Step 1: Concept
First of all, the arm must be able to pick up the egg without dropping it. Secondly, the egg must not break when it is picked up. As a result, there should be a range of forces we can use on the egg.
The design of the arm will consist of two four-bar linkages for the two sides of the gripper, with a piston supplying the force. The head of the gripper will be coated in rubber.
Step 2: Simulation - Check range of motion
To see whether it will pass our one-inch clearance requirement, we can trace the tips of the gripper to see its arc of motion.
Looking at the graph information, we can see that the peak displacement for each side of the gripper is 1.018”, so this design does indeed pass our clearance requirement.