Computational analysis of multibody dynamic systems using nonlinear recursive formulation

In this paper the computer implementation of the nonlinear recursive formulation in multibody dynamics systems is described. The organization of the computer algorithm which is used to automatically construct and numerically solve the system of loosely coupled dynamic equations expressed in terms of the absolute and joint coordinates is discussed. The inertia projection schemes used in most existing recursive formulations for the dynamic analysis of deformable mechanisms lead to dense coefficient matrices in the equations of motion. Consequently, there are strong dynamic couplings between the joint and elastic coordinates. By using the inertia matrix structure of deforrnable mechanical systems and the fact that the joint reaction forces associated with the elastic coordinates do represent independent variables, a reduced system of equations whose dimension is dependent of the number of elastic degrees of freedom is obtained. This system can be solved for the joint accelerations as well as the joint reaction forces. The multibody flexible four-bar system is used as an example to demonstrate the use of the procedure discussed in this paper.