The concept behind the designs are to emulate the natural eyeblink to maximal degree possible. Specific designs are discussed in their subpages, overall requirements and a description of anatomy is provided here.
Eyelid closure occurs naturally via the activation of the sphincter like orbicularis oculi (OOc) muscle (pictured above, image from Grey's Anatomy). The eyelid is kept tonically open via the levator palpebrae superioris muscle (LPS) which becomes inactive during the blink impulse. The eyelid is brought downwards slightly due to passive muscle tension prior to activation of the OOc. The contraction of the sphincter like OOc muscle around the eyelid pushes folds of skin in the eyelid downwards and closed in a complex motion.
It should be clarified - the design is not required to account for eyelid opening. The LPS is generally unaffected and can open the eyelid open, only closure needs to be addressed.
Other key requirements are outlined.
Effectiveness of Closure
The device should achieve full closure. The force and displacement requirements are difficult to estimate as the vary for different closure mechanisms. However, for the linear sling design used by Tollefson and Senders to create an implantable closure device (effective on cadavers), force requirements were 654mN and 8mm closure (see reference  in Background). The actuator should ideally (although not necessarily) exceed these minimum requirements.
Closure should ideally occur within 80-100ms (natural closure times), however slower times are acceptable.
Ease of Use & Comfort
The device should be easy to apply and remove.
Closure should not be uncomfortable.
The device should not apply excessive force or displacement such that tissue is injured. It shouldn't cause irritation over long term usage (although this is hard to measure in this study.