I want to find the formula for how circular vertical movement affects horizontal movement. Imagine you set your elbow down and using a pen you move up and down(forming a portion of a circle), how much do you have to move your hand in the $x$ direction in order to make a straight vertical line rather than a circular one.
The outer line is the farthest possible position, the inner line is the closest position. The distance between them is $85$ mm. The movement in the $x$ direction(between the two circles, $85$ mm) is in counts of $0-179,000$ $x$-unit. The movement in the circular $y$ motion is in counts of $2200-48500$($0 - 46300$) $y$-units.
The question I'm asking is how many $x$-units should I move with every $y$-unit change?