I did a rough sketch of how to look at the build area in this post.
I suggest you aim for a rounded triangle, with each vertex close to the base of the closest pillar. That way, there are no points in the travel of any arm that are excluded by mechanical constraints. To do this, you need to set up the ratios so that one arm is completely vertical when the other two are completely horizontal. I can do up the math for you if you want, but I don't have time to look at it just now.
I suggest you aim for a rounded triangle, with each vertex close to the base of the closest pillar. That way, there are no points in the travel of any arm that are excluded by mechanical constraints. To do this, you need to set up the ratios so that one arm is completely vertical when the other two are completely horizontal. I can do up the math for you if you want, but I don't have time to look at it just now.