MODELING OF MULTIBODY SYSTEMS CONNECTED BY STANDARD ENGINEERING JOINTS

This paper demonstrates that, when modeling multibody systems connecte d by standard engineering joints, the resulting mathematical model can be cast in a singularly perturbed formulation. The modeling method de scribed here may be used to model mechanical joints that admit microsc opic deformation that can be numerically evaluated on widely available 64-bit computers. As opposed to classical multibody modeling methods, the singularly perturbed formulation produces the dynamic equations i n an explicit state-space form that is well-suited for parallel proces sing. Furthermore, the main advantage of singularly perturbed formulat ion is the ease with which it can be implemented. This paper first giv es a theorem which demonstrates that standard, non-abstracted, kinemat ic joints can be modeled in a singularly perturbed formulation. Furthe rmore, the perturbation parameters are shown to be capable of modeling joint clearance and stiffness. Power conservation principles are then used to provide a set of basic functions that can be grouped to obtai n a differential equation description of various kinematic joints. Fin ally, a general form of the aggregate dynamic equation of multibody sy stems modeled in singularly perturbed formulation is constructed. This form, which is cast in state space, demonstrates the explicit nature of the singularly perturbed formulation of multibody systems.