RC Servos are great because they are low cost, widely available, easy to control, and pretty accurate. One disadvantage is that they usually have very limited range of motion. This is because they are mostly for use on actuating RC control surfaces that rarely move more than 120 degrees.
Our FTC robotics teams uses them a lot; but, often we need to rotate more than 120 deg and often would like 360 deg or more. Robot design requires the solution to be small and light weight as it will usually be at the end of an extension arm. The game rules (and practicality) requires the solution to use a 3-wire RC servo. Also, space and alignment issues usually make using external gear sets problematic.
Last season we needed a large "grabber" at the end of our arm and resorted to using a continuous rotation servo the rotated until it torque limited. This worked but was far from ideal as it over-stressed the servo and we had minimal control on the "grabber" - we could open it or close it.
Our ideal solution would be small, light-weight, and inexpensive (add less than 50% to the weight, cost, or the length of any dimension of motor).
Given our constraints, how can we rotate an axis more than 360 deg and still maintain positional accuracy?