The Theory of Bonds: A New Method for the Analysis of Linkages
  In this paper we introduce a new technique, based on dual quaternions, for the analysis of closed linkages with revolute joints: the theory of bonds. The bond structure comprises a lot of information on closed revolute chains with a one-parametric mobility. We demonstrate the usefulness of bond theory by giving a new and transparent proof for the well-known classification of overconstrained 5R linkages. 
G\'abor Heged\"us, Josef Schicho, and Hans-Peter Schr\"ocker
math.AG cs.RO math.MG math.RA