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The belt problem. The belt problem is a mathematics problem which requires finding the length of a crossed belt that connects two circular pulleys with radius r 1 and r 2 whose centers are separated by a distance P. The solution of the belt problem requires trigonometry and the concepts of the bitangent line, the vertical angle, and congruent ...
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 internal and external tangent lines are useful in solving the belt problem, which is to calculate the length of a belt or rope needed to fit snugly over two pulleys. If the belt is considered to be a mathematical line of negligible thickness, and if both pulleys are assumed to lie in exactly the same plane, the problem devolves to summing ...
An automotive belt with the number "740K6" or "6K740" indicates a belt 74 inches (190 cm) in length, 6 ribs wide, with a rib pitch of 9 ⁄ 64 of an inch (3.6 mm) (a standard thickness for a K series automotive belt would be 4.5mm). A metric equivalent would be usually indicated by "6PK1880" whereby 6 refers to the number of ribs, PK refers to ...
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
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
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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.