The present disclosure provides a polar coordinate positioning system. The system can be used, for example, to sample a microtiter plate or sample tubes. In some embodiments, the system orients a sample with respect to a sampling tool using polar coordinates. In some embodiments, the sample is configured to rotate about an axis and move linearly in a direction transverse to the axis, and the sampling tool is configured to move linearly in a direction transverse to the linearly movement of the sample.