Cooperative robotic systems for vitreoretinal surgery can enable novel surgical approaches by allowing the surgeon to perform procedures with enhanced stabilization and high accuracy tool movements. This paper presents the optimization and design of a four-bar linkage type tilt mechanism for a novel Steady-Hand Eye Robot (SHER) which can be used equivalently on both, the left and right patient side, during a bilateral approach with two robots. In this optimization, it is desirable to limit the workspace needed for compensation motions that ensure a virtual remote center of motion (V-RCM). The safety space around the patient, the space for the surgeon's hand and maintaining positional accuracy are also included in the optimization. The applicability of the resulting optimized mechanism was confirmed with a design prototype in a representative mock-up of the surgical setting allowing multiple directions of robot approach towards a medical phantom.