fulling block
砧 centers on a sturdy stone block used for fulling cloth: a flat surface where fabric is beaten to clean or thicken it.
砧 combines 石 (stone) with 占, which likely contributes the sound. Together they indicate a stone block used for beating cloth.
A stone (石) block that takes up (占) space in the workshop: imagine a heavy stone fulling block where cloth is beaten.
For チン, picture a chin (チン) resting on the stone block while the cloth is being fulled: chin -> チン.