A mechanical system opens a selected drawer in a multiple-drawer cabinet. The drawers are arranged in rows and columns. A selected drawer is unlatched by moving a rod which has protruding fingers, only one of which is positioned to engage a latch in a column of drawers. When the rod moves longitudinally, the selected drawer becomes unlatched. The unlatched drawer can open only to a distance determined by a cable which unwinds from a drum and passes around a pulley attached to the drawer. Thus, by controlling the rotation of the drum, the system can be programmed to open the drawer only to a distance which exposes the first non-empty compartment in the drawer. A computer controls the selection and opening of the drawers. The computer keeps a record of which compartments of each drawer have been emptied. Each time a drawer is opened, it is opened to the next non-empty compartment, allowing access to one and only one compartment in the drawer. The invention is therefore especially useful in dispensing medications and other similar articles in a hospital environment.