A three-dimensional printer positions a tool such as an extruder in three-dimensional space using a passive, i.e., non-motorized, z-axis alignment technique that generates z-axis movement based upon motorized movements along another axis. In this manner, intermittent z-axis step movements such as those from layer to layer in a multi-layer fabrication process can be performed without the need for an additional, dedicated motor for z-axis movement. The passive system may employ a variety of different gearing techniques to convert x-axis or y-axis movements into a z-axis movement under various conditions. For example, the three-dimensional printing tool may move to a predetermined position along a first axis (e.g., an x-axis or y-axis) where a passive gear assembly engages a rack or the like. When in this predetermined position along the first axis, the tool can move along a second axis and create a resulting movement on a third axis (e.g., the z-axis).