This design uses two cams; one for the segments A, B, G and F (the upper cam), and a second for the segments C, D and E (the lower cam). 

The two cams are synchronized by three gears, the center gear being driven by a single inexpensive stepper motor. 

The cams are designed to move seven "slides" in a specific sequence in order to produce the displayed digits of 0 through 9.  Each cam has one slot for each slide under its control, and a pin on each slide rides in the slot of the cam controlling it.  As the cam rotates, the slots induce a linear motion for each slide from 0mm to 3.5mm.

Each of the slides drives a single segment.  A pin on the slide fits into a slot on the segment.  Slide movement from 0 to 3.5mm induces a rotational movement of the segment of 0 to 90 degrees.