<p>This study investigates hunting-type shimmy oscillations of the Automated People Mover (APM) running gear induced by contact clearance between guide wheels and rails. A nonlinear dynamic model with five degrees of freedom is established, where clearance-induced contact forces are characterized using third- and fifth-order polynomial fits. Numerical simulations conducted via the generalized-<i>α</i> integration method demonstrate stable limit cycle oscillations under specific conditions, exhibiting typical shimmy behavior. The simulation results indicate vibrations dominated by yaw and lateral dynamics, prompting the construction of a simplified model preserving the primary dynamic characteristics. Stability mechanisms influenced by restoring stiffness and damping are systematically revealed through eigenvalue analyses, and an analytical expression for critical speed is derived using Hopf bifurcation theory. Additionally, the First and Second Lyapunov coefficients under nonlinear contact conditions are computed by the projection method to determine the Hopf bifurcation type (subcritical or supercritical). Bifurcation diagrams under various parameter conditions are plotted using the shooting method. Furthermore, a Generalized Hopf bifurcation is identified and analyzed, and a two-parameter bifurcation diagram is constructed to characterize its dynamic regions. To validate the theoretical model, a comparative simulation model is constructed using the UM multibody dynamics platform. Results show that restoring stiffness effectively extends the stable operating region, while restoring damping significantly increases the critical speed; both parameters distinctly regulate the evolution of limit cycle amplitudes and present two main bifurcation forms. The UM simulation results show good agreement with the theoretical and numerical analyses in terms of both vibration trends and dominant yaw frequencies, indicating that the proposed model and method are accurate and practically applicable.</p>