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Question is in the title.

In other words: why aren't the cones made in such way that you can tighten them with a "normal" wrench? Is this only for historical reasons, or does it have any actual purpose?

Wikipedia article implies that the reason is that adjusting cone needs "lower torque". Fair enough, but how does the slightly different shape and the wrench being thinner ensure this "lower torque"? If that was really the purpose, then the cone wrench would need some ratcheting mechanism, otherwise, I could still use full force (and thus high torque) to tighten the cone.

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Isn’t it simply because there is not enough space for normal nuts/wrenches without increasing dropout-width?

You don’t need full-size nuts because those cones and nuts don’t really need much torque. It’s not done to limit torque, it’s simply exploiting the low torque requirements to build narrower.

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    Agreed. There's only 100 mm between locknuts. The only way to put wider wrench flats on the cones is to make the hub shell narrower to accommodate that width. That would reduce the bracing angle of the spokes, making the wheel weaker against lateral loads.
    – Adam Rice
    Jul 22, 2021 at 13:10
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    Other side of the answer is that in the bad old days bikes often came with a multitool for cones, bottom brackets, etc that was stamped from sheet metal. They were thin, and adding normal-sized wench flats would have increased manufacturing costs without any benefit.
    – ojs
    Jul 22, 2021 at 15:59
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Michael's answer is good - there isn't enough space for a full size nut.

But this leads to the next question.
Instead of having special wrenches why not just use normal nuts and get the spacing from somewhere else?

You'd have to make the hub flanges narrower or the drop outs wider and the axle longer. Everything is a trade-off.

If you make the flanges narrower you would reduce the lateral stiffness of the wheel.

Most front wheels are stiffer than similar rear wheels. Structurally, this is because front hub flanges are typically wider than rear hub flanges. Rear hub-flange spacing is constrained by industry-standard dimensions, such as cassette width, dropout spacing and symmetrical frames. Wheel Stiffness Test

If you keep the hub flange width the same the axle would need to be longer and the drop out wider.
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I'm probably saying this wrong (my physics friends please correct me)
The distance from the bearing to the drop out is longer meaning greater leverage for the forces transferred back and forth between the wheel and the frame.

The thinner cone and nut allows the axle to be as short as possible, the drop outs are closer together and the distance from the bearing to the drop out is reduced.

Thin cones and nuts also have benefits in frame design.

A bicycle is a system with a multitude of design trade-offs that impact one another.
Many rear wheels have spacers on the drive side that dramatically increase the axle length on one side in order to accommodate sprocket clusters. That being said, a thick cone to accommodate a normal wrench would only make it worse.

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