A network approach to mechanisms and machines: Some lessons learned

• Graph theory is used to assemble matrices in adaptations of Kirchhoff's equations.
• Those matrices, when transposed, are used again in virtual power equations.
• 25 publications that make use of these equations are cited.
• 10 lessons learned are explained in the Discussion section.
• One lesson introduces dual laws: the zeroth laws of mechanics.

This is essentially a review paper describing progress made in treating mechanisms and machines as networks. Some of the terminology that is helpful to this approach is explained. Relevant elements of graph theory are mentioned. The original aim was to find a robust procedure for finding the instantaneous relative motion of all pairs of bodies within a kinematic chain. The manner in which this was achieved produced several other results that have found unanticipated applications. These are mentioned and publications are cited. Lessons have been learned and these are discussed in Section 11.