Vertical precision positioning is distinguished from positioning in horizontal plane due to the presence of gravitational forces that work differently in “lifting” and “lowering” modes. Vertical positioners also need a “locking mechanism” to avoid the unintentional lowering of the platform. We present a vertical precision positioner that works according to the “stick–slip” phenomenon. Using an adjustable offset coupling, the linear motion of a piezoelectric actuator is converted to the rotational motion of a low friction lead screw which results in the vertical motion of the screw. A microcontroller can adjust the grip, and hence the friction, between the coupling and the lead screw to ensure the uniformity of motion in lifting and lowering modes. The dynamic model of the mechanism is extracted, and simulations are performed to discover how the peak voltage and frequency of the saw-tooth signal affect the stick–slip motion of the mechanism. Additionally, equations are verified by comparing simulation results and experiments. They can be used in the control system design in future works.