Apparatus and method for measuring displacements of a rotary or linearly-displaceable member by counting periods of displacement thereof along a predetermined displacement path, including a pulse generator located at a pulse-generation station proximate to the displacement path; and an electrical circuit controlled by the pulse generator to actuate a first sensor to sense the status of the displaceable member at the particular instant one of said second machine-sensible elements passes through the pulse-generation station, and to increment a counter in accordance with said status determination. In the described preferred embodiments, the second machine-sensible elements are magnetic elements; and the pulse generator includes a coil, a magnetic core magnetically coupled to the coil, and a spring-mounting for the magnetic core causing the core to move from an initial position in one direction with respect to the coil when aligned with one of the second machine-sensible elements, and to be returned in the opposite direction by the spring to its initial position, whereby the coil generates pulses during such movements of the magnetic core.