As mentioned previously, I went through several iterations of the design before settling on the final design that met my requirements. My first iteration did not even involve a geared five-bar mechanism - it was a simpler four-bar mechanism, with a similar spinning platter for the paper as the final design. The spinning platter in this design was coupled directly to the input of the four-bar linkage via two gears, meaning that the motions of the platter and the input link were always in phase. In my prototype of this design, the gear of the input link and the gear of the platter had a 1:3 ratio, resulting in the motion seen in the video below. I suspect that for gear ratios where neither number is 1, the motion would be slightly more complex, and the end of the line drawn by the pen would take much longer to meet back with the start.
In the end, I decided that the pattern produced by this mechanism was not interesting enough, so I moved to the next iteration of the design (still using the four-bar linkage). A CAD model of this iteration can be seen in Fig. 5. I thought that by decreasing the gear ratio between the input gear and the platter, I would be able to slow down the rotation of the platter and create a more complex design. Thus, this iteration involved a geartrain, which would have resulted in a 4:25 reduction in angular speed from the input gear to the platter. At this point, the mechanism seemed a little too complex, and the geartrain was taking up too much space. Thus, to increase the complexity of the mechanism's movement without too much added complexity, I settled on the geared five-bar linkage seen in the final mechanism.
Figure 5. CAD model of the second prototype iteration.
For the final mechanism, most of the gears were laser-cut out of 3mm thick acrylic, with a few gears made laser-cut with 3mm thick plywood. I chose these materials since they were easily accessible for free at Texas InventionWorks, and I decided on using acrylic for the majority of the mechanism since it doesn't splinter like plywood does when machined (although cracking turned out to be a slight concern later on). The gears and linkage were fixed to a 1ft x 1ft piece of acrylic for structural rigidity using M3 bolts and nuts, since they were also accessible and easy to use. To solve the issue of the platter not spinning slow enough, a second stepper motor was used to drive the platter in the final mechanism. Although this does not align with the initial project goal of creating a 1-DoF mechanism, it enabled far more customization and simplified the building process significantly.
