• Research paper •

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

Qi Zhaohui

• Received:2007-11-26 Revised:2008-04-08 Online:2008-09-25 Published:2008-09-25

Abstract: With the recursive kinematics relationship between the two bodies interconnected with a joint, it is showed that the interaction between the outermost body and the inboard body in a tree-type multibody system can be measured by the transmission of the inertia mass and forces. The non-ideal constraint forces and the constraint forces at the cut-joints in a closed-loop multibody system can be viewed as external applied forces, therefore, any mutibody system corresponds to an equivalent tree-type system. Moreover, the general accelerations of the system appearing in the constraint equations can be systematically replaced by the Lagrange multipliers which are related to the constraint forces. Based on the above ideas, a recursive method is presented, by which, any closed-loop flexible multibody system with non-ideal constraints can be dynamically reduced to an equivalent system with only one body in a recursive manner. Consequently, the inverse of the mass matrix of multibody systems is not involved in the calculations of the general accelerations, and the number of equations to solve the non-ideal constraint forces can be reduced to minimum. An example is analyzed to illustrate and validate the presented method in details.