grind, rub, study, research
揅 centers on the idea of polishing or refining through persistent effort: grinding or rubbing something smooth, and by extension, studying or researching to refine knowledge.
揅 is a rare character that combines 研 (grind, polish) with 手 (hand), reinforcing the idea of grinding or polishing by hand. The exact historical development is uncertain, but the component structure suggests a hand action related to grinding or study.
The top part 研 means to grind or polish, and the bottom 手 is a hand. Picture a hand holding a whetstone, grinding and polishing a blade until it is sharp—just like studying refines the mind.
For ケン, imagine a hand grinding a stone to sharpen a Ken (剣, sword): Ken -> ケン, and the grinding action connects to the kanji's meaning.