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Instrument for drafting Archimedean spiral 2

When green crank turns, orange roller traces on ground an Archimedean spiral. It is said in a book. However I do not know how to prove this. It is a dynamic problem, not purely kinematic.

Friction between the roller and the ground must be adequate to prevent the roller moving along its rotary axis.

In case no friction contact between the roller and the ground, the mechanism has two degrees of freedom.

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