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Chain whips on the market can be classified into ones:

Yet both amateur and pro mechanics report that the fixed-gear variety works just fine for all sprockets. This makes sense, if the main difference between a fixed-gear chain and a 12/13-sprocket chain is mainly the length of the pins, with minimal difference in the thickness of the side plates, then a fixed-gear chain can be used. It is just that the torque will be offset, applying forces outside the plane of the cog. Out-of-plane forces on a cog should be of no concern. They would be no different than someone trying to switch gears while climbing—when the chain will also pull on a cog out of its plane. It's not ideal, but within working tolerances.

Why are there so many varieties of chain whips when a fixed-gear chain whip works for all styles?

Is it only that the chain whip wraps well around just the smaller cogs, where a wider chain wouldn't fit, but does not quite hold leverage around largers cogs, where it would fit, albeit askew?

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    I have exactly one chain whip, and it works on everything. Guessing it might have an issue on a cassette where the tooth count different is so small that a chain has to sit between two adjacent sprockets, but that's unlikely on the big cogs where one would use a chain whip for leverage. Perhaps an 11-20 corncob style of cassette would do this? Great question
    – Criggie ♦
    Mar 3, 2022 at 21:52
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    Because no self respecting fixie rider would allow non-fixie tools near their bike.... :)
    – mattnz
    Mar 4, 2022 at 0:30
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    Just in case there's a customer who buys every tool available?
    – ojs
    Mar 4, 2022 at 8:32
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    @ojs Until now I hadn't really laughed on bicycles.SE. Thank you. What you wrote is funny (intentional or not) because I'm just at that stage where I have too many tools to store in toolboxes, but too few to display.
    – Sam7919
    Mar 5, 2022 at 4:01

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This answer is an educated guess.

Any chain whip will wrap around a cassette's smallest cog. A wider (fixie) tool will protrude, but that's not a problem. There will still be plenty of room left for the lockring tool.

A fixie (or in general wider) chain whip cannot be set on the second (from smallest) to, maybe, sixth cog (image source). The pins of the chain are too long, and the two adjacent cogs on both sides will impede proper wrapping of the chain whip. The side plates will basically sit on the next smaller cog.

On the larger cogs on an MTB (7-11, maybe) the diameter difference to the next smaller cog will be large enough that once again any tool can be used.

On most road bikes the chain whip needs to have a narrow enough chain, or use a fixie chain whip on the smallest cog, or on the largest, if the whip's chain will not scratch the spokes (or the plastic disk).

Examples

To use the third cog as Calvin Jones does here, the right sized chain whip is needed.

chain whip on third cog

To use the first cog, any chain whip will do.

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  • Using the small cog isn’t a great idea because it usually has the least engagement area with the splines (with HG drivers at least.) Also, you may run into clearance issues with the dropout.
    – MaplePanda
    Mar 5, 2022 at 15:42
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    I generally wrap the chain whip around the second or third largest cog because the risk of damaging spokes is lesser in case the whip jumps off the teeth.
    – Carel
    Mar 31, 2022 at 14:24

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