This may best be posted in "Linear and Rotary Motion" under "Mechanical Engineering".
You didn't give much information...
How much travel will there be?
How much weight are you moving?
How fast does it need to move?
You might take a look at the method used in some older photo copiers and flat bed scanners for moving the scan head/lamp assembly. They used a small drum with plastic coated steel cable wrapped around it attached at the center. With a couple of wraps from the center of the drum on one side, the cable then extends the length of the bed, around a pully, and back to the scanner head positioned near the drum. Many wraps (just a bit longer than the travel) are wrapped from the center on the other side, and then attached to the scanner head. Turning the drum moves the scan head. The cable on the drum does not over lap, just a single layer.
I scrapped a tape archive library machine that used this method for linear motion in both X and Y axis. The motors and drums were stationairy.