Atlases of admissible graphs of geared kinematic chains (GKCs) had been enumerated through the studies of topological synthesis for decades. However, these enumerated GKCs are mostly synthesized according to the prescribed numbers of DOFs and links. Investigation on the topological and kinematic relations among GKCs of various DOFs and links is few. Motivated by the fact that the topological structure and the number of DOFs of a GKC can be changed by engaging clutches or brakes to connect two or more coaxial links, this work is aimed to reveal how non-fractionated GKCs of higher-DOF are related to those of lower-DOF. The process of connecting coaxial links, leading to the degeneration of DOFs of a GKC is defined as the mobility degeneration of a GKC. It is shown that the mobility degeneration of GKCs depends both on the locations of coaxial links as well as on the configuration of the fractionated kinematic units (KUs) within the GKC. In this paper, characteristics and rules to obtain changed GKCs based on mobility degeneration is developed and degenerated isomorphism of GKCs is discussed. Kinematic families of GKCs with up to three-DOF and eight-link are classified. It is shown that GKCs of different DOFs can be associated to form several kinematic families, indicating that these GKCs of various DOFs are not as independent as previously considered.

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