One physical gesture sits at the heart of this root: dragging, hauling a weight that resists. Pour the three letters into the pa'al and you drag (לִגְרֹר); into the nif'al and you are dragged along, often against your will. The same root gives the tow truck (גְּרָר) and, by metaphor, the drag of physics and the idea that one thing drags another after it as a consequence. This is a geminate root, the second and third letters are the same ר, so it stays compact and never grows a huge family. 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.
The core pair is pa'al (drag) and nif'al (be dragged), active and passive of the same pull. The pi'el לְגָרֵר exists but is rare and shifts sense toward "grate" (a kitchen action where you drag food across a blade). No hif'il, pu'al, huf'al or hitpa'el are lexicalized; geminate roots like this one stay lean.
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.