One interesting problem with closed chain

[ValeryOchkov]

(Bicycle) chain is slung over two blocks.

Given: r1, r2, x2, y2 (x1=y1=0) and L.

Find: a form of the chain.

Слабо?

If r1 and r2  -> 0 (or L -> infinity) we have this problem - see here.

[ValeryOchkov]

One solution at r1=r2 and y2=0 (two picture and Mathcad 15 sheet in attach).

[Fred_Kohlhepp]

Your two pictures assume that one side (either the top or the bottom) is taunt--a straight tangent.  But bike sprockets can introduce torque (see your picture in the first post.  You can have any intermediate configuration between your two extremes.  There's another variable--sprocket torque.

[ValeryOchkov]

Thanks Fred!

(More) correct result

[ValeryOchkov]

… and animation with different guess values!