Tracer, clamp, and object engager for holding and tracing a lens mount of an eyeglass frame, a lens, and/or a lens pattern, to reliably detect a shape thereof even when the shape includes high wrap

A tracer is provided for tracing a lens mount of an eyeglass frame, a lens or a lens pattern. The tracer comprises an object engager and an actuator. The object engager is adapted to engage the lens mount, the lens or the lens pattern. The actuator is adapted to move the object engager into contact with and then along the lens mount, the lens or the lens pattern in such a way that during movement therealong, the object engager remains against the object being traced even when the shape thereof includes high wrap. Preferably, the tracer has a shift mechanism adapted to shift the object engager from alignment with the lens mount to alignment with a second lens mount of the eyeglass frame. The actuator preferably is further adapted to trace the second lens mount in substantially the same way as the first. The actuator further includes a rotator and a pivot mechanism. The rotator is adapted to rotate the object engager along the object being traced. The pivot mechanism facilitates movement of the object engager toward or away from the axis as the object engager is actuated along the object. The object engager can extend or retract along the pivot mechanism. A clamp for the tracer and an object engager also are provided.