A positioning system for a sample testing machine includes a base pan and a set of independent drive systems for sliding a sample tray across the base pan. Each of the drive systems includes a paddle that engages a side of the sample tray. The paddle is slideably mounted to a shaft with a collar that slides over the shaft. A motor and drive belt is provided to move the collar along the shaft, causing the paddle to engage the side of the sample tray and slide the sample tray across the base pan. Track sections are provided in the base pan to prevent the sample tray from rotating as the paddle slides the sample tray across the base pan.