Linear actuators of the type you describe have been used for years in tape archive robotics. Most use a stepper motor driving a taut wire rope (aircraft cable) over pulleys in a continuous loop. One of the largest I worked on was an Ampex ACR225.
http://www.lionlamb.us/quad/acr225.html
This machine could hold up to 256 D2 video cassettes and pick and inject a tape in one or two seconds. (Depends on where the arm is located, what cassette it is commanded to pick and what transport it is loading.) The robotics assembly required interlocks as the mechanism moved so quickly it would easily take your hand off if it were in the way. The
linked in the article above shows the front of the machine. The black area is the tape cassette storage. The robotics needed a calibrate routine where the picking arm would need to sense the edges of each of the cassette bins. It did this by using a touch sensor and moving until the sensor touched the sides and bottom edge of each of the 256 bins. This routine took quite a while but it was fascinating to watch. The pick mechanism was an X-Y robot with grabbers that would position at a bin opening, grab the cassette, pull it out of the bin and then place it in one of four tape transports. Each cassette had a bar code label that the machine would use to identify the location of each cassette. The robotics rarely needed calibration but they did require regular maintenance. The vertical and horizontal devices moved on polished shafts with high speed linear bearings. Keep it cleaned and lubed and it didn't give us any problems. Same type of X-Y system is used in robotic inventory systems.