A linkage characteristic polynomial is defined as the characteristic polynomial of the adjacency matrix of the kinematic graph of the kinematic chain. Some terminology and definitions, needed for discussions to follow in a companion paper, are stated. A rule from which all coefficients of the characteristic polynomial of a kinematic chain can be identified by inspection, based on the interpretation of a graph determinant, is derived and presented. This inspection rule interprets the topological meanings behind each characteristic coefficient, and might have some interesting possible uses in studies of the structural analysis and synthesis of kinematic chains.

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