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Journals / Turkish Journal of Mathematics / 2008 / Cilt: 32 - Sayı: 4

Dual Quaternions in Spatial Kinematics in an Algebraic Sense

Bedia AKYAR
Pages
373–391
Publication Date
2022-11-05
DOI
—
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AI Summary & Key Takeaways

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

By considering operations on screw motions, representation of spatial displacements is also given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper presents the finite spatial displacements and spatial screw motions by using dual quaternions and Hamilton operators.
📊
Key Findings & Data:The representations are considered as 4 \times 4 matrices and the relative motion for three dual spheres is considered in terms of Hamilton operators for a dual quaternion.
💡
Conclusion & Impact:By considering operations on screw motions, representation of spatial displacements is also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Dual quaternions · Hamilton operators · Lie algebras

Abstract

This paper presents the finite spatial displacements and spatial screw motions by using dual quaternions and Hamilton operators. The representations are considered as 4 \times 4 matrices and the relative motion for three dual spheres is considered in terms of Hamilton operators for a dual quaternion. The relation between Hamilton operators and the transformation matrix has been given in a different way. By considering operations on screw motions, representation of spatial displacements is also given.

Özet

This paper presents the finite spatial displacements and spatial screw motions by using dual quaternions and Hamilton operators. The representations are considered as 4 \times 4 matrices and the relative motion for three dual spheres is considered in terms of Hamilton operators for a dual quaternion. The relation between Hamilton operators and the transformation matrix has been given in a different way. By considering operations on screw motions, representation of spatial displacements is also given.

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Cite This Article

AKYAR, B. (2022). Dual Quaternions in Spatial Kinematics in an Algebraic Sense. Turkish Journal of Mathematics, Cilt: 32 - Sayı: 4, 373–391. https://ajindex.com/articles/609047

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References (4)

  1. Agrawal O. P.: Hamilton Operators and Dual-number-quaternions in Spatial Kinematics, Mech. Mach. Theory 22, 569-575, (1987).
  2. Akyar B., Köse Ö: An algebraic approach to the mathematical methods in Spatial kine— matics, Pure and Appled Mathematika Sciences XLVH, 1-13, (1998). Blaschke W.: Kinematik und Quaternion, VEB Deutscher Verlag der Wissenschaften, Berlin, 1960. Chevallier D. P.: Lie algebras, modules, dual quaternions and Algebraic methods in Kine- matics, Mech. Mach. Theory 26, 613-627, (1991). Curtis M. L.: Matrix Groups, Second Edition, Springer Verlag, 1987. Herve J. M.: The mathematical group structure of the set of displacements, Mech. Mach. Theory 29, 73-81, (1994).
  3. Hiller M., Woernle C.: A unified representation of spatial displacements, Mech. Mach. Theory 19, 477-486, (1984). [8] Rooney J.: A comparison of representations of general spatial screw displacement, Envi- ronment and Planning B 5, 45-88, (1978). [9] Veldkamp G. R.: On the use of dual numbers, vectors and matrices in instantaneous, Spatial Kinematics, Mech. Mach. Theory 11, 141-156, (1976).
  4. Yang A. T., Freudenstein F.: Application of dual-number quaternion algebra to the analysis of spatial mechanisms, Transactions of the ASME, 300-308, (1964). Bedia AKYAR Received 26.09.2008 Dokuz Eylül University Faculty of Arts and Sciences Department of Mathematics Kaynaklar Yerleşkesi 35020 İzmir—TURKEY e—mail: [email protected]