Araştırma Makalesi
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Bazı Küresel Mekanizma Hareketlerinin ve Mafsal Tasarımlarının Yeni SLERP İnterpolasyonları ile İncelenmesi

Yıl 2022, Cilt: 25 Sayı: 4, 1513 - 1521, 16.12.2022
https://doi.org/10.2339/politeknik.757983

Öz

Küresel mekanizmaların hareketleri robotik çalışmalarda önemli bir yer almaktadır. Çalışmamızda küresel mekanizmalardaki mafsalların tasarımı ve yörünge hareket denklemleri ilk defa tanımladığımız dizisel SLERP, dizisel fast SLERP, De-Moivre ile dizisel SLERP ve modüler SLERP interpolasyon yöntemleri ile verilmiştir. Bununla birlikte, küresel mekanizmalardaki mafsalların konumları için geometrik SLERP interpolasyon eğrisinin Serret-Frenet çatısı ve eğrilikleri hesaplanarak sayısal bir örnek verilmiştir. Ayrıca makalenin sonunda, iki ve üç serbestlik dereceli küresel mekanizmaların hareket denklemlerini üreten interpolasyon denklemleri ile ilgili birkaç sayısal örneklendirme de yapılmıştır.

Kaynakça

  • [1] Hamilton W.R., “On quaternions, or on a new system of imaginaries in algebra”, Philosophical Magazine, Vol. 25, n 3. p. 489–495, (1844).
  • [2] Hamilton W.R, “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, (1848).
  • [3] Hamilton W.R., “Elements of quaternions”, Chelsea Pub., New York, Vol. I, 3rd Ed., (1969).
  • [4] Hanson A. J., "Visualizing quaternions", Elsevier, Morgan Kaufmann, San Francisco. ISBN 0-12-088400-3, (2006).
  • [5] Vince J., “Quaternions for computer graphics”, Bournemouth Un., Bournemouth, UK, (2011).
  • [6] Hacısalihoğlu, H.H., “Motion geometry and quaternions theory”, Gazi Uni., Ankara, (1983).
  • [7] Sheomake K., “Animating rotation with quaternion curves”, San Francısco, 19(3): 245-254, (1985).
  • [8] Dam E.B, Koch M. and Lillholm M., “Quaternions, interpolation and animation”, Institute of Computer Science University of Copenhagen, (1998).
  • [9] Hast A., Barrera T. and Bengtsson E., “Shading by spherical linear interpolation using de Moivre’s formula”, Proc. 11th Int. Conf. Central Europe on Computer Graphics, Visualization, and Computer Vision, (2003).
  • [10] Hast A., Barrera T., Bengtsson E., “Incremental spherical linear interpolation”, In The Annual SIGRAD Conference. Special Theme-Environmental Visualization, 13,7-10. Linköping University Electronic Press, (2004).
  • [11] Kremer V.E., “Quaternions and Slerp”, Department for the Computer Science University of Saarbrücken, (2008).
  • [12] Jafari M., Molaei H., “Spherical linear interpolation and Bezier curves”, General Scientific Researches, 2(1): 13-17, (2014).
  • [13] Kuşak Samancı, H., Çelik S., İncesu M., “The Bishop frame of Bézier curves”, Life Science Journal, 2015, 12(6): 175-180.
  • [14] Gündüz H., Kazan A., Karadağ H.B., “Rotational surfaces generated by cubic Hermitian and cubic Bezier curves”, Politeknik Dergisi, 22(4): 1075-1082, (2019).
  • [15] Incesu M., “The new characterization of ruled surfaces corresponding dual Bézier curves”, Mathematical Methods in the Applied Sciences, (2021).
  • [16] Alizade R., Gezgin E. and Kilit Ö., “A new method in computational kinematics of a spherical wrist motion through quaternions”, Intl. Workshop on Comp. Kinematics, Cassino, p.32, (2005).
  • [17] Gezgin E., “Biokinematic analysis of human arm”, Phd Thesis, İzmir Yüksek Teknoloji University, İzmir, (2006).
  • [18] Kilit Ö., “The Kinematical design and analysis of the spherical mechanisms”, Phd Thesis, Ege University Institute of Science and Technology, İzmir, (2007).

The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations

Yıl 2022, Cilt: 25 Sayı: 4, 1513 - 1521, 16.12.2022
https://doi.org/10.2339/politeknik.757983

Öz

The movements of the spherical mechanisms take an important place in the robotic studies. In this paper, the design and the trajectory motion equations of the joints in the spherical mechanisms were presented by the methods of the sequential SLERP, sequential fast SLERP, sequential SLERP with De-Moivre, and modular SLERP interpolation that we firstly defined. Additionally, the Serret Frenet frame and curvatures of the geometrical SLERP interpolation curve for the locations of the joints in the spherical mechanisms were computed, and then, several numerical examples on the interpolation equations that produce the motion equations of the spherical mechanisms with 2 and 3-degree of freedom were given at the end of the paper.

Kaynakça

  • [1] Hamilton W.R., “On quaternions, or on a new system of imaginaries in algebra”, Philosophical Magazine, Vol. 25, n 3. p. 489–495, (1844).
  • [2] Hamilton W.R, “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, (1848).
  • [3] Hamilton W.R., “Elements of quaternions”, Chelsea Pub., New York, Vol. I, 3rd Ed., (1969).
  • [4] Hanson A. J., "Visualizing quaternions", Elsevier, Morgan Kaufmann, San Francisco. ISBN 0-12-088400-3, (2006).
  • [5] Vince J., “Quaternions for computer graphics”, Bournemouth Un., Bournemouth, UK, (2011).
  • [6] Hacısalihoğlu, H.H., “Motion geometry and quaternions theory”, Gazi Uni., Ankara, (1983).
  • [7] Sheomake K., “Animating rotation with quaternion curves”, San Francısco, 19(3): 245-254, (1985).
  • [8] Dam E.B, Koch M. and Lillholm M., “Quaternions, interpolation and animation”, Institute of Computer Science University of Copenhagen, (1998).
  • [9] Hast A., Barrera T. and Bengtsson E., “Shading by spherical linear interpolation using de Moivre’s formula”, Proc. 11th Int. Conf. Central Europe on Computer Graphics, Visualization, and Computer Vision, (2003).
  • [10] Hast A., Barrera T., Bengtsson E., “Incremental spherical linear interpolation”, In The Annual SIGRAD Conference. Special Theme-Environmental Visualization, 13,7-10. Linköping University Electronic Press, (2004).
  • [11] Kremer V.E., “Quaternions and Slerp”, Department for the Computer Science University of Saarbrücken, (2008).
  • [12] Jafari M., Molaei H., “Spherical linear interpolation and Bezier curves”, General Scientific Researches, 2(1): 13-17, (2014).
  • [13] Kuşak Samancı, H., Çelik S., İncesu M., “The Bishop frame of Bézier curves”, Life Science Journal, 2015, 12(6): 175-180.
  • [14] Gündüz H., Kazan A., Karadağ H.B., “Rotational surfaces generated by cubic Hermitian and cubic Bezier curves”, Politeknik Dergisi, 22(4): 1075-1082, (2019).
  • [15] Incesu M., “The new characterization of ruled surfaces corresponding dual Bézier curves”, Mathematical Methods in the Applied Sciences, (2021).
  • [16] Alizade R., Gezgin E. and Kilit Ö., “A new method in computational kinematics of a spherical wrist motion through quaternions”, Intl. Workshop on Comp. Kinematics, Cassino, p.32, (2005).
  • [17] Gezgin E., “Biokinematic analysis of human arm”, Phd Thesis, İzmir Yüksek Teknoloji University, İzmir, (2006).
  • [18] Kilit Ö., “The Kinematical design and analysis of the spherical mechanisms”, Phd Thesis, Ege University Institute of Science and Technology, İzmir, (2007).
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Hatice Kusak Samancı 0000-0001-6685-236X

Çetin Kuşçu 0000-0003-1674-9801

Yayımlanma Tarihi 16 Aralık 2022
Gönderilme Tarihi 25 Haziran 2020
Yayımlandığı Sayı Yıl 2022 Cilt: 25 Sayı: 4

Kaynak Göster

APA Kusak Samancı, H., & Kuşçu, Ç. (2022). The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations. Politeknik Dergisi, 25(4), 1513-1521. https://doi.org/10.2339/politeknik.757983
AMA Kusak Samancı H, Kuşçu Ç. The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations. Politeknik Dergisi. Aralık 2022;25(4):1513-1521. doi:10.2339/politeknik.757983
Chicago Kusak Samancı, Hatice, ve Çetin Kuşçu. “The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations”. Politeknik Dergisi 25, sy. 4 (Aralık 2022): 1513-21. https://doi.org/10.2339/politeknik.757983.
EndNote Kusak Samancı H, Kuşçu Ç (01 Aralık 2022) The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations. Politeknik Dergisi 25 4 1513–1521.
IEEE H. Kusak Samancı ve Ç. Kuşçu, “The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations”, Politeknik Dergisi, c. 25, sy. 4, ss. 1513–1521, 2022, doi: 10.2339/politeknik.757983.
ISNAD Kusak Samancı, Hatice - Kuşçu, Çetin. “The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations”. Politeknik Dergisi 25/4 (Aralık 2022), 1513-1521. https://doi.org/10.2339/politeknik.757983.
JAMA Kusak Samancı H, Kuşçu Ç. The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations. Politeknik Dergisi. 2022;25:1513–1521.
MLA Kusak Samancı, Hatice ve Çetin Kuşçu. “The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations”. Politeknik Dergisi, c. 25, sy. 4, 2022, ss. 1513-21, doi:10.2339/politeknik.757983.
Vancouver Kusak Samancı H, Kuşçu Ç. The Analysis of Some Spherical Mechanism Movements and Joint Designs by The New SLERP Interpolations. Politeknik Dergisi. 2022;25(4):1513-21.
 
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