Abstract: In a plastic lens grinding machine of the type having a head mounted on a base and adapted to carry a lens pattern and a plastic lens having a base curvature, the head is capable of movement parallel to the axis of rotation of the plastic lens. A carriage is mounted on the base and is movable perpendicular to said axis of rotation, with the carriage having an improved rotatable cutter with a cutting edge made of a metal of high hardness and adapted to be rotated at high speed in order to be self-coolant. A hydraulic damper is mounted on the carriage and connected to the base for regulating the gravitational movement of the carriage towards the axis of rotation of the plastic lens, thus regulating the engagement of the metallic cutter blade with the periphery of the plastic lens. An improved bevel aligning device is provided having a base curve cam connected to the head and a cam tracer connected to the carriage, with the cam having a surface forming the same base curvature as the plastic lens.