3-parametric robot manipulator with intersecting axes
Applications of Mathematics (1995)
- Volume: 40, Issue: 2, page 131-145
- ISSN: 0862-7940
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topGądek, Jerzy. "3-parametric robot manipulator with intersecting axes." Applications of Mathematics 40.2 (1995): 131-145. <http://eudml.org/doc/32909>.
@article{Gądek1995,
abstract = {A $p$-parametric robot manipulator is a mapping $g$ of $\mathbb \{R\}^p$ into the homogeneous space $P=(C_6\times C_6)/\mathop \{\rm Diag\}(C_6\times C_6)$ represented by the formula $g(u_1,u_2,\dots ,u_p)=\exp (u_1 X^1)\cdot \dots \cdot \exp (u_p X^p)$, where $C_6$ is the Lie group of all congruences of $E_3$ and $X^1,X^2,\dots ,X^p$ are fixed vectors from the Lie algebra of $C_6$. In this paper the $3$-parametric robot manipulator will be expressed as a function of rotations around its axes and an invariant of the motion of this robot manipulator will be given. Most of the results presented here have been obtained during the author’s stay at Charles University in Prague.},
author = {Gądek, Jerzy},
journal = {Applications of Mathematics},
keywords = {differential geometry; kinematic geometry; robotics; invariant of motion; Lie group; Lie algebra},
language = {eng},
number = {2},
pages = {131-145},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {3-parametric robot manipulator with intersecting axes},
url = {http://eudml.org/doc/32909},
volume = {40},
year = {1995},
}
TY - JOUR
AU - Gądek, Jerzy
TI - 3-parametric robot manipulator with intersecting axes
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 2
SP - 131
EP - 145
AB - A $p$-parametric robot manipulator is a mapping $g$ of $\mathbb {R}^p$ into the homogeneous space $P=(C_6\times C_6)/\mathop {\rm Diag}(C_6\times C_6)$ represented by the formula $g(u_1,u_2,\dots ,u_p)=\exp (u_1 X^1)\cdot \dots \cdot \exp (u_p X^p)$, where $C_6$ is the Lie group of all congruences of $E_3$ and $X^1,X^2,\dots ,X^p$ are fixed vectors from the Lie algebra of $C_6$. In this paper the $3$-parametric robot manipulator will be expressed as a function of rotations around its axes and an invariant of the motion of this robot manipulator will be given. Most of the results presented here have been obtained during the author’s stay at Charles University in Prague.
LA - eng
KW - differential geometry; kinematic geometry; robotics; invariant of motion; Lie group; Lie algebra
UR - http://eudml.org/doc/32909
ER -
References
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- Space kinematics and Lie groups, Gordon and Breach, New York-London, 1985. (1985) MR0801394
- Two parametric motions in , Apl. mat. 32 (1987), 96–119. (1987) MR0885757
- 10.1007/BF00822203, Acta Appl. Math. 18 (1990), 1–16. (1990) MR1047292DOI10.1007/BF00822203
- Robot modelling, Springer Verlag, Berlin, 1985. (1985)
- On E. Cartan’s method of moving frames, Proc. Colloq. Differential Geometry, Budapest, 1979. (1979)
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