General-purpose expression of structural connectivity in the parallel solution scheme of inverse dynamics

The main purpose of this study is to deal with a sudden change of dynamics in link systems, not by using integrated systems of different software, but by using a single solution scheme based upon a single theory. An algorithm for the general-purpose expression of structural connectivity is developed and implemented into the parallel solution scheme, which was previously proposed and successively applied to the feed-forward control of link mechanisms under various boundary conditions. The algorithm expresses the connectivity of link members explicitly, regardless of the structural complexity. The parallel solution scheme calculates the inverse dynamics of link systems with equations of motion expressed in the dimension of force. It enables us to obtain numerical torque values in parallel by using a matrix-form equation separated into terms of different parameters. Therefore, the connectivity of link members can be expressed explicitly by one of the matrices, the member length matrix. We describe the forming process of the matrix and verify the validity of the calculated torque values, by presenting simple numerical results and experimental results for complex systems such as multibranch link systems. It is confirmed that a sudden structural change of link systems is dealt with only by a revision of input data, which makes it highly reliable in fail-safe systems.