Kinematics of a bicone on sharp–edged rails. (5th August 2014) - Decuyper, M.
An analytical solution is proposed for the problem of the contact between a pair of conical wheels and a sharp–edged straight track. The problem is dealt with using analytical geometry, in such a way that no approximation is needed and that a full nonlinear solution is obtained without any iterative procedure. The sequence of calculations is rather intricate, but quite elementary to implement on a computer. Linear and quadratic approximations of these calculations lead to explicit expressions for the kinematical constraints and for the coordinates of the contact points. Separate analyses of the pure yawing and rolling motions are given as geometrical confirmation and for interpretation of the results obtained, referring in particular to the fixed and rolling centrodes theory; they clearly show that for large conicities or non–traditional configurations, the stiffnesses (e.g. gravitational) may change sign. The results of these calculations may be used as a kinematical basis for the study of wheelset dynamics.