A relative displacement control apparatus provides both coarse and extremely fine precise control over displacements between a sample and a detecting probe as required, e.g. in operations of optical instruments, analyzing instruments and scanning tunneling microscopes. This precise fine displacement is produced through a double-lever-action which is created substantially by means of an arm assembly preferably with a piezoelectric drive for precise displacement control, a support pivotally holding the arm assembly, a rigid arm fixed solidly atop the support and a pointed stop or "foot" fixed in the proximity of the free end of the rigid arm.