Abstract
Gears are simple, but clever mechanisms. They have been invented more than 2000 years ago and today their use is widespread in almost every machine with mechanical parts. Finding optimal gear shapes is a interesting mathematical and technical problem. Surprisingly it is possible to design non circular gears that mesh perfectly. The article present some of the subtleties of gear design and shows some fascinating models with unconventionally shaped gears.
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References
C.C. Barratt, Time machines: steampunk in contemporary art. Neo-Vic. Stud. 3(1), 167–188 (2010)
M. Burrows, G. Sutton, Interacting gears synchronize propulsive leg movements in a jumping insect. Science 341(6151), 1254–1256 (2013)
N. Cohn, The Visual Language of Comics: Introduction to the Structure and Cognition of Sequential Images (Black, London, 2013)
W.P. Crosher, A Gear Chronology, Significant Events and Dates Affecting Gear Development (Xlibris Corporation, USA, 2014)
L. Da Vinci, Codex Madrid (Castrovilli Giuseppe, 1998). Available online: http://leonardo.bne.es/index.html. Accessed 6-Jan-2018
Fellow corp., Design of involute gear teeth, in Issue of Gear Technology, Oct./Nov. 1984. Available online: https://www.geartechnology.com/issues/1084x/back-to-basics.pdf. Accessed 7-Jan-2018
R. Ferréol, A. Esculier, Roads and Wheel (2017). http://www.mathcurve.com/courbes2d.gb/engrenage/engrenage2.shtml. Accessed 14-Jan-2018
T. Freeth, Ancient Computer (Scientific American, USA, 2009). Available online: http://www.cs.virginia.edu/~robins/Decoding_an_Ancient_Computer.pdf. Accessed 14-Jan-2018
Gearify, https://www.gearifysoftware.com/. Accessed 14-Jan-2018
R. Hessmer, Cycloidal Gear Builder (2012). http://www.hessmer.org/blog/2012/01/28/cycloidal-gear-builder/. Accessed 14-Jan-2018
Internet Craftsmanship Museum, The “Do Nothing” Machine—it produces nothing except smiles. http://www.craftsmanshipmuseum.com/Wahlstrom.htm. Accessed 14-Jan-2018
M. Masal, S. Ersoy, M.A. Güngör, Euler–Savary formula for the homothetic motion in the complex plane C. Ain Shams Eng. J. 5(1), 305–308 (2014). Available online: http://www.sciencedirect.com/science/article/pii/S2090447913000920. Accessed 14-Jan-2018
Pure Emotions CAT-RAT, https://youtu.be/MMaNRZYQ2Hk. Accessed 14-Jan-2018
S.P. Radzevich, Theory of Gearing: Kinematics, Geometry, and Synthesis (CRC Press, Boca Raton, 2012)
Shuanghuan Transmission Research Institute, Gear University. http://www.precision-sh.com/en/yanfazhongxin/chilundaxue/38.html. Accessed 14-Jan-2018
H. Sparks, Designing Cycloidal Gears (2013). https://www.csparks.com/watchmaking/CycloidalGears/index.jxl. Accessed 14-Jan-2018
D. Taimina, Geometry and motion links mathematics and engineering in collections of 19 th century kinematic models and their digital representation, in ICME, 5-8 March 2008
Teatro di Roma, CATRAT, http://www.teatrodiroma.net/doc/2742/catrat. Accessed 14-Jan-2018
I. Zarębski, T. Sałaciński, Designing of non-circular gears. Arch. Mech. Eng. 55(3), 275–292 (2008). Available online: http://prozamet.pl/art_2008_3_08.pdf. Accessed 6-Jan-2018
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Todesco, G.M. (2018). Weird Gears. In: Emmer, M., Abate, M. (eds) Imagine Math 6. Springer, Cham. https://doi.org/10.1007/978-3-319-93949-0_16
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DOI: https://doi.org/10.1007/978-3-319-93949-0_16
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