Recursive method for modeling flexible multibody systems with non-ideal constraints

With the recursive kinematics relationship between the twobodies interconnected with a joint, it is showed that the interactionbetween the outermost body and the inboard body in a tree-type multibodysystem can be measured by the transmission of the inertia mass and forces.The non-ideal constraint forces and the constraint forces at the cut-jointsin a closed-loop multibody system can be viewed as external applied forces,therefore, any mutibody system corresponds to an equivalent tree-typesystem. Moreover, the general accelerations of the system appearing in theconstraint equations can be systematically replaced by the Lagrangemultipliers which are related to the constraint forces. Based on the aboveideas, a recursive method is presented, by which, any closed-loop flexiblemultibody system with non-ideal constraints can be dynamically reduced to anequivalent system with only one body in a recursive manner. Consequently,the inverse of the mass matrix of multibody systems is not involved in thecalculations of the general accelerations, and the number of equations tosolve the non-ideal constraint forces can be reduced to minimum. An exampleis analyzed to illustrate and validate the presented method in details.