# On the historical overview of geometric algebra for kinematics of mechanisms

### Reference:

Lee, C. C., Stammers, C. W. and Mullineux, G., 2009. On the historical overview of geometric algebra for kinematics of mechanisms. *In*: Yan, H.-S. and Ceccarelli, M., eds. *International Symposium on History of Machines and Mechanisms, Proceedings of HMM 2008. Vol. 4.* Dordrecht, Netherlands: Springer Netherlands, pp. 21-34. (History of Mechanism and Machine Science)

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### Official URL:

http://dx.doi.org/10.1007/978-1-4020-9485-9_2

### 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.

### Details

Item Type | Book Sections |

Creators | Lee, C. C., Stammers, C. W. and Mullineux, G. |

Editors | Yan, H.-S.and Ceccarelli, M. |

DOI | 10.1007/978-1-4020-9485-9_2 |

Uncontrolled Keywords | clifford algebra, historical survey, quaternion algebra, rigid body motion, geometric algebra |

Departments | Faculty of Engineering & Design > Mechanical Engineering |

Research Centres | Innovative Design & Manufacturing Research Centre (IdMRC) |

Status | Published |

ID Code | 15160 |

Additional Information | Symposium held at the National Cheng Kung University (Tainan, Taiwan) on November 11-14, 2008 |

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