Abstract
Plücker 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 Plücker 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barnabei, M., Brini, A., and Rota, G.-C.: 1985, On the exterior calculus of invariant theory,J. Algebra 96, 120–160.
Chou, S., Schelter, W., and Yang, J.: 1987, Characteristic sets and Gröbner bases in geometry theorem proving, in H. Crapo (ed.),Computer-Aided Geometric Reasoning, INRIA Rocquencourt, France, pp. 29–56.
Crapo, H. and Whiteley, W.: 1982, Statics of frameworks and motions of panel structures, a projective geometric introduction,Structural Topology 6, 43–82.
Doubilet, P., Rota, G.-C., and Stein, J.: 1974, On the foundations of combinatorial theory: IX, Combinatorial methods in invariant theory,Studies Appl. Math. 53, 185–216.
Hodge, W. and Pedoe, D.: 1968,Methods of Algebraic Geometry, Vols 1 and 2, Cambridge Univ. Press, Cambridge.
Hunt, K.: 1978,Kinematic Geometry of Mechanisms, Clarendon Press, Oxford.
Klein, F.: 1939,Geometry, Dover Publications, New York.
Kutzler, B. and Stifter, S.: 1986, On the application of Buchberger's algorithm to automated geometry theorem proving,J. Symbolic Comput. 2, 389–398.
Lipkin, H. and Duffy, J.: 1982, Analysis of industrial robots via the theory of screws,Proc. 12th Internat. Symp. Industrial Robots, Paris.
White, N. and Whiteley, W.: 1983, The algebraic geometry of stresses in frameworks,SIAM J. Algebraic Discrete Methods 4, 481–511.
White, N.: 1991, Multilinear Cayley factorization,J. Symbolic Comput. 11, 421–438.
Whiteley, W.: 1991, The combinatorics of bivariate splines, in P. Gritzmann and B. Sturmfels (eds),Applied Geometry and Discrete Mathematics, the Victor Klee Festschrift, AMS Press, Providence.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
White, N.L. Grassmann—Cayley algebra and robotics. J Intell Robot Syst 11, 91–107 (1994). https://doi.org/10.1007/BF01258296
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01258296