On the historical overview of geometric algebra for kinematics of mechanisms

Chung Ching Lee, Charles W Stammers, Glen Mullineux

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this article, a historical survey of geometric algebra also called Clifford algebra is first undertaken in chronological order. This new algebra is ascribed to Grassmann and Clifford. The quaternion algebra originated from Hamilton can be considered as its special version. Next, in terms of geometric algebra notation, we further deal with the representation of the classical problems about the single finite rotation, first derived by Euler, and the composition formula of two successive finite rotations, originally proposed by Rodriques. Finally, the rigid body motion in the four dimensional geometric algebra G4 is introduced for the basis of possible future applications using geometric algebra and a general rigid body motion related to the 4×4 homogeneous transformation matrix in Euclidean space is then elucidated.
Original languageEnglish
Title of host publicationInternational Symposium on History of Machines and Mechanisms, Proceedings of HMM 2008
EditorsHong-Sen Yan, Marco Ceccarelli
Place of PublicationDordrecht, Netherlands
PublisherSpringer
Pages21-34
Number of pages14
Volume4
ISBN (Print)978-1-4020-9484-2 (Print) 978-1-4020-9485-9 (Online)
DOIs
Publication statusPublished - 11 Jan 2009
EventInternational Symposium on History of Machines and Mechanisms, Proceedings of HMM 2008 - Tainan, Taiwan
Duration: 10 Nov 200814 Nov 2008

Publication series

NameHistory of Mechanism and Machine Science
PublisherSpringer Netherlands

Conference

ConferenceInternational Symposium on History of Machines and Mechanisms, Proceedings of HMM 2008
CityTainan, Taiwan
Period10/11/0814/11/08

Keywords

  • Clifford algebra
  • Historical survey
  • Quaternion algebra
  • Rigid body motion
  • Geometric algebra

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  • Cite this

    Lee, C. C., Stammers, C. W., & Mullineux, G. (2009). On the historical overview of geometric algebra for kinematics of mechanisms. In H-S. Yan, & M. Ceccarelli (Eds.), International Symposium on History of Machines and Mechanisms, Proceedings of HMM 2008 (Vol. 4, pp. 21-34). (History of Mechanism and Machine Science). Springer. https://doi.org/10.1007/978-1-4020-9485-9_2