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Linear Algebra and Its Applications 31 (1980) 81-91. doi:10.1016/0024-3795(80)90209-8Received by publisher: 1979-07-02Harvest Date: 2016-01-04 12:20:29DOI: 10.1016/0024-3795(80)90209-8Page Range: 81-9

Abstract. PlUcker coordinates are a suitable way to represent lines in space for purposes of studying instantaneous motions of robot arms. Similarly, we can represent any affine subspace of Euclidean space of any dimension. This can be useful for studying motion spaces of robot arms. In this paper, after we introduce Pltieker coordinates and develop a few of their basic properties, we present them in a somewhat more abstract setting, called the Grassmann-Cayley algebra. Several other applications of this algebra are also described.