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

Abstract

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.

20 pages, 2 figures

References in corpus (1)

• The Theory of Bonds: A New Method for the Analysis of Linkages

Cited by in corpus (5)

• A Technique for Deriving Equational Conditions on the Denavit-Hartenberg Parameters of 6R Linkages that are Necessary for Movability
• On the existence of paradoxical motions of generically rigid graphs on the sphere
• A Survey on the Theory of Bonds
• From the Fundamental Theorem of Algebra to Kempe's Universality Theorem
• The Kinematic Image of RR, PR, and RP Dyads