Wheelset hunting is a motion with two degrees of freedom. The second degree of freedom of hunting is investigated in this paper. Rolling radius difference is commonly understood as the root cause of wheelset hunting. Normally, hunting will begin as soon as the truck begins to move. Rolling radius difference will initiate the hunting and can only be used to determine the configuration of the first quarter of a hunting cycle. Then a mechanism will come into exist to determine the configuration of the second quarter of the hunting cycle, which is exactly the same as the one of first quarter but in the opposite direction. The second half of the hunting cycle is a mirror of the first half. The information from wheelset hunting is too large and too complicated for people to understand and analyze. However, the radius of curvature of wheelset circular motion can be calculated exactly, especially at some special configurations, even though the radius of curvature of wheelset circular motion keeps changing in both magnitude and direction. Furthermore, comparison of the radii of curvature between hunting curve and a cosine curve shows that the curve for the wheelset in hunting motion is sinusoidal. This is proven mathematically in the paper. The limits in Klingel's results were discussed. Due to the fact that Klingel's results are unable to provide a strong theoretical base for further understanding the complicated dynamic characteristics caused by hunting, misleading in hunting is overwhelmed. After understanding the principles of wheelset hunting, three critical speeds in hunting and dynamic loading for truck design in three directions were calculated; wheelset hunting curve while curving was generated; wheelset dynamic interaction was analyzed and the question "Why trains stay on tracks" was answered correctly, just to name a few. Thus, a total solution to the hunting problems can be expected and was discussed in the paper.
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