About the Mechanism
The mechanism lifts the weight by using the servo to rotate a long lever arm with a light counter-weight. The lever arm is supported by a truss designed to be stiff in both bending and torsion. The truss is supported by a single aluminum U-channel for simplicity and ease of construction. The U-channel is securely attached to the base and further reinforced to make it as rigid as possible.
Theoretical Analysis
The design project requires that a mechanism be built which can lift a 1 lb weight, 2 inches with a standard servo motor in one continuous rotation. The main constraints on the mechanism are the limitations of the servo motor and the 20 ounce weight limit on the mechanism. First, static analysis of the lever arm used to lift the weight must be performed. Since the mechanism must not be initially in contact with the weight, it can be reasoned that the servo must be able to maintain the lever arm in static equilibrium under both conditions of not lifting and lifting the weight. In the following figure, these two configurations are modeled by a lever arm with constant linear density and a counterweight.
From these equations it is clear that the maximum length of a is entirely dependent on known constraints; the weight and maximum servo torque. Furthermore b is dependent on the chosen counterweight and linear density of the lever arm.
Since a constraint of the design project is the 20 ounce total weight, q and C should be chosen to minimize weight. The following figure shows two contour plots, total weight (curved lines) and total length (straight lines), versus linear density and counterweight.
The lever arm must resist bending in both directions perpendicular to its length, so the provided aluminum strips must be bent into an L-shape along its length. Furthermore, the aluminum strip must be wide enough so that it can be bent and easily attached to the servo. These two conditions led to the decision to use the 0.75” wide aluminum strip, which has a linear density of 0.0297 oz/in. Additionally, the bending brake available in the undergraduate lab is 42” wide, so the maximum length of the lever that can be made in this design is 42”. Therefore, from the contour plot, the counterweight must be about 0.7 ounces.
In the construction of the prototype, the group made a lever arm a total length l of 42”, length a of 5”, and counterweight of 0.7 ounces. Substituting these values into the static equilibrium equation above yields:
Additionally, using length a of 5” and servo angular range θ of 100 degrees, the lift height h is:
Since the maximum torque of the servo is 42 oz-in, only 83% of the maximum servo torque is necessary to lift the weight. The theoretical distance is much greater than the necessary distance of 2", although the actual distance lifted will be less than the theoretical distance since the lever arm cannot maintain contact with the weight through the entire range of motion.
Unique Feature
The mechanism uses a 42 inch long lever arm that hangs off the side of the table and drops below the plane of the playing field as it lifts the weight. This design feature enabled the team to use a very light 0.7 ounce counter-weight, in contrast to the much heavier weights used by other teams. This, combined with the single piece construction of the lever arm, minimized the total weight of the mechanism. The analysis section above provides further explanation of the reasoning and evidence to support this design decision.
