2012 Stress Analysis Project: Group 39
Christopher Holliday, Bryan Leach, Dan Murby
How the Mechanism Works:
Our mechanism uses a minimalist design that, given the moments caused by the large arm, exploits the fact that the materials we used were stronger in tension and compression than in bending. Our design features a cubic structure, with arms extending off one side of the top to provide the necessary angle for our T-beam arm to reach the weight through the smaller of the two holes. While we didn't use any reinforcements on the cubic structure itself, we used one reinforcement in compression and one in tension that connect the arm itself to the clamped base. Also, every component in our structure other than those expressly in tension were bent to have a more sturdy L-beam geometry. We used a T-beam geometry for the arm, because it maximized the moment of inertia so the deflection in our arm was minimized. We contemplated the stiffer I-beam design, but the stresses involved were not high enough to warrant the extra weight. The servo motor is encased in ¾ inch-wide aluminum, which was screwed into 1/8” thick extension from our arm. We chose this design to avoid torque about the axis of our arm, which caused excessive twisting in the arm itself. We determined that a 3.75” long lifting arm attached to the motor would provide enough height to clear the 2” minimum, but wouldn't exceed the 72 oz-inch maximum torque provided by the motor. After testing, the our mechanism provided 2.25” of lift and weighed only 9.5 ounces.
Motor Attachment: Our motor attachment used a very simple design. We screwed the servomotor to an L shaped component which was attached to the arm. We chose this because it allowed the downward force of the weight to be applied along the axis of the arm so bending would only occur in our arm's strongest direction.
We included one pre-compressed component extending from the clamped base to the point on the arm closest to the motor that we could reach. This caused an upward force on the cantilevered arm that helped minimize downward deflection.
A pre-tensioned component was also used to pull down on the furthest end of the arm. This served to alleviate deflection in our cube structure and direct more of the forces to points located near the clamps.
For our first design, we tried to go through the larger of the two holes. After attempting this, we realized that this caused a lot of unwanted torque in our structure, because we had to extend arms from our base much further than we do in our current design. Going through the smaller hole allowed us to more directly access the weight, so that we were able to directly attach to our base at one point, and use a small extension for the second point of contact.
Calculations and Predictions:
Our basic design principle was to use L-beams in our cube structure, to eliminate buckling in components in the base that were in compression. Our lifting arm was constructed from two L-beams connected to for a T-beam, which is stiff in the z-plane. Using this knowledge, we aligned the motor such that the forced was applied in-line with the z-plane, causing no torque around the axis of the arm.
In a world without friction losses or deflection in our project, an arm of 3.25” rotating trough 90 degrees would lift the weight 4.5”. However, due to deflection in the arm and base of our design, we lost about 0.5” of lift. Also, when our arm reached a certain point, it caused the motor to reach its stall torque. This accounted for the other 1.75” discrepancy between the ideal world and the actual results. At first, we did not believe that we would be able to apply enough torque lift the weight, so we were going to include a counter weight. However, when we looked at the calculations we determined that with a small enough lever arm, and if we could get the motor close enough to the weight for the arm to reach, we could lift the weight 2” without a counter weight.