Spirograph

Pin a toothed ring to the table, roll a smaller gear around the inside of it, and drop a pen through one of the little holes. The pen never lifts — it just gets carried around twice at once, and the loops it leaves behind are decided entirely by the two tooth counts. The drawing closes back on itself only when the gear returns to the tooth it started on.

drawing
90/34·27
loops45
turns to close17
gear ratio17:45

Gears

Distance from the gear's centre. At 0 the pen sits dead centre and draws a plain circle.

Readout

0%drawn
0/17turns done

Loops and turns are worked out from the teeth, not guessed: divide both counts by their largest common factor and you get turns : loops exactly. Two gears that share no factor take the longest to come home.

Motion & ink

Your system asks for reduced motion, so each pattern is drawn complete in one go instead of animating.

Gear pairs