To investigate the effects of various factors on the swaying characteristics of landing gear under conditions with transmission clearance, a theoretical analysis was first conducted to reasonably design anti-sway damping for a gear-driven steering system of the nose landing gear. Subsequently, the coupled rigid-flexible multibody dynamics simulation model for landing gear swaying was validated through both theoretical analysis and swaying test results. For the first time, nonlinear factors such as gear transmission clearance and axial/radial transmission clearance of the torque arm were simultaneously incorporated into the swaying dynamics analysis, enabling the establishment of a coupled rigid-flexible nonlinear dynamics model for landing gear with transmission clearance. Based on this model, a comprehensive study was conducted to analyze the differences in swaying response characteristics influenced by multiple factors. The results revealed that the presence of clearance can cause the landing gear to enter a state of constant-amplitude oscillation. Both gear transmission clearance and torque arm clearance amplify the swaying angle of the wheel, with gear transmission clearance having a greater influence than torque arm clearance. Overall, the size of the clearance exhibits a roughly proportional amplifying relationship with the wheel swaying angle, necessitating strict control of clearance size through assembly and manufacturing processes. Additionally, it was found that under a fixed clearance, increasing vertical load can help mitigate swaying, while variations in aircraft taxi speed can affect the swaying frequency of the wheel. These findings provide valuable references for the design of future anti-sway systems for landing gear.