Pulley and chain

Question

Find the length of an endless chain which will hang over a. Circular pulley of radius a so that it is in contact with two thirdsof the. Circumference of the pulley?

I saw this question in a test. I didn't quite understand the question. Can someone give a hint

Answer 1

Find the length of an endless chain which will hang over a circular pulley
of radius a so that it is in contact with two thirds of the circumference
of the pulley?

We have two pulleys (driver and driven).

Pulley "a" is bigger than pulley (say) "b", because has contact angle of 240 degrees (two thirds of the circumference = two thirds of 360 degrees).

We don't know :

a radius

b radius

center to center distance

For the formulas involved see "The pulley problem" in: https://en.wikipedia.org/wiki/Belt_problem

Formulas are the same for belts and chains.

So you can express total length as a function of both radii and center to center distance.

Answer 2

Here the endless chain means a chain whose ends are united by a link.

That should help you to understand the question.

This is a common catenary problem.

Read the proof from here http://mysite.du.edu/~jcalvert/math/catenary.htm