Picture a wheel with a ring of small teeth standing out around its edge. The teeth are not there to meet another wheel; they are there to drop into gaps — the links of a chain, or the row of little holes punched along a strip of film. Turn the wheel and the teeth pull that band along, one notch at a time. Every use of sprocket can be traced back to that one idea: a small tooth sticking out, fitting into a gap.
From the word’s history
Wiktionary records the origin as unknown, first attested in the 16th century, and only guesses at a link with spoke, spike or spur. That guess is not settled, but it points in the same direction as the modern picture: something that sticks out to a point.
Wiktionary 說這個字的來源不明，最早見於十六世紀，只推測它可能和 spoke、spike、spur 有關。這個推測沒有定論，但方向和今天的畫面一致：一個往外凸出、帶尖的東西。
Wiktionary entry for sprocket (kaikki:3f6f69a190036ae4:1039331668): Unknown. First attested in the 16th century. Perhaps related to Italian rocchetto, spoletta, sprone, or English spoke, spike, spur.
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