A relative contact formulation for multibody system dynamics

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Dynamic analysis of many mechanical systems is often involved with contacts among bodies. This paper presents a relative contact formulation for multibody dynamics in the context of the compliance contact model. Many conventional collision detection algorithms are based on the absolute coordinate system. This paper proposes to use the relative coordinate system in detecting a contact. A contact reference frame is defined on the defense body of a contact pair. Since all geometric variables necessary to detect a contact are measured relative to the contact reference frame attached to the defense body, the variables for a defense body are constant, which significantly reduces computation time. Therefore, the contact frame plays a key role in developing an efficient contact search algorithm. Contour of a defense body is approximated by many piecewise straight lines, while contour of a hitting body is represented by hitting nodes along its boundary. Bounding boxes containing each body of a contact pair are defined at a pre-search stage to eliminate the exhaustive contact inspection process when two bodies are in a distance. Domain of the bounding box for a defense body is divided into many sectors each of which has a list of line segments lying inside or on the sector boundary. Post-search for a contact is processed in the sequence of broad and narrow phases. In the broad phase, the bounding boxes of a contact pair are inspected for a contact. If two boxes are in a contact, each node on the hitting boundary is inspected to find out to which sector the node belongs. Since each domain sector of the defense body has a list of line segments, each node on the hitting boundary is tested for a contact only with the line segments in the list. In the narrow phase, actual contact calculation is carried out to find the contact penetration used in calculating the contact force. Since the searching algorithm is coupled with the stepping algorithm of the numerical integration, a strategy for deciding an integration stepsize is proposed. One numerical example is presented to demonstrate the validity of the proposed method.