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Note: Velocity Analysis and Mechanical Advantage was not calculated as the velocity at which the mechanism moves does not matter as long as the mechanism reaches its final position. Additionally, there is no output force the mechanism has to output as it operates, however, at the end the mechanism becomes static and will hold a certain force (but that is a statics problem).
A static force analysis of the tray in the final resting position was conducted by modeling the tray as a simple beam supported by two point loads (the pin joints P1 and P2) counteracting the force of a hypothetical mass that would be placed on the tray at an arbitrary distance b away from P2. Summing the forces and moments together found that the forces experienced by the pins in the y-direction were equal to the equations found in the table below
| Force | Equation |
|---|---|
| P1y | (-mgb)/3.25 |
| P2y | (3.25mg+mgb)/3.25 |
The mass of the tray itself would also, in practice, add some amount of force to the pin joints. For the purpose of this analysis, we assumed that the weight of the material would be so small as to be negligible. At this stage of the design, many of the measurements and properties are still theoretical.
Physical Prototype
Our final prototype is seen in the figures below. Here, the 3D mechanism is shown, however, the cupholder “top” has not been attached. Instead, two frames exist which will deploy at the same time. For the final product, the box surrounding the mechanism will be wood. The top of the cupholder (the part that deploys) will also be wood, and will be between 4-6” wide, giving plenty of space for a cup. It can be seen in both the deployed and stowed position, very similar to the iteration.
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