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The capstan equation [1] or belt friction equation, also known as Euler–Eytelwein formula [2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan).
The equation used to model belt friction is, assuming the belt has no mass and its material is a fixed composition: [2] = where is the tension of the pulling side, is the tension of the resisting side, is the static friction coefficient, which has no units, and is the angle, in radians, formed by the first and last spots the belt touches the pulley, with the vertex at the center of the pulley.
The first electric-powered torque amplifier was invented in 1925 by Henry W. Nieman of the Bethlehem Steel Company of Bethlehem, Pennsylvania. [1] It was intended to allow manual control of heavy equipment; e.g., industrial cranes, artillery, etc. Vannevar Bush used Nieman's torque amplifier as part of his differential analyzer project at M.I.T in the early 1930s. [2]
This does cause frictional shear stresses in the contact area. In the final situation the bollard exercises a friction force on the rope such that a static situation occurs. The tension distribution in the rope in this final situation is described by the capstan equation, with solution:
Prony brake dynamometers at a tractor contest in 1910 Schematic of a Prony brake Actual Prony Brake built for testing 5HP Steam Engine. The Prony brake is a simple device invented by Gaspard de Prony in 1821 to measure the torque produced by an engine.
For a toothed belt drive, the number of teeth on the sprocket can be used. For friction belt drives the pitch radius of the input and output pulleys must be used. The mechanical advantage of a pair of a chain drive or toothed belt drive with an input sprocket with N A teeth and the output sprocket has N B teeth is given by
Capstan equation, formula to describe hold-force in relation to load-force for flexible lines around a cylinder; Horse capstan, a device similar to a windlass used in mining; also called a whim; Slingsby Capstan, a British two-seat glider of the 1960s; Capstan (software), audio restoration program by Celemony which eliminates wow and flutter
This friction material is flush with the steel on the coil shell or rotor, since if the friction material was not flush, good magnetic traction could not occur between the faces. Some people look at electromagnetic clutches and mistakenly assume that, since the friction material is flush with the steel, that the clutch has already worn down ...