To enhance the motion stability of the lifting and transfer robot, the vibration suppression and structural optimization of the grasping mechanism under static and dynamic characteristics. were investigated. First, a virtual prototype model of the entire machine was constructed, which served as the foundation for multi-rigid-body dynamics and rigid-flexible coupled dynamics analysis. The center of mass motion trajectories of the grabbing mechanism in rigid and flexible states were extracted from these analyses. By comparing the rigid and flexible body center of mass curves, displacement deviations and the causes of vibration were analyzed, and vibration suppression methods were proposed. Next, a finite element model of the hook was constructed to analyze its static and dynamic characteristics. The results indicate that the hook has sufficient safety margins in both static and dynamic properties, providing boundary conditions for subsequent optimization work. Then, the grabbing mechanism was topologically optimized with the objectives of minimizing flexibility and maximizing natural frequency. The optimized model was subjected to dynamic analysis and revalidation of static and dynamic characteristics. Finally, an experimental test platform was built, and corresponding test plans were designed. Experimental comparisons were made between the optimized and non-optimized hooks, analyzing their vibration amplitudes and damping trends. The experimental results confirm that the optimized grabbing mechanism significantly improves vibration suppression, meeting design expectations. Through structural optimization and vibration suppression methods, the stability of the lifting and transfer robot is effectively enhanced, providing a practical and feasible solution for the real-world application of such material-handling machinery.