3-parametric robot manipulator with intersecting axes

Jerzy Gądek

Applications of Mathematics (1995)

  • Volume: 40, Issue: 2, page 131-145
  • ISSN: 0862-7940

Abstract

top
A p -parametric robot manipulator is a mapping g of p into the homogeneous space P = ( C 6 × C 6 ) / Diag ( C 6 × C 6 ) represented by the formula g ( u 1 , u 2 , , u p ) = exp ( u 1 X 1 ) · · exp ( u p X p ) , where C 6 is the Lie group of all congruences of E 3 and X 1 , X 2 , , 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.

How to cite

top

Gądek, 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

top
  1. Geometry of the motion of robot manipulators, Manuscripta Math. 62 (1988), 115–126. (1988) Zbl0653.53007MR0958256
  2. Space kinematics and Lie groups, Gordon and Breach, New York-London, 1985. (1985) MR0801394
  3. Two parametric motions in E 3 , Apl. mat. 32 (1987), 96–119. (1987) MR0885757
  4. Classification of three parametric special motion with a transitive group of automorphisms and three-parametric robot manipulator, Acta Appl. Math. 18 (1990), 1–16. (1990) MR1047292
  5. Robot modelling, Springer Verlag, Berlin, 1985. (1985) 
  6. On E. Cartan’s method of moving frames, Proc. Colloq. Differential Geometry, Budapest, 1979. (1979) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.