo execution remains the dominant source along steady-line segments, whereas the contributions of planning and directional interaction increase near corners. These findings provide an interpretable account of contour-error formation in terms of its planning and execution components rather than the final error magnitude alone.