What was the initial function of the earliest devices separating pedal speed from wheel speed?

Answer

To increase wheel rotation relative to the pedals or to introduce a freewheeling mechanism.

Before the comprehensive multi-speed systems emerged, the earliest mechanical tinkerings focused on solving the immediate limitations of direct drive on high-wheelers. This involved initial attempts to achieve a mechanical advantage that sped up the wheel relative to the leg cadence, or conversely, to introduce a way for the wheel to continue spinning when the rider stopped pedaling (freewheeling). These efforts laid the conceptual groundwork for variable transmission even if they did not immediately result in selectable, rider-controlled ratios.

What was the initial function of the earliest devices separating pedal speed from wheel speed?
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