Slipping-rolling transitions of a body with two contact points

In this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

Automated summary

This paper analyzes the general kinematics and dynamics of a rigid body in contact with two rigid surfaces in the presence of dry friction, exploring the characteristics of contact forces and the conditions of static friction forces in two-point rolling. The issue is resolved by analyzing the system's vector field, leading to a method to determine the conditions for the realization of two-point rolling without slipping based on the concept of limit directions of codimension-2 discontinuities.