Many biomolecular motors catalyze the hydrolysis of chemical fuels, such as adenosine triphosphate, and use the energy released to direct motion through information ratchet mechanisms. Here we describe chemically-driven artificial rotary and linear molecular motors that operate through a fundamentally different type of mechanism. The directional rotation of [2]- and [3] catenane rotary molecular motors and the transport of substrates away from equilibrium by a linear molecular pump are induced by acid-base oscillations. The changes simultaneously switch the binding site affinities and the labilities of barriers on the track, creating an energy ratchet. The linear and rotary molecular motors are driven by aliquots of a chemical fuel, trichloroacetic acid. A single fuel pulse generates 360 degrees unidirectional rotation of up to 87% of crown ethers in a [2] catenane rotary motor.