When I first did this type analysis, it was in the medieval ages, that is the only computers were main frames or micro-computers built and used by hobbyist. I used paper, pencil and a scientific calculator. It took about 1/2 a day to work out the basics and get initial results. Later on, as the world evolved, I used spreadsheet programs (SuperCalc was the first one I used, one of the early spreadsheet programs that you've probably haven't heard of). I've stayed with spreadsheet programs for this type of analysis, partly because I've never become comfortable using 3D CAD or solid modeling programs. Either 3D CAD or solid modeling programs should work, particularly if you need 3D graphics or animation. To my knowledge there are no rail or subway specific programs; I have seen several such animations and 3D models of station areas, track / train/ and adjacent construction that was done with off the shelf CAD and modeling programs. My personal opinion is that unless the problem under study is complex, they are not worth the time and cost of applying them, just because they can show pretty pictures. The problem is only 2D, hence I've never felt the need to do other than spreadsheets, of course your results may vary.
I've made a simple 2D drawing that shows the primary geometry. Hopefully I'll be successful in uploading it. This drawing is not to scale, the curve radius is much tighter, compared to the vehicle length than would be actual. Once you've got the basic geometry worked out, the various allowances become adds (or subtracts) from the offsets. In practice you can figure all the offsets as being parallel to the car's longitudinal center line. The several dimensions I've indicated are: Lcb/2 = 1/2 car body length, Lbogies/2 = 1/2 the distance between bogy centers, Offset mid = radial offset from the track center line at the mid car, Offset door = radial offset at center of a doorway from the track center perpendicular to the car body center line, W = car body width.
You probably have some specific designs and dimensions to work with, but some typical values I've encountered are vehicle lengths of 16 to 22 m, bogies spaced at approximately 60% of the vehicle length, curve radii on operating lines (not in yards and storage areas) greater than 200 m.
There are railroad standards and engineering analysis available, and these are often used, as appropriate for subways. However, most subway systems have many unique aspects that prevent wholesale use of the railroad standards. Each subway system is usually unique from others, which has kept the industry from standardizing much of the engineering into codes or handbooks. That is not to say that subway engineering isn't soundly based on recognized practice, but there is a strong element of picking and choosing the practice to be used at that site.
With regard to the comments raised about how rail vehicles negotiate curves, there is a common misconception that the flanges on the wheels steer the bogies and car around a curve. They don't, except in extreme situations. Most rail vehicles have wheels that are tapered (smaller diameter to the outside, larger diameter to the inside, toward the flange). As an axle set enters a curve the rail contact point moves laterally across the wheel, toward the flange on the outside of the curve (larger wheel diameter), away from the flange (smaller wheel diameter) on the inside of the curve. This difference in wheel diameters causes the axle set and bogie to steer into the curve. This coupled with a small amount of compliance in the axle's mounting results in a only a small increase in drag due to the curving. It also greatly aids axle and bogie stability, below the critical speed.
I hope this helps you. You are probably getting the idea that I am not going to give you a cook book, and that is correct as I don't have one to give.
