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Classification of three-parametric spatial motions with a transitive group of automorphisms and three-parametric robot manipulators

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Abstract

The paper deals with the differential geometry of submanifolds of the ‘kinematical space’ of Euclidean space kinematics, which is a six-dimensional pseudo-Riemannian symmetric space of signature (3, 3). The main result is in the proof of the classification theorem for three-dimensional Euclidean space motions with a transitive group of automorphisms. All of them are products (in the group multiplication) of homogeneous spaces and their list is provided. All three-parametric robot manipulators with constant invariants are found as an application of the classification theorem.

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  1. Matematicko-Fyzikalni Fakulta University Karlovy, Sokolovská 83, 186 00, Prague, Czechoslovakia

    Adolf Karger

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  1. Adolf Karger
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Karger, A. Classification of three-parametric spatial motions with a transitive group of automorphisms and three-parametric robot manipulators. Acta Appl Math 18, 1–16 (1990). https://doi.org/10.1007/BF00822203

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  • DOI: https://doi.org/10.1007/BF00822203

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