Comparison of practically applicable mathematical descriptions of orientation and rotation in the three-dimensional Euclidean space

  • Rainer Müller
  • Matthias Vette
  • Ali KansoEmail author
Conference paper


In the handling technique, the orientation in the three-dimensional Euclidean space is considered or predefined for several assembly tasks. There are different mathematical methods to describe them. Euler presents 24 different conventions that describe any rotation in the space by a rotation about three orthogonal axis. These conventions are singularitydependent and their deployment is restricted to certain applications and domains. Quaternions overcome the disadvantages of the above mentioned conventions. They are numerically stable and efficient and describe the orientation by a rotation about one axis. This article deals with the comparison of practice-relevant mathematical descriptions.


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Copyright information

© Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.ZeMA - Zentrum für Mechatronik und Automatisierungstechnik gemeinnützige GmbHSaarbrückenDeutschland

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