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This paper presents a unified mathematical framework for modeling and evaluating the performance of multiple robotic arms that operate on hollow suspended organs. This framework is applied to a novel two-armed hybrid robotic system being developed for ophthalmic vitreous surgeries. Four cases are designated to capture the general movements required for any surgical procedure associated with hollow suspended organs. Dexterity measures, based on multiple characteristic lengths, are presented for procedures corresponding to these manipulation cases. Simulation results of the dual-arm robotic system for ophthalmic surgery are presented for all four manipulation cases. A comparison of this robotic system with current surgical tools shows a significant improvement in intraocular dexterity.