A machine for grinding the peripheries of ophthalmic lenses to predetermined outlines is characterized by a head having a rotatable workholder for moving an edge of a lens against a rough grinding or finishing wheel and a pattern holder positioned vertically above the workholder for controlling movement of the lens toward and away from the grinding wheel. The head is mounted for horizontal, vertical and pivotal movement, is allowed to freely pivot during finishing or bevel edging of a lens but not during rough grinding, and is automatically locked against pivotal movement upon completion of bevel edging so that the lens may, if required, be returned to the same position against the finishing wheel. Circuitry controls movement of the head in accordance with the base curve of a lens to precisely position the lens with respect to the finishing wheel, and maintains the machine in each of its rough grinding and finishing stages for a period of time which is sufficient to complete the grinding operation and independent of the number of rotations of the workholder.