My problem is linear motion in a vertical position I'm moving a slider up and down that moves a 0.5mm thick cross hair laser line at 4 meters from its target.
The sliders are being moved by a parallel system using micro sliders from igus at 50.4mm apart from each other.
The motion system is to one side of the slider it is a nut and screw system the screw is 4mm dia with a lead of 0.5mm with an anti backlash nut.The nut
Is attached to the slider and the screw to a fixed base. When the screw turns vertical up or down my laser cross hair shows an odd movement (example vertical up) as it moves upward it has a down step
It's swaying up and down with the rotation of the screw on its's way up. Any ideas on how to prevent this from happening.

I'm having a hard time visualizing what your system consists of. Could you post a drawing of how it works?