ANALYSIS
Review of Design 1 Analysis
In our initial design, assuming that the arm would begin angled 45° below the horizontal and would rotate the full 90° counterclockwise, we calculated the maximum lift height using the distance from the servo to the hook (3.25in). For this calculation, we also assumed that the servo would remain stationary and that the hook would move the weight strictly vertically. This way we could just compute the hypotenuse and therefore lift height to be about 4.5in.
Changes implemented in Design 2
Although our calculations were correct for the lift height, we had failed to consider the effects bending and twisting of the arm would have on the overall displacement of the weight. This was primarily because the arm we constructed couldn't be modeled as a simple structure such as an I-beam or C channel because of the braces within. Initially, we treated the arm as a C channel but it turns out although the arm looked like a C-channel, the internal forces were far greater due to the anisotropic design.
Our lift issues were further exacerbated by repeated testing and use, which led to permanent deformations over time that angled the lever arm downwards rather than parallel to the horizontal.
At this point we decided to make several key changes to improve our crane:
1) We rebuilt the base supports so that the loads exerted were more axial than bending.
2) We added a strut from the base to the lever arm to reduce the deformations caused by extensive use. This strut was able to act as a two-force member which reduced the length over which the arm could bend, making it more rigid.
3) We changed our hook grabbing system so the hook could adjust to provide the necessary force for vertical lift. Although we did not pay significant attention to how our arm contacted the weight, it turns out that this was key if the motor were to provide any vertical force rather than an angled force.
Results
Our crane managed to lift the weight 1.5 inches consistently. The theoretical lift height for a 90 degree rotation is about 2.3 inches. Theoretically, about 32% of the maximum torque provided by the counterweight and servo should have been needed to lift the 1 pound weight. It's not entirely clear why the crane wasn't able to achieve its theoretical maximums. The lever arm wasn't able to rotate through its entire range of motion. The weight may have been getting stuck on the hook as it didn't allow for a very large range on motion for the contact of the weight. It also seems that the servo may have gotten weaker after repeated use as earlier tests produced a lift of about 2 inches. We don't believe bending or twisting made a significant contribution to the observed discrepancy in lift height. The bending and twisting were severely reduced from the first design review where they made a significant impact on performance.