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Robotics pp 9-22 | Cite as

Homogenous transformation matrices

  • Tadej BajdEmail author
  • Matjaž Mihelj
  • Jadran Lenarčič
  • Aleš Stanovnik
  • Marko Munih
Chapter
Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA, volume 43)

Abstract

In the introductory chapter we have seen that robots have either translational or rotational joints. We therefore need a unified mathematical description of translational and rotational displacements. The translational displacement d, given by the vector
$$\textbf{d} = a\textbf{i} + b\textbf{j} + c\textbf{k},$$
(2.1)
can be described also by the following homogenous transformation matrix H
$$\textbf{H} = Trans(a,b,c) = \left[\begin{array}{llll} 1 & 0 & 0 & a\\ 0 & 1 & 0 & b\\ 0 & 0 & 1 & c\\ 0 & 0 & 0 & 1 \end{array}\right].$$
(2.2)

Keywords

Reference Frame Coordinate Frame Robot Manipulator Mechanical Assembly Rotational Joint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Tadej Bajd
    • 1
    Email author
  • Matjaž Mihelj
    • 1
  • Jadran Lenarčič
    • 2
  • Aleš Stanovnik
    • 1
  • Marko Munih
    • 1
  1. 1.Fac. Electrical EngineeringUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Inst. J. StefanUniversity of LjubljanaLjubljanaSlovenia

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