Reading the "Account of Egypt" by Herodotus, it says of the great pyramid of "Cheops" (Macauley translation):
This pyramid was made after the manner of steps which some called "rows" and others "bases": and when they had first made it thus, they raised the remaining stones with machines made of short pieces of timber, raising them first from the ground to the first stage of the steps, and when the stone got up to this it was placed upon another machine standing on the first stage, and so from this it was drawn to the second upon another machine; for as many as were the courses of the steps, so many machines there were also, or perhaps they transferred one and the same machine, made so as easily to be carried, to each stage successively, in order that they might take up the stones; for let it be told in both ways, according as it is reported.
This may just be a Greek or late Egyptian technology being anachronistically supposed to have been used in the past, but nevertheless, it is interesting to ponder what kind of machines the Egyptians could have had that fit this description. Some of the larger stones in the pyramid weight 10 metric tonnes, so the machines would have to have that capacity.
The only machines I have found depicted in ancient Egyptian wall reliefs and paintings have been chariots and balances. I have not been able to find any examples of cranes.
One book I found is called "Ancient Egyptian Construction and Architecture" by Somers and Engelbach (1930) which seems to describe some of their technology for construction. Another book is "Ancient Egyptian Materials and Technology" by Nicholson and Shaw.