The structure of nonsingular robot compliance is investigated by applying screw theory to two eigenvalue problems. For the first problem the eigenscrews are demonstrated to be Ball’s (1990) principal screws of the potential. Several new propositions are presented characterizing compliance matrix eigenstructure. Using a novel formulation, the second eigenvalue problem generalizes the three wrench-compliant axes of Dimentberg (1965) to include three twist-compliant axes. These two types of compliant axes are shown to be reciprocal and define conjugate screw systems. The wrench- and twist-compliant axes are demonstrated to the general elements of a compliant axis hierarchy.

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