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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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The object of this paper is to obtain some properties of non-degenerate quadric primals in the projective geometry in [s] over a Galois field of order n. It will be shown that, if s is even, there is only one type of quadric, but that, if s is odd, there are two types of quadric. The number of points on a quadric of each type, and the number of quadrics of each type, will be found. Finally, a possible application to statistics will be indicated.

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