A Recursive Formulation for the Dynamic Analysis of Open Loop Deformable Multibody Systems

In this paper, a recursive formulation for the spatial kinematic and dynamic analysis of open chain mechanical systems containing interconnected deformable bodies, each of which may undergo large translational and rotational displacements, is developed. While approximation techniques such as the finite element method, Rayleigh-Ritz methods, or experimentally identified modal parameters can be used to introduce the elastic coordinates that describe the deformation of the bodies with respect to selected body references, the large rotational and translational displacements of a set of intermediate joint axes are described using a minimum set of relative translational and rotational coordinates. A set of time-invariant quantities that depend on the assumed displacement field and provide a systematic approach to study the spatial dynamics of open loop mechanical systems are obtained. The method developed is applicable to open loop mechanical systems containing revolute, prismatic and cylindrical joints. Furthermore, the formulation developed is independent of the type of finite element or the modal identification technique used.