Picture one round body that keeps turning over as it travels. That turning is the whole word. A wall gets painted because the round body rolls up it; a lawn gets pressed flat because the round body rolls over it; a heavy boat moves because round logs turn under it; hair holds a curl because it is wrapped round a small tube; a wave arrives because a long wall of water has rolled all the way in from the open sea. Change the size, and change what it touches, and you have almost every meaning of roller.
From the word’s history
Wiktionary records roller as Middle English rollere, that is roll plus -er: the thing (or person) that rolls. The modern uses all sit directly on that literal build.
根據 Wiktionary，roller 來自中古英語 rollere，也就是 roll（滾）加上 -er（做這件事的東西或人），字面就是「會滾的那個」。今天所有的用法都還貼著這個最字面的組合走，沒有走遠。
Wiktionary entry 'roller' (packet source_ref kaikki:3f6f69a190036ae4:1014155456): "From Middle English rollere, equivalent to roll + -er."
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