It is believed that all noun measure words originate from nouns. Actually, verbs can also be used as measure words in Chinese, for example, "担 (carry on a shoulder pole): 一担水 (two buckets of water)."
That the verb indicates the action implemented on the object can function as a measure word for the object is an interesting characteristic of Chinese measure words. For example:
"一封信" (a letter): the word "封" , which is also a verb meaning "to seal, to close" , works as a measure word here.
抹上 (smear/ put on/apply): 一抹浓眉 (heavy eyebrows)
摞起来 (pile up): 一摞纸 (a pile of paper)／一摞讲义 (a pile of teaching materials)
堵上 (block up): 一堵墙 (a wall)
贴上 (plaster): 一贴膏药 (a plaster)
挂起来、挂上 (hang): 一挂竹帘 ( a curtain)／一挂鞭炮 (a string of firecrackers)
截开、截断 (cut): 一截木棍 (a section of a log)
套上 (harness): 一套马具 (a set of harness)
张开 (open): 一张嘴 (a mouth)／一张网 (a net)
出来 (come out), 出去 (go out), 演出 (perform): 一出戏 (a play)／一出杂耍 (a vaudeville)
支起来, 支上 (prop up/ put up): 一支箭 (an arrow)／一支枪 (a gun)
扇动 (flap/fan): 一扇门 (a door)／一扇窗子 (a window)
When encountering such nouns, you can figure out what verbs can be used to modify them and use the verbs as measure words for them.
Note that some verbs as measure words don't indicate the actions implemented on the head words. For example, rather than function as a verb meaning "to secure with a hook ", "钩" in the phrase "一钩月亮" is a noun, referring to "a hook". It is used in this way because a crescent moon looks like a hook. Similarly, the two "弯" in "一弯月" and "弯起来" are also different in that the former is an adjective, which means "curved", while the latter is a verb meaning "to twist, to bend".