Rolling Rigid Objects

Simulating the dynamics of rigid bodies plays an important role in virtual reality applications such as virtual assembly planning and ergonomy studies but also in the field of computer animation. In order to decrease the complexity of the object representations and to increase the accuracy of the simulation algorithms one goal is to deal with objects with curved surfaces directly instead of approximating them by polyhedra. One important aspect of the dynamic behaviour of objects with curved surfaces is the rolling process. In this paper we develop the dynamics equations that describe the rolling motion of arbitrarily shaped rigid objects that are in a oneor two-point contact with an arbitrary surface. As a method to keep track of the pairs of closest points we use techniques from differential geometry.