Study on redundant constraints in multibody systems

Being resulted from singular configuration and cut jointconstraint equations generated in a programmed way, redundant constraints inmultibody systems exert great influence on the methods for modeling andsolving multibody systems. It is necessary to select a group of independentequations from whole constraint equations in order to keep the systemcontrol equation solvable. It is observed that results of numerical analysisusually being changed by different choices. However it is not true intheory, as proven rigorously in this paper. Due to constraints violation,many methods for solving DAE lose their effectiveness near by the positioncorresponding to the singular configuration of multibody systems. Based onthe combination of constraints stabilization and elimination of constraintviolation, we present a method to overcome such difficulties and testify itsvalidness by an example. It is the greatest negative effect brought byredundant constraints that forces of interaction between bodies may be notunique. A criterion to certify which and when a constraint force would bedefinite is given. It is known that when a pair of bodies is linked by morethan one joint, the reaction forces in those joints would be ambiguous. Thispaper present a method of making the reaction forces definite in such caseby replacing those joints with a single composed one.