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.
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.
Three branches
咬住鏈條的齒輪，和它的齒
這一族就是核心畫面本身，只差在你看的是整個輪子還是其中一顆齒。
noun · C1
A wheel with teeth around its edge. The teeth fit into the gaps in a chain, or into the row of holes along a strip of film, so that when the wheel turns it pulls the chain or the film along with it.
鏈輪
屋簷下墊高的那一小塊
共通的地方是「從邊緣凸出來的一小塊」。這是形狀上的聯想，用來幫助記憶，不是說它和鏈輪出自同一條歷史線——這個字的字源本身就沒有定論。
noun · C2
In building work, a short piece of wood fixed at the bottom edge of a sloping roof. It lifts that edge a little, so the last part of the roof is less steep and rain runs off further from the wall.
屋簷起翹墊木
舉例時借來當產品名
正因為鏈輪是個沒人會特別在意的小零件，它才好用：拿來當例子時，沒有人會去想那是什麼，注意力就留在數字和論點上。
noun · C1
A made-up name for some product that nobody needs to name, used in examples, maths problems and business talk when it does not matter what the thing actually is. It is usually paired with widget.
隨便舉例用的產品名