Unique minimum norm solution to redundant reaction forces in multibody systems

Abstract

Multibody system models that rely on the rigid body assumption are used in many engineering applications. In such models redundant constraints often appear, which is caused by a lack of information about the physical system. This prevents the unique determination of all reaction forces associated with the constraints. Sometimes the resultant effect of these redundant constraints can be considered instead of computing individual constraint reactions. When, on the other hand, individual reactions are key, additional assumptions and methods have to be considered. This paper analyzes the conditions under which the minimum norm solution to this problem is non-unique, provides a physical interpretation of the issue, proposes a simple method to normalize the minimum norm solution and make it unique, and extends these principles to unilaterally constrained multibody systems. The theoretical development and validation are carried out on the basis of meaningful examples, namely, two pendulum-type systems, a box on a plane, a one-degree-of-freedom mechanism, and a 33-degree-of-freedom chain.