Simulation of Robotic Arm Gripper

Every year, I participate in a challenge called the FIRST Robotics Competition. I and my team must come up with a robot design that must meet certain specifications in order to compete successfully. Most years, my team has built prototypes to see whether a design has merit. Here, I show an alternate method, using a physics simulation application, Autodesk ForceEffect Motion (available on your favorite iOS device), to test designs in a similar manner.

As an example, suppose I was to build a mini robot arm to pick up a chicken egg. We would like to pick up the egg easily, so we will require there to be an inch of clearance on each side when the gripper is open. Such an arm might look something like this. Some considerations must be taken into account in order to pick up the egg successfully.

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.

Now, we have a potential design that we would like to see if it meets our criteria. Here is the design sketched using Autodesk ForceEffect 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.

Now, we need to make sure that we do not crack the egg. To ensure this, we need some parameters. After a quick search, large eggs have an average mass of 57.4g with a breakage force of 43N. Lastly, the coefficient of static friction between a large egg and rubber is .079.

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.