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Three-parametric robot manipulators with parallel rotational axes. (English) Zbl 1164.53310
Summary: 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.

MSC:
53A17 Differential geometric aspects in kinematics
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References:
[1] J. Denavit, R. S. Hartenberg: A kinematics notation for lower-pair mechanisms based on matrices. ASME J. Appl. Mech. 22 (1955), 215–221. · Zbl 0064.15603
[2] S. Helgason: Differential Geometry and Symmetric Spaces. Academic Press, New York-London, 1962. · Zbl 0111.18101
[3] A. Karger: Geometry of the motion of robot manipulators. Manuscr. Math. 62 (1988), 115–126. · Zbl 0653.53007 · doi:10.1007/BF01258270
[4] A. Karger: Classification of three-parametric spatial motions with a transitive group of automorphisms and three-parametric robot manipulators. Acta Appl. Math. 18 (1990), 1–16. · Zbl 0699.53013 · doi:10.1007/BF00822203
[5] A. Karger: Robot-manipulators as submanifold. Mathematica Pannonica 4 (1993), 235–247. · Zbl 0793.53011
[6] A. Karger: Curvature properties of 6-parametric robot manipulators. Manuscr. Math. 65 (1989), 311–328. · Zbl 0687.53012 · doi:10.1007/BF01303040
[7] A. E. Samuel, P. R. McAree, K. H. Hunt: Unifying screw geometry and matrix transformations. Int. J. Robot. Res. 10 (1991), 454–472. · doi:10.1177/027836499101000502
[8] J. M. Selig: Geometrical Methods in Robotics. Springer-Verlag, New York, 1996. · Zbl 0861.93001
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