Square(ish) Orbit Mechanism

Observing the brightly coloured marker at the end of any arm, you’ll see it follows a square(ish) path, thanks to a short but cunningly contrived train of gears near the centre.

Questions

  1. Can you think of the piece of equipment, used daily in many households, where movement like this would bring real benefits?
  2. Can you work out the gear ratio needed to achieve this motion?

Answers in the comments please!

Near-miss Answers

1a) A Meccanograph incorporating this idea might produce interesting patterns, but it’s hard to see how to avoid them being rather wobbly.

1b) This idea has been proposed for boring square holes, but I’m not aware of anyone making it robust enough to work with real materials. (Nowadays spark erosion or electro-chemical erosion would probably be far more practical for boring a square hole in metal.)

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