Augmented Lagrangian formulation: Geometrical interpretation and application to systems with singularities and redundancy

A geometric interpretation of the augmented Lagrangian formulation of Bayo et al. (Comput. Methods Appl. Mech. Engrg. 71, 1988, 183-195), applied to equations of motion in relative and Cartesian coordinates, is presented. Instead of imposing constraints on a system in the traditional sense, large artificial masses resisting in the constrained directions are added, and the system motion is enforced to evolve primarily in the directions with smaller masses (in the unconstrained directions). Then, the residual motion in the constrained directions is removed by applying the constraint reactions to the system, estimated effectively in few iterations. The formulation is comparatively simple and leads to computationally efficient numerical codes. Useful applications of the formulation to the dynamic analysis of constrained multibody systems with possible singular configurations, massless links and redundant constraints are shown. The theoretical background is followed by some remarks on the modeling precautions and assisted computational peculiarities of the method. The results of numerical simulation of motion of a parallel five-bar and a parallel four-bar linkage are reported.