The workspace of a three-axis, turning-pair connected robot arm of general proportions has been analyzed in terms of the volume swept out by the surface of a skew torus rotating about an offset axis in space. The algebraic geometry of this configuration has been utilized in the determination of workspace characteristics. Algebraic criteria have been derived for extreme axial and radial reach and the elimination of two types of voids which were found to be characteristic of the 3-R robot configuration. These criteria can be used both in the analysis and synthesis stages of robot design.

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