It'd probably be best to contact you nearest JD AG dealer. If your not sure where one would be, here is a link to the main USA John Deere site.
John Deere Products & Services At the very top of the page, just to the right of where it says Unted States, in smaller print is the dealer locator. Click on it, and enter your zip code. It should show your nearest dealer,and those within a 75 - 100 mile radius.
I did a search on their site for manuals for the 640 rake. All they have are an Operator's manual, and a parts manual. Being you can use their online parts store, you can look parts up for it that way. Here is a link showing manuals available, but no prices.
John Deere Ag - New Equipment: Technical Publications - Publications Search
I'm not sure how expensive they are, but did a search on ebay,and found 3 for the 640 rake. They range from $12.57 to $25.00. I'd say the one for $12.57 with free shipping would be a deal.
John Deere 640 side delivery rake | eBay
To find the online parts for the rake, click on this link, then click on the 897 - 640 side delivery rakes in the menu.
John Deere - Parts Catalog
A window should pop up on the right side of the screen, that has the manual. Scroll down through, and you'll get exploded views of every component of your rake, along with part numbers and description of said part. If you go back to the main site, and open another window to the "buy parts online", you should be able to go back to the online parts manual, copy an paste the part number, then go to the "buy" page, and enter the number. It then should show you the price of the parts needed. It may save you some sticker shock before hand, if you plan on getting parts though your nearest dealer.
Hope this helps..!!
