roll, wind, coil, turn pages, roll up sleeves, strip off, be turned, be rolled up
捲 centers on the action of rolling or winding something, often with the hands. This covers physical actions like rolling up sleeves, coiling a rope, turning pages, or stripping something off by rolling, as well as the passive state of being rolled up.
捲 combines the hand radical 扌 with 卷, which likely contributes both sound and the idea of rolling or curling. The character originally expressed the action of rolling something with the hands.
The hand radical 扌 beside 卷 (a shape associated with rolling or curling) shows a hand rolling something up, like a scroll or a sleeve.
For ケン, imagine a hand rolling up a long piece of canvas: can -> ケン, and the hand rolls the canvas into a coil.
to turn up; to roll up (e.g. sleeves)
to be turned up; to be turned inside out; to ride up; to be lifted (e.g. by wind)
to turn over; to turn (pages); to leaf through (a book, etc.)
program board (concert, theatrical production); act-announcement sheets
unframed painting; unframed drawing
doing something multiple times
to do over and over again
lifting a girl's skirt; flipping up a skirt
rolling one's kimono up to one's waist
to tuck (e.g. sleeves); to roll up
mekuri karuta; deck of 48 (later 49) cards or the fishing game played with it, esp. popular in the late Edo period
recouping one's strength for a renewed attack; making another attempt with redoubled efforts
crimp; crinkle; waviness
detour (around a waterfall, etc. when gorge-climbing)