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2021 | OriginalPaper | Chapter

5. Loci Generated by the Points on a Bar Which Slides with the Heads on Two Fixed Lines

Authors : Iulian Popescu, Xenia Calbureanu, Alina Duta

Published in: Problems of Locus Solved by Mechanisms Theory

Publisher: Springer International Publishing

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Abstract

A straight-line slide with its heads on the axes of the system. The points on this line generate ellipses (example point C), composed of two halves, one for the + sign and the other for the—sign in front of a radical. Successive positions generate asteroids [1, 2]. Diagrams are given with the variations of some coordinates of the tracer point. From the ends of the sliding line we draw parallel lines to the axes of the reference system, establishing the trajectory of their intersection, the point D. The result is a circle containing the ellipse generated by the first point. In another case, the length of the line AB that has the ends on the two fixed lines was considered to be variable depending to the length of xB, i.e. the stroke of the leading element, so AB = q * xB, where q is conveniently adopted. It was found that in this case the trajectory of C point is a line parallel to the abscissa, and that of D point is an inclined line. The case where the fixed lines are inclined to the axes of the system was also studied, resulting in many curves dependent on the inclinations of these lines.

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Literature
1.
go back to reference Popescu I, Sass L, Duţă A, Romanescu AE (2019) Double-heart curve generated by original mechanism. În: J Ind Des Eng Graph. Papers of the International Conference on Engineering Graphics and Design, IGEGD, 15–17 May 14 Issue 1 2019, Craiova, pp 41–46 Popescu I, Sass L, Duţă A, Romanescu AE (2019) Double-heart curve generated by original mechanism. În: J Ind Des Eng Graph. Papers of the International Conference on Engineering Graphics and Design, IGEGD, 15–17 May 14 Issue 1 2019, Craiova, pp 41–46
2.
go back to reference Sass, Ludmila; Duţă, Alina; Popescu, Iulian—Nature gives us beauty, insoiring the technical creativity. J Ind Des Eng Graph. Papers of the International Conference on Engineering Graphics and Design, Section 3: Engineering Computer Graphics Sass, Ludmila; Duţă, Alina; Popescu, Iulian—Nature gives us beauty, insoiring the technical creativity. J Ind Des Eng Graph. Papers of the International Conference on Engineering Graphics and Design, Section 3: Engineering Computer Graphics
Metadata
Title
Loci Generated by the Points on a Bar Which Slides with the Heads on Two Fixed Lines
Authors
Iulian Popescu
Xenia Calbureanu
Alina Duta
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-63079-9_5

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