<p>One characteristic of rack-and-pinion drives is backlash. In non-high-precision machine tools, a certain amount of backlash is tolerable. Nevertheless, monitoring the size of this backlash gives more insights into the condition of the whole machine tool. Usually, rack-and-pinion drives do not have an output-side position measurement, and therefore, measuring the backlash size is an extensive manual operation using additional measuring equipment. In this work, a method for an automatic estimation of the backlash size is presented. During a small positioning step of the drive train, the accelerations of the motor and the moved mass are measured. For this purpose, an additional accelerometer is mounted on the moved mass. The section where the tooth flanks of the rack to the pinion change is identified out of the recorded acceleration curves using different supervised learning classification methods. The classifiers are trained with simulation data and the trained model is applied to measurement data. A random forest classifier and a <i>k</i>-nearest neighbour algorithm achieve the best estimation accuracy. From the identified backlash section, the size of the backlash gap can be calculated. With this method, a robust backlash detection is possible without previous test measurements on the individually investigated machine and without manually tuning the estimation algorithm.</p>