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 r1 and r2 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 angles.

In addition, triangles ACO and BEO are similar.

Therefore angles CAO, DAO, EBO and FBO are all equal.

(denominated in radians), the length of the belt is This exploits the convenience of denominating angles in radians that the length of an arc = the radius × the measure of the angle facing the arc.

In the pulley problem the length of the belt is where r1 represents the radius of the larger pulley, r2 represents the radius of the smaller one, and: The belt problem is used [1] in the design of aeroplanes, bicycle gearing, cars, and other items with pulleys or belts that cross each other.