One spatial idea drives this large family: behind / after. Stand behind something and it is at your back (achor); come after in time and you are late (me'uchar); the one who is not this one is the other (acher). Even responsibility (achrayut) is here, the one who stands behind a thing and answers for it. Watch a single "behind" stretch across space, time, otherness, and accountability. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Modern Hebrew lexicalizes only the pi'el verb "to be late", being after the appointed time. The rest of the root lives as prepositions, adjectives, and abstract nouns rather than as more verbs.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.