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The pitch diameter is useful in determining the spacing between gear centers because proper spacing of gears implies tangent pitch circles. The pitch diameters of two gears may be used to calculate the gear ratio in the same way the number of teeth is used.
The involute gear profile, sometimes credited to Leonhard Euler, [1] was a fundamental advance in machine design, since unlike with other gear systems, the tooth profile of an involute gear depends only on the number of teeth on the gear, pressure angle, and pitch. That is, a gear's profile does not depend on the gear it mates with.
Coupled with a 700c wheel (622 mm diameter) and a 23 mm tire size (which approximately adds 2×23 mm to the wheel diameter), this gives an approximate diameter of 0.645 metres (depending on various factors such as air pressure, tire and rim), resulting in an estimated rollout distance of: π ⋅ 0.668 m ⋅ 52 ⁄ 14 ~ 7.53 m
Multiplication by a further factor is needed to allow for any other selected hub gear ratio [3] (many online gear calculators have these factors built in for various popular hub gears). Gear inches = Diameter of drive wheel in inches × (number of teeth in front chainring / number of teeth in rear sprocket). Normally rounded to nearest whole ...
The cylindrical gear tooth profile corresponds to an involute (i.e. a triangle wave projected on the circumference of a circle), whereas the bevel gear tooth profile is an octoid [definition needed] (i.e. a triangle wave projected on the normal path of a circle of a sphere).
Module is a direct dimension ("millimeters per tooth"), unlike diametral pitch, which is an inverse dimension ("teeth per inch"). Thus, if the pitch diameter of a gear is 40 mm and the number of teeth 20, the module is 2, which means that there are 2 mm of pitch diameter for each tooth. [56]
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Pressure angles. Pressure angle in relation to gear teeth, also known as the angle of obliquity, [1] is the angle between the tooth face and the gear wheel tangent. It is more precisely the angle at a pitch point between the line of pressure (which is normal to the tooth surface) and the plane tangent to the pitch surface.