[2.70] Saint-Venant/ Shaft Torsion Board Problem

If you use a shaft to couple two gears-rack actuators to a carriage, how much positioning error and "racking" wobble result from having the motor offset to the side? How can I avoid such errors while bypassing Saint-Venant issues (due to actuating both ends of the carriage)?

Of course, there are other ways of getting away with the offset-motor problem. The carriage on a lathe is driven by a leadscrew mounted directly below one of the rails, which generally have one of these shapes:

2.70 2017 Lecture Week 2

You'd expect lathes to have the same binding/ yaw problems as the board problem above. Furthermore, several of them have a single dovetail rail:

Sharp 118H precision lathe

This includes the compound, which you could argue receives the same yaw-reaction moments from the tool without being as large as the carriage proper:

Hardinge DRC compound

A giant advantage these carriages have is that their direction of travel is parallel with the leadscrew, so shaft torsion-twisting is a non-issue. Their length/width ratio is also much better than the board-problem carriage - enough to avoid binding from Saint-Venants. They're also much more rigid, though rigidity of the carriage itself was not considered on the board.

So that's promising; if I wanted to use a long, central carriage for the desk I might not need to worry about centrally-locating the lead-screw. Something to think about.