I'm envisaging a solution where each cylinder/axis has some sort of position encoder attached which sends a train of pulses to the Arduino, and the Arduino determines the average pulse frequency over some time period and calculates a surface speed from that. Is that the sort of thing you're looking for?
I haven't quite figured out what units you're working in. What sort of range of rotational speed are you going to need to measure? How precisely do you need to know the speed, and how often do you need to measure it? (Average per revolution? Average per hour? Average per degree of rotation?)