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2021 | OriginalPaper | Chapter

3. Loci Generated by the Point of Intersection of Two 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

We consider two straight lines (cranks) with one end fixed at the base (frame) and we are looking for the trajectory of their intersection point when both straight lines rotate. The mechanism is constructed for the case when a line has a finite length and shows the successive positions and the trajectory of their intersection point [1], which is an incomplete circle. Both straight lines with infinite lengths are considered, resulting another equivalent mechanism with two leading elements. Depending on the correlation between the angles of rotation of these lines, many trajectories result, some being known curves, others unknown [3], with several incomplete branches [2]. The successive positions of the equivalent mechanism are also given. In another case, one of the lines is no longer connected to the base by a R coupling, but by a P coupling, so it slides on a fixed line. Numerous successive curves and positions are also obtained. Another case has in B only two couplings, the trajectory being a straight line.

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Literature
1.
go back to reference Popescu I, Romanescu AE, Sass L (23–25, September, 2016) A locus problem solved through methods from the theory of mechanisms. În: International conference: innovative manufacturing engineering and energy, IManE, p 7. Kallithea Chalkidiki Greece Popescu I, Romanescu AE, Sass L (23–25, September, 2016) A locus problem solved through methods from the theory of mechanisms. În: International conference: innovative manufacturing engineering and energy, IManE, p 7. Kallithea Chalkidiki Greece
2.
go back to reference Popescu I, Luca L (2015) Geometric locus generated by a mechanism with three dyads. În: Analele Universităţii «Constantin Brâncuşi» din Târgu-Jiu, Seria Inginerie, nr. 3, pp 29–37 Popescu I, Luca L (2015) Geometric locus generated by a mechanism with three dyads. În: Analele Universităţii «Constantin Brâncuşi» din Târgu-Jiu, Seria Inginerie, nr. 3, pp 29–37
3.
go back to reference Sass L, Duţă A, Popescu I (2017) Nature gives us beauty, insoiring the technical creativity. J Ind Design Eng Graphics (1):41–46. Papers of the international conference on engineering graphics and design, section 3: engineering computer graphics, Nr. 12 Sass L, Duţă A, Popescu I (2017) Nature gives us beauty, insoiring the technical creativity. J Ind Design Eng Graphics (1):41–46. Papers of the international conference on engineering graphics and design, section 3: engineering computer graphics, Nr. 12
Metadata
Title
Loci Generated by the Point of Intersection of Two Lines
Authors
Iulian Popescu
Xenia Calbureanu
Alina Duta
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-63079-9_3

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