The John Deere 6510 from the 6010/6010SE range is well covered here, with more than 600 parts in groups such as lighting, trailer couplings and electrics.
More than 600 parts are matched to the John Deere 6510 on this page, from GRANIT, HELLA, ROCKINGER, Scharmüller and Wabco. They run from an oil pump O-ring to a cab hinge, and a few groups stand out for this tractor.
A cab door that drops, will not stay open or rattles over rough ground usually comes down to tired gas struts or a worn hinge. For the 6510 there are door gas struts and cab hinges. Change gas struts with the door held open by a helper or a prop, and fit the new strut with the rod pointing down so its seal stays lubricated. If the hinge pin has worn, the door will sit low and the lock will not line up, which is worth fixing before the seals on the door frame start to suffer.
When fitting a new thermostat, always renew the gasket and clean both mating faces thoroughly, since a scrap of old gasket is enough to cause a leak.
The 6510 also has external and internal plates for the front axle, parts for forced steering with ball ends on both sides, and automatic drawbars and drawbar frames from ROCKINGER and Scharmüller. Replace axle plates as a set and on both sides together, keeping external and internal plates in the order they came out.
The rating plate tells you it is a 6510. For O-rings, gaskets and plates, the reference number on the old part settles it. If it is unreadable, lay old and new side by side and compare shape, holes and thickness.
With forced steering, the ball ends on both sides are under real load, especially on tight headland turns. Check them for play regularly by rocking the rod by hand, and replace any ball end with play straight away, before it lets the trailer wander and wears the rest of the system.
The 6510 is part of the John Deere 6010 series, and other tractors from that range have their own page: John Deere 6010, John Deere 6110, John Deere 6210, John Deere 6410 and John Deere 6810. Order for each type from its own page. Running another model from this maker? Browse the overview of John Deere parts.