The present invention relates to an apparatus for pumping or compressing a fluid, the apparatus characterized by a compression chamber including an inlet and outlet, opposed front and rear vane members disposed inside said compression chamber, each vane member including at least one axially extending vane segment and at least one radially disposed open segment adapted to receive a vane segment of the opposed vane member, wherein adjacent vane segments of mating vane members form radial compartments there between. The assembly further includes a swing arm assembly for effecting equal and opposite rotational oscillation of the front and rear vane members such that adjacent vane segments oscillate toward and away from one another simultaneously, thereby creating a bellowing effect which draws fluid into the chamber via the inlet and discharges fluid out of the chamber via the outlet. The invention further relates to an assembly for translating rotational motion of an input shaft to oscillatory motion of the vane members.