inner fitting within a block or pulley over which the rope runs.

Merriam-Webster Online Dictionary
sheave (noun)
a grooved wheel or pulley (as of a pulley block)
sheave (verb)
transitive verb
to gather and bind into a - sheaf
sheave (Wikipedia)
Pulley block including sheave.

A sheave (/ʃv/) is a pulley with a grooved wheel for holding a belt, wire rope, or rope. The grooved wheel spins on an axle or bearing inside the frame of the block. This allows the wire or rope to move freely, minimizing friction and wear on the cable. Sheaves can be used to redirect a cable or rope, lift loads, and transmit power. The words sheave and pulley are sometimes used interchangeably.

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