Reflecting on how often this type of enquiry crops up on the internet, and wondering about the difficulty of accessing information on the subject, this morning I googled "crossbow/history" and first on the list was a Wikipedia reference to Payne-Galllwey, so knowing the "quality" of so much of the Wikipedia content, I then googled Payne-Gallwey and third on the list was his "Book of the Crossbow" listed by Amazon.
From my own copy, a few extracts, though I will first say that a quick look at pages 3 to 10 "The Military Crossbow" would have rendered this question pretty much redundant.
Whatever, a few additional extracts...
From page 5:
"It should be remembered that the bows of the Genoese at Crecy were doubtless composite ones, made of wood, horn, sinew and glue, bows of steel being of later introduction."
He further describes how the string on such bows would be rather slack braced and the consequences of the affect of moisture or immersion oon such a string.
As to the method of drawing and the dates of different methods.
Page 84: The Goats Foot Lever.
"Not represented until the middle of the 14th C."
Page 90: The Windlass.
"First alluded to in contemporary accounts of sieges and battles which occurred shortly before the last quarter of the 14thC."
Page 134: The Cranequin.
" I can find no cranequin or even an illustration of one of a date previous to 1480.
Though I know of several crossbows made about 1460 that have the projecting pins through their stocks
which indicate that cranequins were applied to bend their bows."
As to the efficacy of equivalent draw weights let me just say that when I last saw the former "Warwick Bowman" shoot a crossbow described as of 100 lb draw weight with a steel prod at a target less than 20 paces away, not only did he miss with his first shot, the prod being misaligned on the stock, but when he hit the safety netting behind the target, the prod bounced off the tightly stretched netting and fell to the ground.
A field pointed 500 grain arrow from my light 54 lb longbow would have most likely passed through such a net and perhaps have been caught by it's fletching, if large enough, though I commonly get pass throughs on two layers of such netting hung slack when shooting at balloons.
The only time I shot a balloon in front of such a net with a bodkin pointed standard arrow out of the same 54 lb bow, the shaft was found about 75 paces beyond the net due to the fletch passing through the net having slowed down the shaft.
FWIW
Rod.