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2021 | OriginalPaper | Chapter

10. Nephroida and Rhodonea as Loci

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

On two intersected lines in C, slide the slides 2 and 5, having the line BG = constant. The trajectories of points E and F on these slides are required. The trajectory of E is a woody, and of F a half branch of nephroid. Taking the symmetrical curves, the complete nephroid results, on which the woodcuts of E are also given. By modifying the distance GF, other curves are obtained. Another nephroid generating mechanism is given. Two intersected straight lines in A fixed, rotate around A, both being conductive elements with movements correlated by the coefficient q, and the line BC = const. slides with point C on AC. Point C will draw a rhodonea. By changing the value of q, variants of rhodoneas with several branches are obtained. The plotted curve has the number of sides equal to q − 2. If the sides AB and BC are equal, other types of rhodoneas are obtained, in which the branches pass through the origin of the axis system.

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Metadata
Title
Nephroida and Rhodonea as Loci
Authors
Iulian Popescu
Xenia Calbureanu
Alina Duta
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-63079-9_10

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