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Journals / International Electronic Journal of Geometry / 2020 / Cilt: 13 - Sayı: 1

Kinematic Comparison of Exponential and Cayley Maps in the Planar Motion Group

İlhan KARAKILIÇ
Soner ERKUŞ
Pages
107–115
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A three joint mechanism is discussed as an application.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, the exponential and the Cayley maps, from the Lie algebra $\mathfrak{se(2)}$ of the planar motion group $SE(2)$, to the group itself are studied.
📊
Key Findings & Data:The comparison between these maps on $SE(2)$ is given by using the Rodrigues vector.
💡
Conclusion & Impact:A three joint mechanism is discussed as an application.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Kinematics · Lie Group · planar motion group

Abstract

In this work, the exponential and the Cayley maps, from the Lie algebra $\mathfrak{se(2)}$ of the planar motion group $SE(2)$, to the group itself are studied. The comparison between these maps on $SE(2)$ is given by using the Rodrigues vector. A three joint mechanism is discussed as an application.

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Cite This Article

KARAKILIÇ, İ., ERKUŞ, S. (2022). Kinematic Comparison of Exponential and Cayley Maps in the Planar Motion Group. International Electronic Journal of Geometry, Cilt: 13 - Sayı: 1, 107–115. https://ajindex.com/articles/539607

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