Year 2021, Volume 13 , Issue 1, Pages 127 - 139 2021-01-18

The New Screw Interpolations and Their Geometric Properties in the Dual Spherical Mechanisms

Hatice KUŞAK SAMANCI [1] , Çetin KUŞÇU [2]


In this paper, some new Sclerp interpolation motions are defined in the dual spherical mechanisms by developing the Sclerp interpolation given by Ravani (1994). These new methods are the sequential Sclerp interpolation, fast dual spherical interpolation, and the fast screw linear interpolation and they will lead to some advantages to Sclerp interpolation. Also, the lengths between the joints in the spherical dual mechanisms are designed by Sclerp interpolation and the Blaschke frame of this dual spherical interpolation curve is analyzed. At the end of the study, a numeric example is given.
Dual Quaternion, Sclerp Interpolation, Fast Sclerp, Mechanism, Dual Space
  • Baky R.A.A, (2002). An Explicit Characterization of Dual Spherical Curve. Commun. Fac. Sci. Univ. Ank. Series Al, 51(2):1-9.
  • Dam E.B, Koch M, Lillholm M, (1998). Quaternions, Interpolation and Animation, Institute of Computer Science University of Copenhagen.
  • Diebel J, (2006). Representing Attitude: Euler Angles Unit Quaternions and Rotation Vectors. Standford University, California: 1-35 Ge Q.J, Ravani B, (1994). Geometric Construction of Bezier Type Motions. ASME of Mechanical Design.
  • Gezgin E, (2006). Biokinematic Analysıs of Human Arm. Yüksek Lisans Tezi, İzmir Yüksek Teknolojisi University İzmir Yüksek Teknolojisi Institue, İzmir.
  • Ghademi R, Rahebi J and Yaylı Y,(2012). A Novel Approach for Spherical Spline Split Quaternion Interpolation Lorentzian Sphere Using Bezier Curve Algorithm. Life Science Journal, 9(4): 3394-3397.
  • Ghademi R, Rahebi J and Yaylı Y, (2012). A Fast Method Based on DeMoivre for Spherical Linear Interpolation in Minkowski Space. Advances in Applied Clifford Algebras. 25(4), 863-873.
  • Ghademi R, Rahebi J and Yaylı Y, (2012). A Fast Method Spherical Linear Interpolation in Minkowski Space. Advances in Applied Clifford Algebras. 25(4), 863-873.
  • Hacısalihoğlu HH, (1983). The Theory of The Motion Geometry and Quaternions. Gazi University, Ankara.
  • Hamilton WR, (1848). On quaternions; or on a new system of imaginaries in algebra, The London, Edinburg, and Dublin Philosophical Magazine and Journal of Science, 33(219), 58-60.
  • Hast A, Barrera T, Bengtsson E, (2003). Shading by Spherical Linear Interpolation Using De Moivre’s Formula, Proc. 11th Int. Conf. Central Europe on Computer Graphics.
  • Hast A, Barrera T, Bengtsson E, (2004). Incremental Spherical Linear Interpolation. In The Annual SIGRAD Conference. Special Theme-Environmental Visualization, 13:7-10. Linköping University Electronic Press.
  • Jafari M, Molaei H, (2014). Spherical Linear Interpolation and Bezier Curves. General Scientific Researches, 2(1): 13-17. Kavan L, Collins S, O’Sullivan C, Zara J, (2006). Dual Quaternions For Rigid Transformation Blending. Trinity College Dublin, Tech.Rep. TCD-CS-2006-46.
  • Kilit Ö, (2007). Kinematic Analysis and Synthesis of Spherical Mechanisms. Doctoral Dissertation, Ege University Institute of Science and Technology, İzmir.
  • Kremer VE, (2008). Quaternions and Slerp. Department for Computer Science Universty of Saarbrücken.
  • Kuşak H, Çalışkan A, (2011). About Dual Spherical Wrist Motion and Its Trajectory Surface as a Ruled Surface. Mathematical and Computational Applications, 16(1): 309-316, 2011.
  • Sheomake K, (1985). Animating Rotation with Quaternion Curves. San Francısco, 19(3): 245-254.
  • Smitth M, (2013). Applications of Dual Quaternions in Three Dimensional Transformation and Interpolation. Department for Computer Science and Software Engineering University of Canterbury, Christchurch, New Zeland.
  • Vince J, (2011). Quaternions for Computer Graphics. Bournemouth Universite, Bournemouth, UK.
Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0001-6685-236X
Author: Hatice KUŞAK SAMANCI (Primary Author)
Institution: Bitlis Eren Üniversitesi
Country: Turkey


Orcid: 0000-0003-1674-9801
Author: Çetin KUŞÇU
Institution: FEN BİLİMLERİ ENSTİTÜSÜ
Country: Turkey


Dates

Publication Date : January 18, 2021

APA Kuşak Samancı, H , Kuşçu, Ç . (2021). The New Screw Interpolations and Their Geometric Properties in the Dual Spherical Mechanisms . International Journal of Engineering Research and Development , 13 (1) , 127-139 . DOI: 10.29137/umagd.756455