A Comparison of Various Methods of Redundant Constraints Handling in Multibody System Simulations

When redundant constraints are present in a rigid body mechanism, only selected joint reactions can be determined uniquely, whereas the other cannot. Analytic criteria and numerical methods of finding joints with uniquely solvable reactions are available. In this paper the problem of joint reactions solvability is examined from the point of view of numerical methods frequently used for redundant constrains handling in practical simulations. Three methods are discussed: elimination of redundant constraints, pseudoinverse-based calculations and the augmented Lagrangian method. In each method the redundant constraints are treated differently which — in case of joints with non-unique reactions — leads to different reaction solutions. Moreover, it is shown that one and the same method may lead to different solutions, provided that input data are prepared differently. Finally, it is illustrated that — in case of joints with solvable reactions — the obtained solutions are unique, regardless of the method used for redundant constraints handling.