DOUBLE-HEART CURVE GENERATED BY AN ORIGINAL MECHANISM

Authors

  • Iulian Popescu Ph.D. Eng. University of Craiova https://orcid.org/0000-0002-9258-4773
  • Ludmila Sass Ph.D. Eng. University of Craiova
  • Alina Duta Ph.D. Eng. University of Craiova
  • Marcela Popescu Ph.D. Eng. University of Craiova
  • Alina Elena Romanescu Ph.D. Eng. University of Craiova

Keywords:

double-heart curve, curve generator mechanism

Abstract

Different variants of cardioids were reviewed and authors decided to an end to focus on the usability of a Double-heart curve. Starting from the geometric information related to its generation, the synthesis of an original generating mechanism was performed firstly, followed by the realization of its structural analysis. Mechanism’s positions were computed and the imposed curve was generated. The variations of certain trajectories were deduced from the corresponding diagrams. The mechanism sizes were modified and a wide class of curves presenting interest from the geometric point of view was obtained. Some mathematical properties of the curves generated by the above mechanism are studied (binormal vector, tangent equation in a current point, normal plane equation, tangent versor, versor of normal to the curve).

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Author Biographies

Iulian Popescu Ph.D. Eng., University of Craiova

Professor Faculty fo Mechanics

Ludmila Sass Ph.D. Eng., University of Craiova

Associate Professor Faculty of Mechanics

Alina Duta Ph.D. Eng., University of Craiova

Associate Professor Faculty of Mechanics

Marcela Popescu Ph.D. Eng., University of Craiova

Associate Professor Faculty of Science

Alina Elena Romanescu Ph.D. Eng., University of Craiova

Lecturer Faculty of Mechanics

References

Popescu, I., Sass, L. (2001). Mecanisme generatoare de curbe, Editura Sitech, ISBN 973-38-0308-1, Craiova

Artobolevskii, I.I. (1959). Teoria mehanizmov dlia vosproizvedenia ploskih crivâh. Izd. Academii Nauk, SSSR, Moskva.

http://mathworld.wolfram.com/HeartCurve.html, Accessed: 2018-10-10.

https://en.wikipedia.org/wiki/Cardioid, Accessed: 2018-10-12

http://www.mathematische-asteleien.de/heart.htm, Accessed: 2018-10-10

http://www.matchcurve.com/courbes2d.gb/doublecoeur/doublecoeur.shtml, Accessed: 2018-09-01.

Popescu, M., Popescu, P. (2002). Algebra liniara si geometrie analitica, Ed. Universitaria, ISBN 973-8043-308-8, Craiova.

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Published

2019-05-20

Issue

Section

Applied Geometry and Graphics