  We analyze in some detail the recently discovered velocity quantization
phenomena in the classical motion of an idealized one-dimensional solid
lubricant, consisting of a harmonic chain interposed between two periodic
sliders. The ratio w = v_cm/v_ext of the chain center-of-mass velocity to the
externally imposed relative velocity of the sliders is pinned to exact
``plateau'' values for wide ranges of parameters, such as sliders corrugation
amplitudes, external velocity, chain stiffness and dissipation, and is strictly
determined by the commensurability ratios alone. The phenomenon is caused by
one slider rigidly dragging the density solitons (kinks/antikinks) that the
chain forms with the other slider. Possible consequences of these results for
some real systems are discussed.
