Recursive projection methods in flexible multibody dynamics

In this investigation, recursive projection methods for the dynamic analysis of mechanical systems that consist of a set of interconnected deformable bodies are presented. The dynamic differential equations of motion are developed for each body using the generalized Newton-Euler equations. The relationship between the actual joint reactions and the generalized forces combined with the kinematic relationships and the generalized Newton-Euler equations are used to develop a large system of loosely coupled equations. Using matrix partitioning and recursive projection techniques based on optimal block factorization, a decoupled rigid body and elastic coordinate recursive formulation is developed and can be used to obtain an efficient solution for the system accelerations. This solution technique yields a much smaller operations count and can more effectively exploit vectorization and parallel processing. The computer implementation of the recursive projection methods in flexible multibody dynamics is also 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. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. The use of the numerical algorithm developed in this investigation is demonstrated using an open-loop space crane and a closed-loop four-bar mechanism.