On the invariants of ruled surfaces generated by the dual involute frenet trihedron

Year 2017, Volume: 66 Issue: 2, 62 - 70, 01.08.2017

Mustafa Bilici

https://doi.org/10.1501/Commua1_0000000801

Cited By: 4

https://izlik.org/JA74JW48ZP

Abstract

The purpose of this paper is to describe ruled surfaces generatedby a Frenet trihedron of closed dual involute for a given dual curve. We identifyrelations between the pitch, the angle of the pitch, and the drall of thesesurfaces. Some new results related to the developability of these surfaces arealso obtained. Finally, we illustrate these surfaces by presenting one example

Keywords

Ruled surface , dual involute-evolute , dual Frenet frame , dual numbers

References

• Kücük, A. Gürsoy, O., On the invariants of Bertrand trajectory surface oğsets, App. Math. and Comp. 151 (2004), 763–773.
• Yang, A. T. and Freudenstein,F., Application of dual-number quaternion algebra to the analysis of spatial mechanisms. J. Appl. Mech. 31 (1964),300–308.
• Özyilmaz, E. and Yayli, Y., On the integral invariants of a time-like ruled surface, Math. Comput. Appl. 6 (2001), 137–145.
• Study, E., Geometrie der Dynamen. Verlag Teubner, Leipzig, 1903.
• Veldkamp, G. R., On the use of dual numbers, vectors, and matrices in instantaneous, spatial kinematics. Mech. and Mach. Theory. 11 (1976), 141–156.
• Hacısaliho¼glu, H.H., On the pitch of a closed ruled surfaces. Mech. and Mach. Theory. 7 (1972), 291–305 .
• Hacısaliho¼glu, H.H., MovingGeometry and Quaternion Theory. Publishings of Science and Art Faculty of Gazi University, Ankara-Turkey, 1983.
• Müller, H. R., Über geschlossene bewegungs vorgange, Monatsh. Math. 55 (1951), 206–214.
• Gürsoy, O., On the integral invariants of a closed ruled surface, J. of Geom. 39 (1990), 89–91.
• Gürsoy, O., The dual angle of pitch of a closed ruled surface, Mech. and Mach. Theory. 25 (1990), 131–140.
• Köse, Ö., Contribution to the theory of integral invariants of a closed ruled surface, Mech. and Mach. Theory. 32 (1997), 261–277.
• Köse, Ö., Nizamo¼glu, ¸S. and Sezer, M. An explicit characterization of dual spherical curves, Do¼ga Turkish J. Math. 12 (1988), 105–113.
• Cliğord, W. K. Preliminary sketch of biquaternions. Proc. London Math. Soc. 4 (1873), 381–
• Yaylı, Y. and Saraço¼glu, S. Ruled surfaces and dual spherical curves, Acta Univ. Apulensis. (2012), 337–354.
• Current address : Ondokuz Mayıs University, Educational Faculty, Department of Mathematics Atakum, Samsun, TURKEY. E-mail address : [e-mail]