This was my third science fair project… in 8th grade. The full title was The Harmonograph’s Lissajous Curves Duplicated by Servomechanisms, and it won first place at Louisville Country Day School (General Division) as well as first place in the Kentucky State Science Fair (Junior Division).
The only photo of the machine that remains is that one at the top of this page, but basically, this had two parts. The first was a harmonograph, a delightful device that used two adjustable pendulums (with poured lead weights and setscrews to affix them to long dowels hanging from needle bearings), with blocks at the top coupled by universal joints to a drawing mechanism that could hold colored felt pens. Like an oscilloscope with sine waves applied to X and Y inputs, this drew Lissajous patterns on a piece of paper taped to the table.
But stopping there would have been boring. I bought some synchros (servomechanisms) from the venerable Herbach & Rademan mail-order surplus outfit in Philadelphia, and coupled them to the blocks at the top of the pendulums with rack and pinion gears. A second drawing table atop the first carried coupled pair of matching servos, which then duplicated the drawing created by the mechanical system.
Enabling this increased the load (I had no servo amplifiers) so the drawing would decay more quickly, and I had fun playing with inversions and swaps to create graphical variations. This was a fun toy, and I miss it!