Abstract: To address issues in traditional precision design, such as over-reliance on empirical knowledge and unclear mechanisms of precision influence, an in-depth study was conducted on the impact of key part tolerances on machining accuracy in form grinding machines. A machining accuracy prediction method based on multi-body system kinematics, screw theory, and Monte Carlo simulation was proposed. Firstly, the mapping mechanism of key part tolerances to the geometric errors of each machine tool motion axis was analyzed. Subsequently, based on the error propagation relationships among motion axes, a comprehensive prediction model was established to link part tolerances to machine tool geometric errors and further to gear flank machining errors. Simulation results demonstrate that the geometric error distribution predicted by the model aligns with engineering practice, and the model effectively quantifies the magnitude and distribution trends of gear flank errors. Theoretical support for the design of machine tool accuracy was provided.