Substrate-handling robots for pick-place operations in semiconductor manufacturing applications are subject to strict substrate placement repeatability specifications. It has been observed that the placement locations at a given workstation tend to exhibit distinct clusters, each of which can be associated with another workstation accessed by the robot in the past, resulting in an undesirable increase of the overall placement repeatability range. In the present paper, this memory-like repeatability phenomenon is studied, and attributed to multistage synchronous belt drives, which are utilized to transmit motion from centralized motors to individual links and end-effectors of the robot arms. The phenomenon is investigated experimentally, and simulated using a simplified lump-parameter model. The effects of selected belt drive design parameters are examined, and the results are utilized to improve the positioning repeatability performance of a typical substrate-handling robot.