Characteristic Directions of Closed Planar Homothetic Inverse Motions

Year 2018, Volume: 6 Issue: 2, 240 - 245, 15.10.2018

Ayhan Tutar Önder Şener Esra İnan

Abstract

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.

Keywords

Steiner formula, polar moment of inertia, planar kinematics, homothetic inverse motions

References

• [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.}