Dual coupling networks

Abstract

Using dual graphs and dual couplings, it is shown how the dual of a coupling network can be found. The actions that can exist within an overconstrained coupling network are shown to be geometrically identical to the motions that can occur within the dual of that coupling network. Most useful coupling networks, such as mechanisms within machinery, are both over-constrained and underconstrained. Motions of machine parts attributable to underconstraint can be seen thereby making the motions easy to imagine from a drawing. Conversely, internal actions attributable to overconstraint cannot be seen and so are difficult to imagine. Such actions could result in fatigue failure. Thus one possible benefit of creating the dual of a coupling network is that internal actions hidden within it become recognisable motions of bodies in its dual. This article could lead to a better awareness of overconstraint and its dangers.