Hypergraphs for the analysis of complex mechanisms comprising planetary gear trains and other variable or fixed transmissions

This article presents a methodology for the kinematic analysis of complex gear trains comprised of planetary gear trains. It is based on the utilisation of hypergraphs, which provides a novel view into the analysis of this type of power trains. The hypergraphs are used to aid in the understanding of the inter-relation between the various branches of the mechanism and to develop the kinematic equations. The method presented here provides a way to define the kinematic relations existing between all the branches of a mechanism, including branches with a variable speed ratio. The time required to determine the equations for the speeds of different branches can be dramatically reduced if this method is followed.