I designed a few mechanisms for rotational-input three-clawed grabbers. Unlike planar two-arm grabbers, it isn't as simple as meshing two partial gears together. Radially symmetrical transmission of torque has to be used to ensure that all three claws receive input force. 

This claw design is based on central linear actuation. All three claws are connected to the same piston, so they all move at the same time. This design could be implemented with a lead screw, rack and pinion, or really any kind of rotational to linear mechanism. I used a crank. 

This design utilizes a central worm gear. Worm gears are radially symmetrical, so all of the claws can draw torque from it. The self-locking nature of worm gears make this mechanism especially resistant to opening. 

This is a close-up view of the worm gear

This is an incomplete implementation of a facial CAM idea for a claw