### 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 language | English |
---|---|

Title of host publication | International Symposium on History of Machines and Mechanisms, Proceedings of HMM 2008 |

Editors | Hong-Sen Yan, Marco Ceccarelli |

Place of Publication | Dordrecht, Netherlands |

Publisher | Springer |

Pages | 21-34 |

Number of pages | 14 |

Volume | 4 |

ISBN (Print) | 978-1-4020-9484-2 (Print) 978-1-4020-9485-9 (Online) |

DOIs | |

Publication status | Published - 11 Jan 2009 |

Event | International Symposium on History of Machines and Mechanisms, Proceedings of HMM 2008 - Tainan, Taiwan Duration: 10 Nov 2008 → 14 Nov 2008 |

### Publication series

Name | History of Mechanism and Machine Science |
---|---|

Publisher | Springer Netherlands |

### Conference

Conference | International Symposium on History of Machines and Mechanisms, Proceedings of HMM 2008 |
---|---|

City | Tainan, Taiwan |

Period | 10/11/08 → 14/11/08 |

### Keywords

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

## Fingerprint Dive into the research topics of 'On the historical overview of geometric algebra for kinematics of mechanisms'. Together they form a unique fingerprint.

## 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