Tires: steering vibration as 60 MPH, independent mechanics, hunter gsp9700

Question
I have a Lincoln LS 2004 with an intermittent shake (vibration) in the steering wheel at 60 MPH. On moving shift out of gear at this speed the vibration continues.  Have tried everything for a year and a half to remove this problem, to no avail.  New tires, balanced, aligned, rims straightened, rotated, talked with at least 6 dealers and independent mechanics.  Cannot reslove problem.  

Any ideas would be appreciated.

Thanks.            Jack

Answer
Jack,

At this point, I think you can rule out pretty much everything from the tire end of things.  Hopefully, the folks doing the diagnostics have used a Hunter GSP9700 Road Force machine - which is quite likely.

I would start to look at other rotating parts - brake rotors, hubs, etc.

But I don't want to shortchange that there maybe a non-rotating parts.  I once chased a vibration that turned out to be a power steering line that was rubbing on the steering mechanism.