CHARACTERISTIC DIRECTIONS OF
CLOSED PLANAR HOMOTHETIC MOTIONS
Ayhan Tutar1, Önder Şener2, Esra İnan3
1,2,3 Ondokuz Mayis University
Arts and Science Faculty
Mathematics Department
Samsun, 55139, TURKEY

Abstract

In this paper, during one-parameter closed planar homothetic 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 moving pole point was given with its components and its relation between Steiner point or Steiner normal was specified. The sagittal motion of a telescopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of telescopic crane and the moving arm of telescopic crane. The results obtained in the first section of this study were applied for this motion.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 2
Year: 2018

DOI: 10.12732/ijam.v31i2.3

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References

  1. [1] W. Blaschke and H.R. Müller, Ebene Kinematik, R. Oldenbourg, München (1956).
  2. [2] H. Dathe and R. Gezzi, Characteristic directions of closed planar motions, Zeitschrift für Angewandte Mathematik und Mechanik, 92 (2012), 731-748.
  3. [3] N. Kuruoğlu, M. Düldül and A. Tutar, Generalization of Steiner formula for the homothetic motions on the planar kinematics, Applied Mathematics and Mechanics (Engl. Edition), 24 (2003), 945-949.
  4. [4] H.R. Müller, Verall gemeinerung einer Formel von Steiner, Abh. Braun- schweig. Wiss. Ges., 29 (1978), 107-113.
  5. [5] H.R. Müller, Über Trä gheitsmomente bei Steinerscher Massenbelegung, Abh. Braunschweig. Wiss. Ges., 29 (1978), 115-119. 210 A. Tutar, Ö. Şener, E. İnan
  6. [6] J. Steiner, Von dem Krümmungs-Schwerpuncte ebener Curven, Journal für die reine und angewandte Mathematik, 21 (1840), 33-63.
  7. [7] J. Tölke, Steiner-Formein für die Bahnflachen geschlossener Aquiaffinbewe- gungen, Sitzungsber. Ö sterr. Akad. Wiss, Math.-Nat. Klasse, 187 (1978), 325-337.
  8. [8] A. Tutar and N. Kuruoğlu, The Steiner formula and the Holditch theo- rem for the homothetic motions on the planar kinematics, Mechanism and Machine Theory, 34 (1999), 1-6.