DYNAMICS OF FLEXIBLE MULTIBODY SPACE CRANES USING RECURSIVE PROJECTION METHODS

In this paper the computer implementation of the recursive projection methods in flexible multibody dynamics is described. The organization of the computer program 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 main processor computer program consists of three main modules: constraint module, mass module and force module. The constraint module is used for the numerical evaluation of the relationship between the absolute and joint accelerations. The mass module is used for the numerical evaluation of the system inertia matrix as well as the nonlinear Coriolis and centrifugal forces associated with the absolute and elastic coordinates. The force module is used to evaluate the generalized external and elastic forces associated with the absolute, joint and elastic coordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. Elimination of the elastic coordinates and projection of the inertia of the child (leaf) bodies into the space of coordinates of the parent (root) bodies lead to small number of equations which can be solved for the joint accelerations. The joint and elastic accelerations are integrated forward in time using direct numerical integration methods. The absolute coordinates and velocities can then be determined using the kinematic relationships. The multibody space crane is used as an example to demonstrate the use of the computational procedure discussed in this paper.