Range of Motion - Volume

I have a kinetic staircase in grasshopper that rotates eccentrically (and shifts slope, scale, etc based on that rotation). I am trying to figure out a way to define the volume that is the sum of all of the possible positions of the staircase, ie. the volume that defines the area within my building that I need to make sure is empty in order to ensure that the staircase will not hit anything as it moves. 

The staircase's movement is all governed by one number slider, so my quick fix was to replace that slider with a series component, which gives a good approximation of the volume I'm looking for (screenshot attached, staircase in red volume in gray- you can see that it jagged since the series only has 50 numbers in it, rather than smooth as it would be if it were infinite). The only problem is that I can't really do anything with this volume afterwards since it is made up of hundreds of boxes. When I try to boolean union these objects in Rhino, it fails, and trying to split a plane through all of these boxes to get an outline causes my computer to freeze. 

Does anyone know of a way to find the true range of motion volume that I am looking for, or a way of working with the output that I already have that won't cause my computer to freeze? 

Thanks!