The Sphere Motion via SLERP

Year 2018, Volume: 10 Issue: 2, 214 - 224, 29.06.2018

Hatice Kuşak Samancı

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.

Keywords

Quaternion, Spherical Motion

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.