Abstract: A variable speed transmission apparatus is disclosed for controlling the rotational speed of a fountain roller in an offset printing press. The apparatus includes a mounting plate adapted to be mounted about the shaft of the fountain roller. A screw mechanism is mounted on the mounting plate and has a sliding block or nut for controlling the position of a first link of a two-bar linkage having a common pivot axis connected to a reciprocating drive in the printing press. The second link of the two-bar linkage is pivotally coupled to oscillate a drive crank with a one-way bearing mounted on the fountain roller shaft. Changing the position of the first bar of the two-bar linkage gives infinitely variable adjustment of the oscillating motion of the crank and thus the rotation of the fountain roller. All of the components being mounted relative to a single mounting plate, the apparatus can be retrofitted to existing fountain roller equipment.