Abstract
Starting from geometry, the equivalent mechanisms that trace ellipses, hyperbolas, or parabolas are built. These mechanisms are studied structurally, and their kinematic analysis is developed, resulting in relations, successive positions, diagrams, tables, and curves traced. Curves are traced either as trajectories of points or by enveloping. On the basis of projective geometry problems, a new mechanism that traces parabolas by enveloping is presented. Starting from an analytical geometry problem, synthesis of a new equivalent mechanism, which traces parabolas by enveloping, is also created. Next, we study a new mechanism, created on a locus problem, reaching the hyperbolas obtained by enveloping. Another problem in geometry allows the synthesis of the mechanism that traces a hyperbola as a trajectory of a point. A locus problem in 1896 allowed the synthesis of a new mechanism that traces ellipses, parabolas, and hyperbolas.
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References
Artobolevskii II (1959) Teoria mehanizmov dlia vosproizvedenia ploskih crivâh. Izd. Academii Nauk SSSR Moskva
Artobolevskii II (1951) Mehanizmî, vol II. Izd. Academii Nauk, SSSR, Moskva
Bernhard A (1993) Geometrie proiectivă. Perceperea spaţiului prin desen, Ed. Tehnică, Bucuresti
Creangă I (1953) Curs de geometrie analitică. Editura Tehnică, Bucureşti
Luca L, Popescu I (2004) Asupra unui nou mecanism parabolograf. In: Mecanisme şi manipulatoare, nr. x/2004, 5pp
Luca L, Popescu I, Cârţână L (2005) The structure and kinematics of Kaminski`s conicograph, In: Proceedings, Sections 7, Transcom 2005, University of Zilina, Slovak Republic, pp 129–131
Luca L, Popescu I (2004) Sinteza unui mecanism parabolograf. În: Construcţia de Maşini, nr. 1-2/2004, pp 117–118
Popescu I, Luca L, Cherciu M (2013) Structura şi cinematica mecanismelor. Aplicaţii, Editura Sitech, Craiova
Popescu I, Sass L (2001) Mecanisme generatoare de curbe, Ed. “Scrisul Românesc”, Craiova
Popescu I (2013) Curbe şi suprafeţe estetice: geometrie, generare, aplicaţii. Editura Sitech, Craiova
Popescu I, Luca L, Mitsi S (2011) Geometria, structura şi cinematica unor mecanisme. Editura Sitech, Craiova
Popescu I, Luca L, Cherciu M (2011) Traiectorii şi legi de mişcare ale unor mecanisme. Editura Sitech, Craiova
Popescu I, Sass L, Luca L (2013) Nou mecanism conicograf. In: Construcţia de maşini, nr. 11/2013
Popescu I, Luca L (2004) Construcţia şi structura unui mecanism hiperbolograf. In: Proceedings scientific conference, 9th edn. Univesity of Târgu-Jiu, pp 39–44
Popescu I, Luca L (2012) Synthesis and analysis of new hyperbolograph mechanism. In: Analele Universităţii «Constantin Brâncuşi» din Târgu-Jiu, Seria Inginerie, nr. 4/2012, pp 65–75
Popescu I, Sass L(2002) Noi mecanisme conicografe, cu elemente flexibile. In: Construcţia de maşini, Nr. 12/2002, pp. 51–53
Popescu I, Romanescu AE, Sass L (2018) Generating ellipses by using mechanisms relying on simple geometrical aspects. In: Confereng 2018, Analele Univ. “C. Brâncuşi”, Târgu-Jiu, nr. 2/2018, pp 18–23
Reuleaux F (1963) The kinematics of machinery. Dover Publications, NY
Reuleaux F, Kennedy ABW (eds) (1876) Kinematics of machinery: outlines of a theory of machines. Macmillan and Co., London
Sass L, Popescu I (2000) La synthese geometrique exacte d’un mecanisme elipsographe et d’un mecanisme de linearite. In: The 8th symposium on mechanisms and mechanical transmissions with international participation, Timişoara, pp 301–306
Sass L, Popescu I (2002) Mecanisme conicografe originale. In: Construcţia de maşini, Nr. 12/2002, pp 48–50
Shigley JE, Uicker JJ (1995) Theory of machines and mechanisms. McGraw-Hill, New York
Taimina D (2004) Historical mechanisms for drawing curves. Cornell University. http://ecommons.cornell.edu/bitstream/1813/2718/1/2004-9.pdf
Teodorescu D, Teodorescu ŞD (1975) Culegere de probleme de geometrie superioară, Ed. Did. Ped., Bucureşti
Teodorescu N ş.a. (1984) Probleme din Gazeta Matematică. Editura Tehnica, Bucuresti
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Popescu, I., Luca, L., Cherciu, M., Marghitu, D.B. (2020). Mechanisms for Generating Conical Curves. In: Mechanisms for Generating Mathematical Curves. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-42168-7_4
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DOI: https://doi.org/10.1007/978-3-030-42168-7_4
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