The theory of bonds: A new method for the analysis of linkages

• Dual-quaternion based characterization of the geometry of three revolute axes.
• Rigorous definition of bonds, (algebraic) joint distances, and connection numbers.
• Visualization of the bond structure in bond diagrams.
• New examples of overconstrained 6R-linkages.
• New proof of Karger's classification result for overconstrained 5R 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.