This paper explores the requirements-based design and static analysis of a 6 Degree-of-Freedom parallel robotic headrest, of novel architecture, to counter head motion in vitreoretinal surgery. Upcoming therapy delivery interventions require micro-precision but should ideally take place under local anaesthesia. Therefore, breathing, spasmodic motions, and even snoring that often occurs need to be accounted for and if possible counteracted. Passive approaches that aim to constrain the patient’s head have not yet been fruitful, while invasive stereotactic fixation is naturally not an option. The proposed design respects ergonomic and surgical constraints to act as a headrest that will ultimately counteract patient motion. Static models are developed to understand the architecture’s characteristics, and performance metrics are devised for design evaluation. Finally, a prototype is presented.