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.
General
Content
Integrations