Three-parametric robot manipulators with parallel rotational axes

Ján Bakša

Applications of Mathematics (2007)

  • Volume: 52, Issue: 4, page 303-319
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Bakša, Ján. "Three-parametric robot manipulators with parallel rotational axes." Applications of Mathematics 52.4 (2007): 303-319. <http://eudml.org/doc/33290>.

@article{Bakša2007,
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.},
author = {Bakša, Ján},
journal = {Applications of Mathematics},
keywords = {local differential geometry; robotics; Lie algebra; asymptotic motion; local differential geometry; robotics; Lie algebra; asymptotic motion},
language = {eng},
number = {4},
pages = {303-319},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Three-parametric robot manipulators with parallel rotational axes},
url = {http://eudml.org/doc/33290},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Bakša, Ján
TI - Three-parametric robot manipulators with parallel rotational axes
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 4
SP - 303
EP - 319
AB - 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.
LA - eng
KW - local differential geometry; robotics; Lie algebra; asymptotic motion; local differential geometry; robotics; Lie algebra; asymptotic motion
UR - http://eudml.org/doc/33290
ER -

References

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  5. Robot-manipulators as submanifold, Mathematica Pannonica 4 (1993), 235–247. (1993) MR1258929
  6. 10.1007/BF01303040, Manuscr. Math. 65 (1989), 311–328. (1989) Zbl0687.53012MR1015658DOI10.1007/BF01303040
  7. 10.1177/027836499101000502, Int. J. Robot. Res. 10 (1991), 454–472. (1991) DOI10.1177/027836499101000502
  8. Geometrical Methods in Robotics, Springer-Verlag, New York, 1996. (1996) Zbl0861.93001MR1411680

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