# 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

top- Geometry of the motion of robot manipulators, Manuscripta Math. 62 (1988), 115–126. (1988) Zbl0653.53007MR0958256
- Space kinematics and Lie groups, Gordon and Breach, New York-London, 1985. (1985) MR0801394
- Two parametric motions in ${E}_{3}$, Apl. mat. 32 (1987), 96–119. (1987) MR0885757
- 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
- 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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