The problem with the Boebot design (which uses a set of struts that form a parallelogram, thus always keeping the ends paralell) is that is still moves the tips of the gripper OUT as it clamps.
That was unacceptable for a gripper I built, so eventually I found a linear roller slide track, combined with a screw thread or acme screw, did the trick. Attach your gripper to the slider, move it with the screw thread or acme screw, turned by a servo or stepper motor.
Got a 4" grip, perfectly linear clamping action.
Have fun!