Motorcycle Dynamic Models for Virtual Rider Design and Cornering Analysis

In this paper, three motorcycle models of increasing complexity are introduced. The first, and most simple, can be considered an extension of the model developed by Neil Getz in which the non-holonomic constraints have been removed to take into account the sideslip in tires. Also, this model can be viewed as an extension of the popular bicycle model, widely used in analyzing car dynamics. It has been extended with an additional degree of freedom essential to study motorcycle dynamics: the roll angle. Such a model, simple yet detailed enough, will be used as the basis in the development of a virtual rider. The second model is much more complex than the previous one. It includes the real geometry of the steering system and circular tire profiles which greatly increases the size of the equations. This is a multibody model of a complete rigid motorcycle (i.e. it has no suspensions) consisting of 4 bodies: rear wheel, main frame, fork and front wheel. The last model incorporates the front and rear suspensions together with all the features of its predecessor. It has 13 degrees of freedom, 11 of the mechanical system and 2 of the tire relaxation equations. It will be used as a full model for simulation and rider validation. The models presented in this article have been developed using Maple mathematical software which allows symbolic manipulation of equations. Thus, with this set of models, one can study in depth the phenomena that govern motorcycle dynamics since all the equations are available symbolically.