11 - Project Analysis and Prototype

Kinematic Analysis

The mobility and grashof conditions were calculated for the team's project as well to determine the number of degrees of freedom and how many links will be able to fully rotate. Since the mechanism has one gear constrained input link that leads into a simple four bar mechanism  the mobility calculation was quite simple. In the end this mechanism has 1 DOF. Additionally, this mechanism is a non-grashof mechanism as the sum of the shortest and longest link lengths are greater than the other two links added together. Therefore, no link will be able to fully rotate in the mechanism.

Below shows the initial position of the mechanism using the position analysis. We can see all the links in their correct positions and ready to be moved.

Additionally, through position analysis we could plot the input length position as a function of the input angle theta2 (for the simple four bar mechanism) as well plotting the x and y coordinates of joint A.

Additionally with these graphs the team also created graphs showing the position of joint B and point C on the mechanism with respect to the input angle theta2 as well as their x and y coordinate.

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

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. 

Iteration Documentation

Our very first iteration was some made of cardstock and thumbtacks. In this way, the desired motion could be visualized. While very simple, this two component iteration allowed us to realize the viability of the project. 

The next iteration was made from Legos. As seen below, it used gears to properly deploy and moved very similarly to the prototype. This helped us figure out exactly how we could use gears to our advantage. At the time, a belt and pulley system was also considered, however, being able to build a system making use of gears helped us decide that would be the path forward. 

The final iteration before prototyping was again just 2 dimensional. It consisted of 3D printed parts that we were able to easily adjust until everything worked as expected. This iteration even made use of a servo motor to ensure the motor would have the torque required to deploy the cupholder.