pursue, follow, expel, drive away
趕 centers on moving after someone or something with intent: pursuing, following, or driving them away. The expel sense is a forceful extension of chasing something out.
趕 combines 走 (run) with 旱, which likely contributes the sound and may suggest dryness or drought, but the exact historical role of 旱 in this character is uncertain.
The running enclosure 走 wraps around 旱, which looks like a sun 日 over a dry stem 干. Picture chasing someone across a dry, sun-baked field: you pursue them relentlessly.
For カン, imagine a can being kicked down the road as you chase after it: can -> カン, and you pursue the rolling can.