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2021 | OriginalPaper | Chapter

14. The Locus for the Cross-Point of the Diagonals in a Pentagon

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

Here we study the trajectories drawn by the points of intersection of the diagonals in a pentagon. When one side is fixed, and the remaining are mobile, there are two conducting elements. Taking two intersecting diagonals, the result is 5 trajectory-generating points. Mechanisms are built for all these cases and the trajectories found are drawn. Many resulting curves are given for each value of q. Successive positions of the created mechanisms are also given. The resulting curves are generally open, with several branches [1]. The length of the sides of the mechanisms did not correlate with conditions like Grashof, so that in general the mechanisms do not work throughout the cycle, but only in certain subintervals of the cycle [2]. The discontinuities that appear are indicated below in the diagrams where the jumps are seen.

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Literature
1.
go back to reference Popescu I (2016) Locuri geometrice şi imagini estetice generate cu mecanisme. Editura Sitech, Craiova Popescu I (2016) Locuri geometrice şi imagini estetice generate cu mecanisme. Editura Sitech, Craiova
2.
go back to reference Popescu I (2017) Curbe de bielă în diferite plane şi locuri geometrice generate de mecanisme. Editura Sitech, Craiova Popescu I (2017) Curbe de bielă în diferite plane şi locuri geometrice generate de mecanisme. Editura Sitech, Craiova
Metadata
Title
The Locus for the Cross-Point of the Diagonals in a Pentagon
Authors
Iulian Popescu
Xenia Calbureanu
Alina Duta
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-63079-9_14

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