| Vehicle steering system shimmy is a kind of complicated vibration. Though many valuable papers have been published domestically and overseas, the problem is still not solved thoroughly. With the raising of the demand of handling stability and riding comfort, classical linear methods can't meet the requirement of automobile systemic modeling and reducing shimmy any more.The nonlinear relationship between slip angle and lateral force has been considered to construct a shimmy model of three degrees of freedom, which includes vibration of front wheels around the king pin axis and vibration of front bridge around the longitudinal axis, the system parameters are based on the NJ-221 cross-country vehicle with depended suspension. The bifurcation characters that the automobile running are studied systematically and comprehensively. The equilibrium positions of the system and their characters are studied by the stability theory of ordinary differential equations, and the further research on complicated equilibrium is carried out. It is found that the Hopf bifurcations are exist in this system and the influences of the automobile parameters on these bifurcations are founded with Hurwitz criterion. The bifurcation characters are analyzed by nonlinear dynamical system theory, the relationship between the amplitude and velocity is discovered and the result is validated by the numerical analysis method. By means of constructing the relations of topology bifurcation solution of this kind of system and unfolding parameters of this system, universal unfolding bifurcation figures are obtained. It is convenient to choice reasonable system parameters according to requisite motion models by these figures. Comprehensive research on the shimmy of front bridge and turning wheel system of depended suspension system is presented, and some quantitative or qualitative regularity are found, which have some directive significance for the design of automobile parameters and dynamics analysis.
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