Modelling of multibody dynamics and a recursive symbolic generation scheme

A modelling method of multibody dynamics and a symbolic generation scheme which generates the symbolic codes of the system equations are proposed. The scheme employs bond graph language which enables us to categorize the required kinematical and dynamical relations into the structural, physical and causal information to visualize them in bond graphs and then to provide necessary functional relations directly from the bond graph. The proposed scheme also employs the so-called diakoptical approach. The system is first reticulated into its constituent units, each of which is called a fundamental pair, and further into their dynamical and kinematical elements. An aggregation of such disconnected elements, which is called a primitive system, is then interconnected through the junction structure or a nonenergic multiport, which is one of the principal tools of the bond graph modelling method proposed in the present paper. The fundamental idea of the nonenergicness which plays a key role in the above interconnection is briefly outlined and it is demonstrated how various kinematical and dynamical relations of the Stanford manipulator, an illustrative example, are described as such nonenergic multiports. Second a causal and causal coefficient matrices are presented, which utilize a tableau expression of the nonenergic multiports. It is also shown how those two matrices play, in the proposed symbolic scheme, an essential role in the elimination process of unnecessary variables like constraint forces, specifically, recursively utilizing intermediate variables associated with the inner bonds. Last a brief comparative study with conventional schemes is presented from the viewpoint of computational efficiency in the symbolic generation.