My current automata project involves several cables to actuate the character's movement. There are some tricks to make what seems simple in concept work efficiently. A lot has to do with the tolerance of the components.
To make a 90 degree rotation it is easy enough to calculate the theoretical amount of cable that runs off a wheel of diameter D. Length=(Pi*D)/4, this of course if the diameter truly is made as D" and that a cable fastener does not alter the arc of the cable path.
Translate this down to where a follower runs on a cam to pull on the cable. Any variation in the cam diameter will cause a little movement on the cable which will potentially move the character. For example the roller on the follower, if used, must be round. The size of the cam itself can have a significant impact on this sensitivity. You most cut the diameter steps on the cam to pull the cable precisely D". Often the pull point of the cable is different than the point where the roller rests on the cam and a multiplier for the correction cable length movement is used to determine cam diameters.
Tightening the cable to the exact length can also be a challenge. Usually the best method is some kind of crimp fitting that can be adjusted on final fit up.
All in all I find it finicky and usually experience many moments of frustration before being satisfied. Such is the life when toying with automata.
Automata is a creative blend of my life interests , engineering, art and woodworking.