The paper introduces an approach for transforming methods and knowledge between different engineering fields through general discrete mathematical models, called graph representations, which carry engineering knowledge of specific systems. The idea is demonstrated by showing the transformation of the known method in planetary gear trains—the Willis method—to two other engineering systems: linkages and trusses. In doing so, two efficient methods were derived: one for analysing compound linkages, such as those containing tetrads, and another for compound trusses. These new methods were derived from two relations characterising graph representations: a representation that is common to two engineering fields and the duality relation between representations. The new approach underlying these transformations is shown to open new ways of conducting engineering research by enabling a systematic derivation of engineering knowledge through knowledge transformations between the graph representations.