Abstract: The complete theory of geometrical contact between wheels and rails is studied. Track is represented by the theory of differential geometry and general functions considered to represent the profiles of wheel and rail, meanwhile so – called “variable track” is used to give a more railway engineering case. The general formulae of the geometrical constraint between wheels and mils are driven up which is an extension of other theories such as De Pnter’s first order theory. The simulation results are presented.

Key words: Contact, Profiles of wheel and rail, Track, Wheel set