The use of rigid-body models during frictional contact is often justified by proving the existence of a unique solution to the forward dynamic equations. The implicit assumption here is that the contact forces so obtained are stable. In this paper, the rigid-body assumption is relaxed and body-to-body contacts are modeled using springs and dampers. A singular perturbation analysis reveals additional necessary conditions to ensure contact force stability in the reduced rigid-body model. Furthermore, the analysis indicates that stability depends on a damping ratio associated with the rigid contacts.

The use of rigid body models during frictional contact is often justified by proving the existence of a unique solution to the forward dynamic equations. The implicit assumption here is that the contact forces so obtained are stable. In this paper, the rigid-body assumption is relaxed and body-to-body contacts are modelled using springs and dampers. A singular perturbation analysis reveals additional necessary conditions to ensure contact force stability in the reduced rigid-body model. Furthermore, the analysis indicates that stability depends on a damping ratio associated with the rigid contacts.

It is well known that the introduction of Coulomb friction in rigid-body dynamics can lead to problems of existence and uniqueness in the forward equations. In this paper, it is shown that these problems relate to jamming and wedging. Separate conditions for jamming and wedging are provided in the three common formulations of constrained systems. These conditions are illustrated with examples.>