# 24-262 Stress Analysis Project

## Brian Ferri, Maxwell Wilson, Krystina Calfo

### How Our Device Works

The primary objective of this project is to construct a servomotor powered mechanism under 20 oz. strong enough to lift a cylindrical weight by at least 2 inches without touching the perimeter of a wooden rectangular hole sitting between a clamping area and a vertical post. In order to accomplish this task, a rectangular base is positioned as the foundation of the mechanism in the clamping region. A triangular arm is attached to the rectangular base and travels through the larger wooden rectangular obstacle to the cylindrical weight. The strength attributable to a triangular cross-section inhibits unwanted torque from twisting and fracturing the arm, while three diagonal cross members mounted to the arm in tension reduce its movement. In addition, the cross beams are constructed so that when the force of the cylindrical weight is applied to the mechanism, they go into tension and not compression, and therefore resist buckling. This was accomplished by bending the aluminum to prevent the beams from bending or buckling, which ultimately prevents failure within the truss. Finally, a servo is mounted on a rectangular lever arm attached to the end of the triangular truss near the vertical post. A 4.0 ounce counterweight is attached at the opposite point where the arm contacts the weight, which aids the servo in providing the required torque to ultimately lift the cylindrical weight. Our mechanism weighs 19.3 ounces and lifts the weight between 2.5-3.25 inches consistently.

### Theoretical Calculations

In designing our device, we were required to consider a variety of stress analysis concepts, including bending, buckling, tension, compression, and torsion, just to name a few. Taking all of these into account, we could build a structurally stable aluminum truss that meets all of the project guidelines. But, what this fails to accomplish is to ensure that the mechanism lifts the one-pound weight a minimum of two inches. This requires an analysis of the torque from the servo and any assistive counterweights. First, it is necessary to determine the fraction of the servo’s maximum torque that is theoretically used to lift the weight:

Second, we must show that the length of the arm can reasonably lift the weight at least two inches. Because our design allows the weight to slide a small amount along the lever arm, there is minimal destructive interference between the weight and the lever arm traveling through its arc of rotation. Therefore, we can use a simplified theory to estimate the theoretical amount of lift. The servo’s angle of rotation is roughly 90 degrees, but the true rotation angle is inconsistent. The length of the lever arm is 5 inches. We can therefore use a right triangle to show that approximately the theoretical lift distance is 7.07 inches. This is obviously not attainable due to other things, such as torque limitations and other disturbances such as vibrations and potential places in the truss where the construction may not be as solid as expected.

### Unique Features

Our structure has three features that are unique, and that we are very proud of. First, we utilized triangle shaped truss to cover the distance from our base to the weight. Many teams seemed to use a rectangle shaped truss; however, we decided that a triangle truss would maximize its resistance to bending while at the same time decrease its weight. The second unique feature of our structure was attaching our counterweight oriented vertically, as opposed to horizontally, along the same plane as the lifting arm. By attaching the counterweight perpendicular to the lifting arm, and at the very end, we maximized the moment provided by the counter weight, because its center as mass was as far away from the fulcrum as we could get it. The final unique feature of our structure was the lifting cage we attached to physically lift the weight. Originally, we just used the black plastic lifting arm to lift the weight; however, the weight would slip off or get stuck and restrict our structures ability to lift. By attaching the cage to our lifting arm, we were able to successfully lift the weight and keep it from losing contact with our device.

This image shows the Delrin lever arm, with the servo approximately in the center, a counterweight on one end, and on the other end, our unique fixture for holding onto the weight while it is being lifted.

### What does this device look like?

This is a view of our entire device. Notice the 6" by 6" base connected to a support truss, which consists of a wider base and a long, slender arm that extends through the hole to reach the one-pound weight.

A close-up view of the long arm. Notice the triangular construction and the three additional diagonal members. The diagonal members are put in tension in order to reduce torsion and increase the structural integrity of the truss.