Methods: To more clearly describe the specific movements of each joint, the local POE method was introduced. For ease of analysis, the structure of the robot's passive arms was simplified using screw theory. A kinematic model for the Delta robot was established using the local POE method. The error model of the robot was obtained through the differential mapping of the exponential product. Based on the derived error model, error sources were subdivided into three major categories: structural errors, actuation angle errors, and spherical joint clearance errors. An in-depth analysis was conducted on how each error source affects the end-effector positioning accuracy of the robot when it moves along the X, Y, and Z directions. A Delta robot with active arm lengths of 400 mm and passive arm lengths of 950 mm was selected as the subject for simulation analysis in MATLAB. The square root of the sum of squared errors in the X, Y, and Z directions was used as a composite error to serve as an evaluation criterion. Results: The simulation results showed that assuming all error sources have a magnitude of 0.100 units (length unit being mm; angular unit being degrees), actuation angle errors had the most significant impact on the end-effector positioning accuracy of the Delta parallel robot, causing a composite error ranging from 1.500 to 2.000 mm. Spherical joint clearance errors caused a composite error of 0.340 mm in the robot. Structural errors exhibited a relatively stable composite error fluctuating around 0.100 mm, with a variation range of approximately 0.010 mm, which can be considered a constant value. Comprehensive analysis indicated that length errors in the active and passive arms significantly influenced end-effector positioning accuracy, with the induced error fluctuations notably larger than those from other sources. Additionally, when the magnitudes of error sources were 0.025 mm, 0.050 mm, 0.075 mm, and 0.100 mm, their impacts on robot positioning accuracy increased proportionally. Conclusions: The Delta robot error analysis model based on screw theory and utilizing the local POE method offers a more intuitive and comprehensive approach to analyzing the impact of major error sources on positioning accuracy compared to traditional error modeling methods. This approach effectively avoids issues of singularity and incompleteness. It provides theoretical reference for error modeling analysis of other parallel mechanisms. Through the assessment of the influence of each error source presented in this paper, during subsequent error compensation phases, more precise corrections can be made to the significantly impactful actuation angle errors, thereby effectively improving the efficiency and effectiveness of overall error compensation.