Nearly all gear wheels manufactured today have teeth with a profile based on the involute of a circle. The story of how this particular curve gained such mundane prevalence can be traced back to the pioneering work of European natural philosophers, in particular Euler. It involves the application of analytical geometry to a real world engineering problem.
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V G A Goss is a Senior Lecturer in Dynamics at London South Bank University. His research interests include nonlinear dynamics, biomechanics and history of technology and engineering. He is course director for a course in Clinical Technology and teaches a variety of subjects in mathematics and mechanics. He is a keen swimmer, rambler, trade unionist and active member of the Mammal Society.
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Goss, V.G.A. Application of analytical geometry to the form of gear teeth. Reson 18, 817–831 (2013). https://doi.org/10.1007/s12045-013-0106-3
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