stem of a feather, quill
翮 centers on the central shaft of a feather, the stiff quill that supports the vane. It refers specifically to the stem or quill of a feather.
翮 combines 羽 (feather) with 鬲, which likely contributes the sound. The character specifically denotes the quill or stem of a feather.
The right side 羽 is a feather, and the left side 鬲 looks like a sturdy vessel. Imagine a feather's central quill as strong as a metal pot, supporting the soft vanes.
For カク, picture a feather quill being used to write a check: check -> カク, and the quill's stem is the writing tool.