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Length of Belt Traversing Three Pulleys

Mechanics and Machine Design
Vee-Belt and Pulley Design

Length of Belt Traversing Three Pulleys

Length of Belt Traversing Three Pulleys

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Length of Belt Traversing Three Pulleys

The length L of a belt traversing three pulleys, as shown in the diagram below, and touching them on one side only, can be found by the following equation.

Referring to the diagram, R1, R2, and R3 are the radii of the three pulleys; C12, C13, and C23 are the center distances; and α1, α2, and α3 are the angles, in radians, of the triangle formed by the center distances. Then:

Length of Belt Equation

Where:

α123 = Degrees
R1, R2, R3 = Radius (in, mm)
C12, C13, C23 = Length (in, mm)

Reference:

Machinerys, 30th edition

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