Abstract
This article deals with investigations by Pafnuty Chebyshev and Samuel Roberts in the late 1800s, which led them independently to the conclusion that for each curve that can be drawn by four bar linkages, there are always three linkages describing the same curve. These different linkages resulting in the same curve can be called cognate linkages.
We will see that Chebyshev and Roberts had very different interests and motivations for studying four bar linkages. Despite of these differences, they came to a similar result concerning cognate linkages.
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References
Thurston, T.: A History of the Growth of the Steam-engine. Appleton and Company, New York (1878)
Muirhead, J.P.: The Origin and Progress of the Mechanical Inventions of James Watt, vol. III. John Murray, London (1854)
Muirhead, J.P.: The Origin and Progress of the Mechanical Inventions of James Watt, vol. II. John Murray, London (1854)
Muirhead, J.P.: The Life of James Watt. John Murray, London (1858)
de Prony, G.: Nouvelles Architecture Hydraulique, vol. I. Firmin Didot, Paris (1790)
de Prony, G.: Nouvelles Architecture Hydraulique, vol. II. Firmin Didot, Paris (1796)
Vincent, A.J.H.: Mémoires de la Société royal des Sciences, de l’Agriculture et des Arts, de Lille (1836, 1837, 1838)
Markoff, A., Sonin, N.: Oeuvres de P.L. Tchebychef, Tome II, l’académie impériale des sciences. St. Petersburg (1907)
Markoff, A., Sonin, N.: Oeuvres de P.L. Tchebychef, Tome I, l’académie impériale des sciences. St. Petersburg (1899)
Roberts, S.: On the Mechanical Description of some Species of Circular Curves of the third and fourth Degrees. Proceedings London Mathematical Society, 125–136 (1869)
Roberts, S.: On three bar motion in plane space. Proceedings London Mathematical Society, 14–23 (1875)
Schor, J.B.: On the theorem of Roberts – Tchebyshev. Journal of Applied Mathematics and Mechanics 5, 323–324 (1941)
Richard de Jonge, A.E.: The Correlation of Hinged Straight-Line Four Bar Devices by means of Roberts Theorem and a New Proof of the Latter. Annals of the New York Academy of Sciences 84, 77–145
Nolle, H.: Linkage Coupler Curve Synthesis: A Historical Review -I and II. Mechanism and Machine Theory 9, 147–168 (1974)
Ceccarelli, M., Vinciguerra, A.: Approximate Four-Bar Circle-Tracing Mechanisms: Classical and New Synthesis. Mechanism and Machine Theory 35, 1579–1599 (2000)
Koetsier, T.: A contribution to the history of kinematics, Part I and Part II. Mechanism and Machine Theory 18, 37–42, 43–48 (1983)
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Verstraten, E. (2012). Cognate Linkages the Roberts – Chebyshev Theorem. In: Koetsier, T., Ceccarelli, M. (eds) Explorations in the History of Machines and Mechanisms. History of Mechanism and Machine Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4132-4_35
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DOI: https://doi.org/10.1007/978-94-007-4132-4_35
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-4131-7
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