On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains

This paper celebrates a particular branch of Crossley's early work dedicated to Mechanism Science, which deals with a rigorous introduction of Graph Theory to the study of some fundamental and intrinsic properties of kinematic chains and mechanisms. Although such idea gave its main outcome in Type and Number Synthesis (which has been much better and extensively described in another paper of the present special issue) some other intriguing side effects appeared, later in Mechanism Science, which yielded several results, and are still in the center of research and industrial world interest, such as, to name but a few, the automatic generation of the equations governing kinematic, static force and dynamic analysis of mechanisms and geared trains, the power flow analysis, the computation of the efficiency and, finally, the never fully explored structure-to-function mapping, which the present contribution points out to be still a challenge in the field.