So I need to control a ring with three pulleys. The pulleys are 120 degrees apart. I want to move the ring 2 inches toward one pulley, how much do the other pulleys have to slack? That's an easy question, but what I really need is an equation to describe and calculate the speed at which each cable lengthens. The speed is not linear for the two adjacent pulleys. I need an equation for each pulley to describe the speed at which it should slacken or tighten in order to move the ring from any location, to any location, in conjunction with the other pulleys, at any defined speed. But the problem can be simplified by treating all the pulleys the same, but just changing the coordinates relative to the pulley. So, it may be reduced to this............ On a standard x,y plane there are two points. If I travel from one point to the other at "v" velocity, what is the rate of change of the length of the line extending from 0,0 to my current position?