The belt problem is a mathematics problem which requires finding the length of a crossed belt that connects two circular pulleys with radiusr1 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.
For fixed P the length of the belt depends only on the sum of the radius values r1 + r2, and not on their individual values.
Pulley problem
The pulley problem
There are other types of problems similar to the belt problem. The pulley problem, as shown, is similar to the belt problem; however, the belt does not cross itself. 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: