This paper presents a theoretical investigation of the dynamics of a cotton tuft moving between a saw-toothed drum and a grid bar grate, as well as the process of large impurity separation. Analytical equations describing the velocity and travel distance of the cotton tuft along the surface of the grid bars were derived by considering the effects of gravitational, frictional, and periodic elastic forces. The influence of grid bar diameter, spacing between adjacent grid bars, contact wrap angle, and grate surface geometry on the cotton flow velocity was evaluated based on the law of conservation of mass. A mathematical model describing the variation of centrifugal force and impurity concentration along the grate arc was also developed. The calculation results show that increasing the wrap angle and the grid bar diameter reduces the cotton flow velocity, whereas increasing the spacing between the grid bars enhances the impact force. Although a smaller grid bar diameter increases the impact intensity and improves impurity removal, it also raises the risk of fiber damage. Conversely, a larger diameter provides a wider contact surface but reduces the impact effect. Based on the theoretical analysis, a grate configuration with a 15 mm grid bar diameter and30 mm spacing between adjacent grid bars was theoretically substantiated as the rational design, ensuring stable cotton flow, efficient separation of large impurities, and preservation of fiber quality.