title: From bicycle chain ring shape to gear ratio: algorithm and examples.
abstract: A simple model of the bicycle drive system with a non-circular front chain ring is proposed and an algorithm is devised for calculation of the corresponding Gear Ratio As a Function Of Crank Angle (GRAFOCA). It is shown that the true effective radius of the chain ring is always the perpendicular distance between the crank axis and the line through the chain segment between the chain ring and the cog. It is illustrated that the true effective radius of the chain ring at any crank angle may differ substantially from the maximum vertical distance between the crank axis and the chain ring circumference that is used as a proxy for the effective chain ring radius in several studies; in particular, the crank angle at which the effective chain ring radius is maximal as predicted from the latter approach may deviate by as much as 0.30 rad from the true value. The algorithm proposed may help in designing chain rings that achieve the desired GRAFOCA.
authors.affiliation: Faculty of Human Movement Sciences, Research Institute MOVE, VU University Amsterdam, van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands. Electronic address: a.j.van.soest@vu.nl.
authors.forename: A J
authors.initials: AJ
authors.lastname: van Soest
mesh_terms: D000465:Algorithms; D001642:Bicycling; D001696:Biomechanical Phenomena; D004867:Equipment Design; D008962:Models, Theoretical
keywords: Algorithm; Bicycling; Effective radius; Gear ratio; Non-circular chain rings