I hope this is a well-defined question!

I'm interested in a general formula for the area shaded in blue as you roll four interlocking (perhaps geared) wheels as shown in the diagram above. Sounds like a nice advanced GCSE or O level question? Assume the wheels have the same radius r. What is the minimum and maximum of the shaded area?

This will stop me playing around with biscuits. Perhaps I need to buy some Meccano.

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