The Simple Machine Calculator includes formulas for Levers, Belts, Pulleys and Gears calculator Lever and Fulcrumcontains equations related to speeds, diameters and RPMs in systems of belts, pulleys and gears. The equations include the following:
A belt and pulley system is characterized by two or more pulleys in common to a belt. This allows for mechanical power, torque, and speed to be transmitted across axles. If the pulleys are of differing diameters, a mechanical advantage is realized. pulley transfer
A belt drive is analogous to that of a chain drive, however a belt sheave may be smooth (devoid of discrete interlocking members as would be found on a chain sprocket, spur gear, or timing belt) so that the mechanical advantage is approximately given by the ratio of the pitch diameter of the sheaves only, not fixed exactly by the ratio of teeth as with gears and sprockets.
In the case of a drum-style pulley, without a groove or flanges, the pulley often is slightly convex to keep the flat belt centered. It is sometimes referred to as a crowned pulley. Though once widely used on factory line shafts, this type of pulley is still found driving the rotating brush in upright vacuum cleaners, in belt sanders and bandsaws. Agricultural tractors built up to the early 1950s generally had a belt pulley for a flat belt (which is what Belt Pulley magazine was named after). It has been replaced by other mechanisms with more flexibility in methods of use, such as power take-off and hydraulics.
Just as the diameters of gears (and, correspondingly, their number of teeth) determine a gear ratio and thus the speed increases or reductions and the mechanical advantage that they can deliver, the diameters of pulleys determine those same factors. Cone pulleys and step pulleys (which operate on the same principle, although the names tend to be applied to flat belt versions and V belt versions, respectively) are a way to provide multiple drive ratios in a belt-and-pulley system that can be shifted as needed, just as a transmission provides this function with a gear train that can be shifted. V belt step pulleys are the most common way that drill presses deliver a range of spindle speeds.
Systems of gears work in a similar fashion to pulleys and belts, two gear system except there is no belt and the gears are inter-meshed with the teeth of one gear turning the teeth of a second gear. In this case, the RPM are a function of the number of teeth on the gear. The relationship between the gears is expressed as follows:
`RPM_1 * Teeth_1 = RMP_2 * Teeth_2`
The assumption is compatible teeth in the two gears.