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Epicyclic Gears

System 1

epicyclic

The grey gear of radius a is fixed, an arm joins the two centres of rotation. For each rotation of the arm the green gear will rotate once plus the ratio of the gear radii.

System 2

epicyclic

The grey gear of inner radius a is fixed, an arm joins the two centres of rotation. For each rotation of the arm the green gear will rotate once minus the ratio of the gear radii.