An eye-contact assembly for stabilizing a patients eye at a selected position in an external coordinate system, comprising an eye-contact member having an inner contact surface for contacting a front surface of a patients eye, an outer surface and, a vacuum port formed within the eye-contact member by which a negative pressure can be applied between a patients eye and the contact surface, to stabilize the position of the eye with respect to the contact member, a positioning arm for positioning the eye-contact member at a selected position, with a patient eye stabilized therein, and releasable coupling members carried on the contact member and positioning arm for releasably coupling the contact member to the arm with a release force sufficient to allow the contact member and a patient eye stabilized therein to be moved by the arm, and to release from one another when an above-threshold force is applied by or to the eye.