Flip-dot displays, which use a matrix of actuators to move mechanical pixels into place, are very interesting. At one time they were even very common for transportation displays and the like, where information changes only incrementally.
While modern makers do experiment with such displays, the basic problem with setting one up is that each display unit requires its own actuator. So a 10x10 display would require 100 servos, electromagnets, etc. to flip the dots – a number which increases with the resolution. Various forms of multiplexing are used to simplify the design of electronics displays, so could the same be done with electromechanical flip-dot outputs?
In the video below, James Bruton answers this question with a five column by three row flip-dot display that employs only three servos, plus a DC motor with an encoder onboard. The DC motor moves the three servos into position with a lead screw, which pushes and pulls the semi-circular dots in position for display via four-bar linkage assemblies An Arduino controls the system, along with an L298 motor driver.
Although a prototype, Bruton is able to use this setup to count up to six using a dice pattern at around 10:00 in the video below. While there is some complication making sure each servo is in position to clear the linkages and the refresh rate is rather slow, Bruton goes over how this could be improved toward the end of the clip. It's still something of a proof-of-concept, but it’s easy to see the benefits of such a system as the number of dots increase.