Contact conditions for cylindrical, prismatic, and screw joints in flexible multibody systems

This paper focuses on the modeling of the contact conditions associated with cylindrical, prismatic, and screw joints in flexible multibody systems. In the classical formulation these joints are developed for rigid bodies, and kinematic constraints are enforced between the kinematic variables of the two bodies. These constraints express the conditions for relative translation and rotation of the two bodies along and about a body-fixed axis, and imply the relative sliding and rotation of the two bodies which remain in constant contact with each other. However, these kinematic constraints no longer imply relative sliding with contact when one of the bodies is flexible. To remedy this situation, a sliding joint and a sliding screw joint are proposed that involves kinematic constraints at the instantaneous point of contact between the sliding bodies. For sliding screw joints, additional constraints are added on the relative rotation of the contacting bodies. Various numerical examples are presented that demonstrate the dramatically different behavior of cylindrical, prismatic, or screw joints and of the proposed sliding and sliding screw joints in the presence of elastic bodies, and the usefulness of these constraint elements in the modeling of complex mechanical systems.