Mostly you can stretch a spring up a little when you get it out of the casing. Otherwise you have to stretch it in phases, by pulling on it with tweezers from loop to loop. It requires a lot of dedication, but should work.
I understand your Photosmart 6510 is printing more of a gray then a black ink, I'd like to help. Please begin with the steps in the following document; Printer Prints a Blank Page or Does Not Print Black or Color Ink for the HP Deskjet Ink Advantage an...
If you complete, or have already completed all of the steps in the document above and the issue continues, my own personal recommendation, not one of HPs, is to use the solution offered in the following video. I only suggest doing this if the printer is out of warranty; How to fix a HP Printer, not printing black ink and missing colours
Based on the comments, it looks like this may help King_Zog wrote:
I tried most of the suggestions in this thread, but stopped short of disassembling the print head. Nothing worked until I saw the video referenced in Sunshyn2005's message. That did work, but not on my first try. For the second attempt, I left the wet paper towels in place for a couple of hours to really soak the print heads. That did the trick.
So, thank you Sunshyn2005, for pointing me to the solution. -Source
Although the printer might be out of warranty, if the issue persists, HP may be able to offer you something. Maybe they can offer you a discount on an alternate model. If you are in Canada or US call 800 474 6836, or you can Contact HP Worldwide.
If this resolves the issue, please let me know so we can help others who may be experiencing the same issue.