<p>The 4–6-stage non-circular planetary gear train (NCPG) is the key element of non-circular hydraulic motors, and its accuracy governs motor life. To suppress vibration-induced instability, a 36-DOF nonlinear dynamic model was built. The bifurcation, shock and dynamic load characteristics of the system under the influence of individual parameters such as excitation frequency, error excitation amplitude, meshing damping ratio and output torque, as well as the coupling effect of two parameters, were studied through bifurcation diagrams, maximum dynamic load coefficient diagrams, phase trajectory diagrams and Poincaré mapping diagrams. The results indicate that variations in excitation frequency lead to a diverse range of motion states and dynamic load impact states within the system. Furthermore, an increase in the amplitude of error excitation significantly expands the chaotic motion range in the medium and low frequency regions, and markedly increasing the dynamic load impact. Conversely, an increase in the meshing damping ratio can substantially reduce or even completely eliminate chaotic motion across the frequency spectrum, as well as significantly diminish dynamic load impacts. Additionally, while an increase in output torque has a certain inhibitory effect on the occurrence of chaotic motion, excessively high output torque results in a continual increase in dynamic load impacts on the system. The findings of this research provide a theoretical basis for the dynamic design, optimal parameter matching, and vibration and noise reduction in non-circular gear transmission systems.</p>