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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

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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, R_{1}, R_{2}, and R_{3} are the radii of the three pulleys; C_{12}, C_{13}, and C_{23} are the center distances; and α1, α2, and α3 are the angles, in radians, of the triangle formed by the center distances. Then:

Where:

α_{1},α_{2},α_{3} = Degrees

R_{1}, R_{2}, R_{3} = Radius (in, mm)

C_{12}, C_{13}, C_{23} = Length (in, mm)

Reference:

Machinerys, 30th edition