Multibody Graph Transformations and Analysis Part II: Closed-chain constraint embedding.

This is the second part of a two-part paper that develops graph theoretic techniques for the topological transformation and analysis of multibody system dynamics. The first part focused on tree systems, and developed systematic and rigorous techniques for the partitioning, aggregation and sub-structuring of multibody dynamics models. This second part, uses the aggregation techniques as the foundation to develop the constraint-embedding technique that enables the transformation of the non-tree system graphs into tree graphs. This enables the application of a large family of analytical and computational techniques for trees to closed-chain systems. This is illustrated through an extension of the low-order articulated-body forward dynamics algorithm for tree systems to closed-chain systems.