J. Baksa, Technical University in Zvolen, Faculty of Wood Sciences and Technology, Department of Mathematics and Descriptive Geometry, T. G. Masaryka 24, 960 53 Zvolen, Slovak Republic, e-mail: baksa@vsld.tuzvo.sk
Abstract: The paper deals with asymptotic motions of 3-parametric robot manipulators with parallel rotational axes. To describe them we use the theory of Lie groups and Lie algebras. An example of such motions are motions with the zero Coriolis accelerations. We will show that there are asymptotic motions with nonzero Coriolis accelerations. We introduce the notions of the Klein subspace, the Coriolis subspace and show their relation to asymptotic motions of robot manipulators. The asymptotic motions are introduced without explicit use of the Levi-Civita connection.
Keywords: local differential geometry, robotics, Lie algebra, asymptotic motion
Classification (MSC 2000): 53A17
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