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    Do the maths. Correct axis distance between sprockets in a roller chain drive is invariant for non-circular sprockets only as long as both sprockets are the same shape and size and they are clocked together. For drives where only one sprocket is non circular, the correct axis distance changes in a way which can be disregarded for practical purposes if the following conditions are met:

    1. The non-circular sprocket has rotational symmetry of order 2n
    2. The axis distance is large compared with the difference between the roller pitch radii of the two sprockets
    3. The drive speed is low enough to permit a large negative tolerance on axis distance because centripetal acceleration of the chain is too small to cause problems

    These conditions are generally met on practical bicycle drives.

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