Limited Animation could be traced back to films like "The Newlyweds" by French animator Emile Cohl (1857-1938). He adopted this film from a popular comic strip by McManus in an American newspaper. It included recurring players, but featured little to no actual animation of them; most of the human figures were static. But it was later that this technique of Limited Animation was popularised.
Traditional animation, another technique in animation considered to have been started by Emile Cohl a French animator in 1908 with his film "Fantasmagorie". Disney later popularized this technique. Here the animation runs on 12-24 frames per second, almost replicating the simulation of reality. Using this heavy approach of animating frame by frame in one or two Disney dominated the Golden age of Animation. It was in this era a handful of Bosko cartoons in the early years of the Looney Tunes series did survive used the technique of Limited Animation.
Using this technique they could produce shorts comparable to the shorts given by Disney in just a half the budget to the budget of Disney. It was "The Drover Boys" 1942 an animated film by Chuck Jones that became the first prototype for Limited Animation but the pressure from Warner Brothers curtailed much further use of this technique. Studios like United Productions of America (UPA), Metro-Goldwyn-Mayer (MGM) and Hanna-Barbera revived this technique of Limited Animation. Initially it was a way to stand apart from Disney, but in very short order it became a popular way to save time and money.
The Animators could experiment with the different medium, style and art to any possibilities using Limited Animation technique. It was only after Bobe Cannon's (an UPA artist) animation "Gerald McBoing Boing" that Limited Animation was accepted in major Hollywood cartoon studios. Gerald McBoing Boing was shown in 1951 and it won an Oscar for that year.
A part of popularity of Limited Animation can also be attributed to the arrival of Television. TV had become a very common commodity in every household; soon everyone was hooked onto TV for entertainment at the expense of going to the Cinema. Weekly cartoon series on TV became popular. This became a challenge for studios to produce more number of animations in a short span of time. It was impossible to produce such mass of animation shorts in a short span of time using the Traditional method but could only be achieved using Limited Animation techniques. Hence, more and more animators and studios started adopting the Limited Animation method.