In this paper, the form of a tooth profile, whose path of contact is a conic curve, is studied mathematically, and various forms of profile are derived as its special cases. First, the profile in an elliptic path of contact is obtained, and, as its special cases, the profiles in hyperbolic, parabolic, circular and straight paths of contact are derived. Next, the inverse curve of a conic section with respect to a focus, or the limacon, is taken as a path of contact, and some profiles, a circle, a straight line etc., are derived by changing the form of the limacon.
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