An improved method is provided, for pumping fluids, such as water and/or hydrocarbons, from a subterranean formation or reservoir, through use of a cranked rod pumping (CRP) apparatus for imparting reciprocating substantially vertical motion to a rod of a sucker-rod pump having a pump stroke. The CRP apparatus includes a motor driven cranked mechanical actuator arrangement. The cranked mechanical actuator arrangement includes a substantially vertically moveable member attached to the rod of the sucker-rod pump for imparting and controlling vertical motion of the rod of the sucker-rod pump. The actuator arrangement may include pneumatic counterbalancing.