It is believed by Egyptologists that the Old Kingdom (ca. 2649-2150 BC) Egyptians understood the pulley (as we know it today) but could not fabricate a practical pulley because they, being in the Early Bronze Age, lacked the requisite metal, e.g., iron, for a high strength pulley axle. In particular, this belief is often proffered in discussions regarding the Great Pyramid construction because the pulley would have been highly useful not only because of the mechanical advantage it offered but because of its rope direction-changing capability -- and its capability of applying a very high pull force in a limited area -- for lifting the 2.3 million, ~5,000 pound stone blocks for the Great Pyramid.
Actually the greater Pyramid construction challenge is much more difficult -- lifting the stone blocks at the rate of one block approximately every five minutes for ~30 years (the generally agreed lift rate by Egyptologists).
It is proposed that Old Kingdom Egyptians did likely create and utilize a simple but robust, durable pulley (made of hardwood, limestone, granite, and/or copper), fully capable of thousands of usage cycles (see Side View Photo below) -- a polished cylinder (see Cylinder Photo below) which rotates in an open sleeve or cradle (see Cradle Photo below) with a polished, mating surface -- what is termed the “Egyptian Pulley”. The portion of the cylinder in contact with the rope would be grooved and/or roughened sufficient to prevent rope slippage. Except for this grooved /roughened area on the cylinder, appropriate lubrication, for example, flax oil or rendered animal fat, would have been utilized on the mating surfaces. Such a simple pulley would have been highly useful not only for Pyramid-related stone lifting challenges but other ones they also faced.
An Egyptian Pulley, fabricated from limestone, was recently used to replicate (pulling a ~5,000 pound weight up a 52 degree incline) that indeed this type of mechanism will function as a true direction changing pulley for a transitioning rope under high tensile load. Calculations show that the use of six (or more) Egyptian Pulleys simultaneously could have met the lift rate of one stone block every five minutes for construction of the Great Pyramid.