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2021 | OriginalPaper | Chapter

2. Loci Generated by the Point of a Line Which Moves One End on a Circle and the Other on a Line

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 start from a simple geometric problem, when a straight line slides with one end on a circle and the other on a straight line (both fixed) and we look for the trajectory of a point on this straight line. We construct the equivalent mechanism which is the rod-crank mechanism, we write the relationships for the positions, we draw the mechanism in several positions and then we obtaine a succession of the curves generated by the points on this line. The case is generalized by replacing the fixed line with a mobile one, resulting a lot of curves, variable depending on the correlation of the angles of the two leading elements. The resulting curves are different from one case to another, being open curves and some having several branches [1, 2] (Luca et al. in Studies regarding of aesthetics surfaces with mechnanisms. In: Mathematical Methods for Information Science and Economics. Proceedings of the 17th WSEAS International Conference on Applied Mathematics (AMATH `12), Montreux, Switzerland, pp. 249–254, 2012; Sass et al. in J Ind Design Eng Graphics. Papers of the International Conference on Engineering Graphics and Design, Sect. 3: Engineering Computer Graphics, Nr. 12, (1):41–46, 2017).

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Literature
1.
go back to reference Calbureanu M, Malciu R, Lungu M, Calbureanu D (May, 2008) The influence of the lubricant from a rectilinear pair above the work accuracy of the elastic elements from the high precision mechanisms. Appl Theoret Mech Manuscript 3(5):176–185, ISSN: 1991–8747 (received Oct. 16, 2007) (revised Apr. 18, 2008) Calbureanu M, Malciu R, Lungu M, Calbureanu D (May, 2008) The influence of the lubricant from a rectilinear pair above the work accuracy of the elastic elements from the high precision mechanisms. Appl Theoret Mech Manuscript 3(5):176–185, ISSN: 1991–8747 (received Oct. 16, 2007) (revised Apr. 18, 2008)
2.
go back to reference Luca L, Popescu I, Ghimiş Ş (December, 2012) Studies regarding of aesthetics surfaces with mechnanisms. In : Mathematical methods for information science and economics. Proceedings of the 17th WSEAS international conference on applied mathematics (AMATH `12), pp 29–31, pp 249–254. Montreux, Switzerland Luca L, Popescu I, Ghimiş Ş (December, 2012) Studies regarding of aesthetics surfaces with mechnanisms. In : Mathematical methods for information science and economics. Proceedings of the 17th WSEAS international conference on applied mathematics (AMATH `12), pp 29–31, pp 249–254. Montreux, Switzerland
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 a Line Which Moves One End on a Circle and the Other on a Line
Authors
Iulian Popescu
Xenia Calbureanu
Alina Duta
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-63079-9_2

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