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.
Step 3: Simulation - Force Range
So, the amount of frictional force required is (.0574 kg)*9.8 m / s^2 = .563 N. This corresponds to a total normal force on the egg of (.563 N)/.079 = 7.12 N, or 3.56 N per side of the gripper. Therefore, we must apply a force between 3.56 N and 21.5 N in order to hold the egg without cracking it.
To find what force we can apply to the piston to achieve these forces at the gripper, we now open the same file in Autodesk ForceEffect, another app for your iOS or Android device
From this, we see that for a 10 lb force applied at the piston, approximately 2.8 lb are applied at the gripper to each side of the egg. Since the forces scale proportionately, for a 1N force at each side of the gripper, we will need to apply 3.57 N at the piston. So, we know that we should use a piston that must supply a force between 12.7 and 77 N in order for our design to succeed.