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Characteristic Directions of Closed Planar Homothetic Inverse Motions

Yıl 2018, Cilt: 6 Sayı: 2, 240 - 245, 15.10.2018

Öz

In this paper, during one-parameter closed planar homothetic inverse motions, the Steiner area formula and the polar moment of inertia were expressed. The Steiner point or Steiner normal concepts were described according to whether rotation number is different zero or equal to zero, respectively. The fixed pole point was given with its components and its relation between Steiner point or Steiner normal was specified. The sagittal motion of a crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of crane and the moving arm of crane. The results obtained in the first sections of this study were applied for this motion.



Kaynakça

  • [1] Blaschke W., M\"{u}ller H.R., \text{Ebene Kinematik}, R. Oldenbourg, M\"{u}nchen, (1956).
  • [2] Dathe H., Gezzi R., Characteristic directions of closed planar motions, \text{Zeitschrift f\"{u}r Angewandte Mathematik und Mechanik}, \text{92} (2012), 731-748.
  • [3] Kuruo\u{g}lu N., D\"{u}ld\"{u}l M., Tutar A., Generalization of Steiner formula for the homothetic motions on the planar kinematics, \text{Applied Mathematics and Mechanics (English Edition)},\text{24} (2003), 945-949. }
  • [4] M\"{u}ller H.R., Verall gemeinerung einer Formel von Steiner, \text{Abh. Braunschweig. Wiss. Ges.}, \text{29} (1978), 107-113. }
  • [5] M\"{u}ller H.R., \"{U}ber Tr\"{a}gheitsmomente bei Steinerscher Massenbelegung, \text{Abh. Braunschweig. Wiss. Ges.}, \text{29} (1978), 115-119. }
  • [6] Steiner J., Von dem Kr\"{u}mmungs-Schwerpuncteebener Curven, \text{Journal f\"{u}r die reine und angewandte Mathematik}, \text{21} (1840), 33-63.}
  • [7] T\"{o}lke J. Steiner-Formein f\"{u}r die Bahnflachen geschlossener Aquiaffinbewegungen, \text{Sitzungsber \"{O}sterr. Akad. Wiss, Math.-Nat. Klasse}, \text{187} (1978), 325-337. }
  • [8] Tutar A., Kuruo\u{g}lu N., The Steiner formula and the Holditch theorem for the homothetic motions on the planar kinematics, \text{Mechanism and Machine Theory}, \text{34} (1999), 1-6.}
Yıl 2018, Cilt: 6 Sayı: 2, 240 - 245, 15.10.2018

Öz

Kaynakça

  • [1] Blaschke W., M\"{u}ller H.R., \text{Ebene Kinematik}, R. Oldenbourg, M\"{u}nchen, (1956).
  • [2] Dathe H., Gezzi R., Characteristic directions of closed planar motions, \text{Zeitschrift f\"{u}r Angewandte Mathematik und Mechanik}, \text{92} (2012), 731-748.
  • [3] Kuruo\u{g}lu N., D\"{u}ld\"{u}l M., Tutar A., Generalization of Steiner formula for the homothetic motions on the planar kinematics, \text{Applied Mathematics and Mechanics (English Edition)},\text{24} (2003), 945-949. }
  • [4] M\"{u}ller H.R., Verall gemeinerung einer Formel von Steiner, \text{Abh. Braunschweig. Wiss. Ges.}, \text{29} (1978), 107-113. }
  • [5] M\"{u}ller H.R., \"{U}ber Tr\"{a}gheitsmomente bei Steinerscher Massenbelegung, \text{Abh. Braunschweig. Wiss. Ges.}, \text{29} (1978), 115-119. }
  • [6] Steiner J., Von dem Kr\"{u}mmungs-Schwerpuncteebener Curven, \text{Journal f\"{u}r die reine und angewandte Mathematik}, \text{21} (1840), 33-63.}
  • [7] T\"{o}lke J. Steiner-Formein f\"{u}r die Bahnflachen geschlossener Aquiaffinbewegungen, \text{Sitzungsber \"{O}sterr. Akad. Wiss, Math.-Nat. Klasse}, \text{187} (1978), 325-337. }
  • [8] Tutar A., Kuruo\u{g}lu N., The Steiner formula and the Holditch theorem for the homothetic motions on the planar kinematics, \text{Mechanism and Machine Theory}, \text{34} (1999), 1-6.}
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Ayhan Tutar

Önder Şener Bu kişi benim

Esra İnan

Yayımlanma Tarihi 15 Ekim 2018
Gönderilme Tarihi 24 Mayıs 2018
Kabul Tarihi 2 Temmuz 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 2

Kaynak Göster

APA Tutar, A., Şener, Ö., & İnan, E. (2018). Characteristic Directions of Closed Planar Homothetic Inverse Motions. Konuralp Journal of Mathematics, 6(2), 240-245.
AMA Tutar A, Şener Ö, İnan E. Characteristic Directions of Closed Planar Homothetic Inverse Motions. Konuralp J. Math. Ekim 2018;6(2):240-245.
Chicago Tutar, Ayhan, Önder Şener, ve Esra İnan. “Characteristic Directions of Closed Planar Homothetic Inverse Motions”. Konuralp Journal of Mathematics 6, sy. 2 (Ekim 2018): 240-45.
EndNote Tutar A, Şener Ö, İnan E (01 Ekim 2018) Characteristic Directions of Closed Planar Homothetic Inverse Motions. Konuralp Journal of Mathematics 6 2 240–245.
IEEE A. Tutar, Ö. Şener, ve E. İnan, “Characteristic Directions of Closed Planar Homothetic Inverse Motions”, Konuralp J. Math., c. 6, sy. 2, ss. 240–245, 2018.
ISNAD Tutar, Ayhan vd. “Characteristic Directions of Closed Planar Homothetic Inverse Motions”. Konuralp Journal of Mathematics 6/2 (Ekim 2018), 240-245.
JAMA Tutar A, Şener Ö, İnan E. Characteristic Directions of Closed Planar Homothetic Inverse Motions. Konuralp J. Math. 2018;6:240–245.
MLA Tutar, Ayhan vd. “Characteristic Directions of Closed Planar Homothetic Inverse Motions”. Konuralp Journal of Mathematics, c. 6, sy. 2, 2018, ss. 240-5.
Vancouver Tutar A, Şener Ö, İnan E. Characteristic Directions of Closed Planar Homothetic Inverse Motions. Konuralp J. Math. 2018;6(2):240-5.
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