drag, tow, throw, twist
拽 centers on forceful movement: pulling or dragging something, towing it along, or throwing it with a twisting motion.
拽 combines 扌 (hand) with 曳, which likely contributes both sound and the idea of dragging or pulling. The exact historical development is uncertain.
The hand radical 扌 beside 曳, which looks like something being pulled along, suggests a hand dragging or towing an object.
For エイ, imagine dragging a heavy crate while saying 'Ayy!' from the effort: 'Ayy' -> エイ, and your hand pulls it along.