We derive relations which describe the nonlinear geometry of contact between a railway vehicle wheelset and rail. Geometric constraint relations are derived and expanded about the central (rest) positions. These are solved for the rolling and vertical motions, instantaneous left and right wheel rolling radii, angles between the contact and horizontal planes, and lateral and longitudinal creepages. The results are given explicitly in terms of the lateral and yawing motions for mildly noncircular wheel and rail profiles. A kinematic (pure rolling) solution is obtained for the case where the wheel profile is sufficiently noncircular to invalidate the classical linear kinematic solution.

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