For theoretical calculations, we assumed an ideal servo lift of 57 oz-in and an ideal weight force of 16 oz. Using a lever attached directly to the servo and an assumed 2 inch lift, we found a max length of 3.56 inches. With the new length, we calculated the max lift from a 90° sweep. The theoretical max lift we got was 5.13 inches.
In practice, things were much more complicated. The direct lever connection was dropped in favor of a moving arm system in an attempt to eliminate the moment on the arm. In this system, there were L-shaped lifters and counterweights. We found that the lift of the servo was a bit less than advertised, settling on a practice torque of 44 oz-in. Also, due to multiple minor resistances due to the construction of the crane and friction points, we added 8.8 oz (generated from testing data) of minor resistances to account for additional forces. In the end, using properties measured from the crane, we ultimately found an actual practice lift of just about 2 inches. Unaccounted for in our calculations are also the minor deflections of, and torque on, the support shaft.
Materials Science Mumbo Jumbo
The components of 3003 Aluminum:
Per the above graph, 300 Aluminum is composed almost entirely of pure aluminum, alloyed with a very small fractional percent of manganese. We considered heat treating the given aluminum pieces, however manganese alloys of the 3xxx aluminum series are not highly responsive to heat treatment due to the fact that the manganese does not become more soluble at higher temperatures. Were the aluminum alloy provided a member of, for example, the 2xxx aluminum series containing alloying copper components, the copper would become more soluble in the solid alloy solution at higher temperatures and thus heat treatment would enable a greater copper inclusion percentage and, consequently, a heat-treatable alloy that could potentially be heated and quenched for increased rigidity and overall greater strength of the aluminum.
That said, the strength of 3003 aluminum can be drastically increased by cold working. This was a motivating factor in the decision to manually bend the provided aluminum pieces into L and U brackets. Permanent plastic deformation of the aluminum introduces and increases the number of defects, namely dislocations, into the material. These dislocations, in addition to the manganese inclusions in the aluminum lattice, eventually pile up in the material, inhibiting movement and ultimately increasing the strength of the aluminum.