Stress Analysis Project
Justin Barsano, Kristen Hauser, Andrew Willig
May 6, 2012
Our mechanism can be broken into three parts: a truss with a 6” x 6” clamped base that extends approximately 11.5” left on the y field to clear the hole, an approximately 24” long I-beam to cover the distance between the truss and the weight, and a lifting mechanism attached to the end of the I-beam that would lift the weight.
The truss is designed to prevent three issues: buckling, twisting, and tipping. We used an L shaped beam frequently throughout the structure to increase the stiffness of each member. Diagonal members prevent twisting at the base under loading. The diagonal L-beams support the left half of the truss, which cannot touch the ground, from tipping. We removed several unnecessary cross pieces to decrease the weight. Similarly, the square piece of sheet metal serving as our base is probably unnecessary and could be either cut down or removed to decrease weight. The directions of all of the diagonal cross beams were chosen to be in tension or compression as needed.
We chose an I-beam shape because it is extremely rigid in the plane of motion. Because the weight is being lifted parallel to the height of the I-beam, torsion and buckling are not significant issues compared to bending. The I-beam is 24 inches long, which allows for a sufficient moment arm between the motor and the weight. The horizontal distance from the motor to the weight is 4.54 inches. The I-beam is 4 inches tall. We had originally made it taller to maximize its strength, but later decided that the extra weight would be better spent on the counterweight portion of the mechanism.
We chose a four-bar parallelogram linkage as our lifting mechanism in order to easily incorporate a counterweight. The bottom parallel bar is attached across the center of the motor, and the top is pinned. The distance between the horizontal beams was defined by the placement of the motor relative to the top of the I-beam. The vertical bars of the parallelogram ensure that both edges move approximately parallel to the weight as it is lifted. This is optimal for two reasons: the counterweight on the other end will only move up and down, and the beam that contacts the weight will remain stationary during lifting. The four-bar linkage is connected to the motor such that the lever arm for the counterweight is 7 inches, and the lever arm to the weight is 5 inches (to a total of 12 inches). We chose to offset the motor to create a bigger counterweight. This assists in lifting the weight.
We calculate the theoretical lift height of our four-bar linkage to be 7.07 inches given the following geometry:
2[5.0sin(45)] = 7.07 inches
The additional inch-long tab used to lift the weight does not affect the lift height because of the geometry of the four-bar linkage. It does, however, affect the torque required to lift the weight:
T = 16oz(4.54”) – 2.0oz(11”) – 72 oz-in
T = -21.36 oz-in
This result confirms that our mechanism can successfully lift the one pound weight. A negative torque corresponds to rotation in the clockwise direction, which is necessary
for the weight to be lifted.
We believe the following aspects of our mechanism are significant:
Four-Bar Linkage system – simplifies the lifting process by maintaining a consistent horizontal distance from the motor
Counterweight – relieves stress on the motor, incorporated without compromising weight
I-Beam – rigid and resistant to bending