The Theory of Bonds II: Closed 6R Linkages with Maximal Genus

In this paper, we introduce a method that allows to produce necessary conditions on the Denavit--Hartenberg parameters for the mobility of a closed linkage with six rotational joints. We use it to prove that the genus of the configuration curve of a such a linkage is at most five, and to give a complete classification of the linkages with a configuration curve of degree four or five. The classification contains new families.