The controller prototypes used in the electrical development lab used a yoke and gimbal mechanism that came from an RC airplane controller kit. This simple design gave smooth linear control and was highly reliable. The production controllers were quite different and a great disappointment to the electrical and software development teams. The design of the analog joystick, which used a weak rubber boot rather than springs to provide centering, proved to be ungainly and unreliable. They quickly became the Achilles' heel of the system because of their combination of an overly complex mechanical design with a very low-cost internal flex circuit system. Another major flaw of the controllers was that the design did not translate into a linear acceleration from the center through the arc of the stick travel. The controllers did, however, include a pause button, a unique feature at the time. Various third party replacement joysticks were also released, including those made by Wico.
Source: Wikipedia, "Atari 5200", available under the CC-BY-SA License.