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The Sphere Motion via SLERP

Year 2018, Volume: 10 Issue: 2, 214 - 224, 29.06.2018
https://doi.org/10.29137/umagd.382450

Abstract

In
this paper, we investigate a brief survey on the three-sphere motion by using
the quaternion interpolasyon SLERP. Firstly, we consider the moving and fixed
quaternion frames for three-sphere motion onto a unit quaternionic sphere. Then
we calculate the equations of the velocity and we investigate some properties
of the canonical relative system. Finaly we give some examples for these
equations.

References

  • [1] Hamilton, W. (1853). Lectures on Quaternions. Hodges Smith&Co.Dublin 350pp.
  • [2] Garnier, R. (1956). Cours de Cinematique, Tome II: Roulement et Vibration-La Formule de Savary et son Extension a l’Espace. Gauthier-Villars, Paris.
  • [3] Müller, HR. (1963). Kinematik Dersleri, Ankara University.
  • [4] Blaschke, W. (1960). Kinematics and Quaternions. VEB Verlag, Berling Math. Monographien Bd.4.
  • [5] Bottema, O. & Roth, B. (1978). Theoretical Kinematics, Amsterdam: North-Holland Publishers Co.
  • [6]Hacısalihoğlu, H.H.,(1983). Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Universitesi Yayınları, Ankara.
  • [7] Hanson, A.J. (2006).Visualizing Quaternion, Morgan-Kaufmann, Elsevier, London.
  • [8] Nixravesh, P.E., R.A. Wehage & O.K. Kwan, (1985). Euler Parameters in Computational Kinematics and Dynamics, Part , ASME J. Mech. Trans, Aut. Des (107) 358-365.
  • [9] Larochelle, P. (2000). Approximate Motion Synthesis via Parametric Constraint Manifold Fitting, Advances in Robot Kinematics, Kluwer Acad. Publ., Dordrecht.
  • [10] Liu X.J., Wang J. & Gao, F. (2003). Workspace Atlases fort he Design of Spherical 3-DOF Serial Wrist, J. Of Intelligent and Robotic Systems 389-405.
  • [11] Yang, A.T. & Freudenstein, F. (1964). Application of dual number quaternion algebra to the analysis of spatrial mechanism, Transactions of the ASNE , 300-308.
  • [12] Alizade R., Gezgin E.& Kilit Ö. (2005). A New Method in Computational Kinematics of a Spherical Wrist Motion Through Quaternions, Intl. Workshop on Comp. Kinematics, Cassino, p.32.
  • [13] Kuşak, H., Çalışkan A., (2011). About Dual Spherical Wrist Motion and its Trajectory Surface as a Ruled Surface, Mathematical and Computational Applications, Mathematical and Computational Applications, Vol. 16, No. 1, pp. 309-316.
  • [14] Shoemake K., (1985). Animating Rotation with Quaternion Curves, in Computer Graphics, SIGGRAPH’85 Proceedings, Vol.19, pp 245-254.
  • [15] Shoemake K., (1987). Quaternion Calculus for Animation, Siggraph’ 89 Course 23:Math for SIGGRAPH.
  • [16] Hanson A.J. (2006). Visualizing Quaternions, Morgan-Kaufmann, ELsevier, London.
Year 2018, Volume: 10 Issue: 2, 214 - 224, 29.06.2018
https://doi.org/10.29137/umagd.382450

Abstract

References

  • [1] Hamilton, W. (1853). Lectures on Quaternions. Hodges Smith&Co.Dublin 350pp.
  • [2] Garnier, R. (1956). Cours de Cinematique, Tome II: Roulement et Vibration-La Formule de Savary et son Extension a l’Espace. Gauthier-Villars, Paris.
  • [3] Müller, HR. (1963). Kinematik Dersleri, Ankara University.
  • [4] Blaschke, W. (1960). Kinematics and Quaternions. VEB Verlag, Berling Math. Monographien Bd.4.
  • [5] Bottema, O. & Roth, B. (1978). Theoretical Kinematics, Amsterdam: North-Holland Publishers Co.
  • [6]Hacısalihoğlu, H.H.,(1983). Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Universitesi Yayınları, Ankara.
  • [7] Hanson, A.J. (2006).Visualizing Quaternion, Morgan-Kaufmann, Elsevier, London.
  • [8] Nixravesh, P.E., R.A. Wehage & O.K. Kwan, (1985). Euler Parameters in Computational Kinematics and Dynamics, Part , ASME J. Mech. Trans, Aut. Des (107) 358-365.
  • [9] Larochelle, P. (2000). Approximate Motion Synthesis via Parametric Constraint Manifold Fitting, Advances in Robot Kinematics, Kluwer Acad. Publ., Dordrecht.
  • [10] Liu X.J., Wang J. & Gao, F. (2003). Workspace Atlases fort he Design of Spherical 3-DOF Serial Wrist, J. Of Intelligent and Robotic Systems 389-405.
  • [11] Yang, A.T. & Freudenstein, F. (1964). Application of dual number quaternion algebra to the analysis of spatrial mechanism, Transactions of the ASNE , 300-308.
  • [12] Alizade R., Gezgin E.& Kilit Ö. (2005). A New Method in Computational Kinematics of a Spherical Wrist Motion Through Quaternions, Intl. Workshop on Comp. Kinematics, Cassino, p.32.
  • [13] Kuşak, H., Çalışkan A., (2011). About Dual Spherical Wrist Motion and its Trajectory Surface as a Ruled Surface, Mathematical and Computational Applications, Mathematical and Computational Applications, Vol. 16, No. 1, pp. 309-316.
  • [14] Shoemake K., (1985). Animating Rotation with Quaternion Curves, in Computer Graphics, SIGGRAPH’85 Proceedings, Vol.19, pp 245-254.
  • [15] Shoemake K., (1987). Quaternion Calculus for Animation, Siggraph’ 89 Course 23:Math for SIGGRAPH.
  • [16] Hanson A.J. (2006). Visualizing Quaternions, Morgan-Kaufmann, ELsevier, London.
There are 16 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hatice Kuşak Samancı 0000-0001-6685-236X

Publication Date June 29, 2018
Submission Date January 22, 2018
Published in Issue Year 2018 Volume: 10 Issue: 2

Cite

APA Kuşak Samancı, H. (2018). The Sphere Motion via SLERP. International Journal of Engineering Research and Development, 10(2), 214-224. https://doi.org/10.29137/umagd.382450

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