Design a logic circuit to indicate when a box is [...]
Do you have to build the physical circuit or is it just a paper design your teacher wants?
So I am having trouble with an actuator that will hold one ball and check if it's defective or not and then releases it at its proper designation.
If you send them down a vertical or slanted tube slighly wider than the largest ball and the smallest ball is larger than around half that width, two solenoids could be used. A blocking pin or a flat piece, spring loaded to block the tube (through the middle of the tube) will stop all balls and a similar second "gate" around a ball diameter lower on the tube will let you release one ball at a time. Each gate pulled open by a solenoid.
The inspection window can be a suitable opening in the side of the tube midway between the gates (as long as it's kept smaller than the balls).
Before releasing gate #2, be sure to close the gate #1 to block the rest of the balls.
If you cut a short piece of the same tubing and connect to the bottom of the first tube by a piece of suitable diameter hose, a servo could easily move the short piece in a semi circle and position it over (flared) tubes, leading to either the box, the reject bin or where else you want it to go.
Ten your logic just need to produce servo signals of the right width to select where the ball should go - after defects checking, but before release of gate #2.
I won't be having trouble with the defect detection because I will just use black-colored ball for defective and white-colored ball for non-defective.
That may get you in trouble, you little redneck - I bet you hailed for a White Christmas as well