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This paper will discuss the stress reduction of the worm wheel for an electric power steering (EPS) system. The research discussed in this paper focused on the worm wheel, the EPS component that determines the maximum diameter of the system. If the stress of the worm wheel could be reduced without increasing in size, it would be possible to reduce the size of the worm wheel and EPS system. In order to reduce the stress of the worm wheel, the conventional design method has extended the line-of-action toward outside of the worm wheel to increase the contact ratio of the gears and these method lead to an increase in the outer diameter. In order to address this issue, past research proposes the basic concept to extend line-of-action toward the inside of the worm wheel. And this new meshing theory was named MUB (Meshing Under Base-circle) theory. In this paper, characteristics of meshing of the gear formed by MUB theory are determined in more detail.