Old and shaky

My Ford F250 XLT (HD) 2 wheel drive has recently developed a shimmy; a shaking of the steering wheel that usually occurs at medium speeds, and seems worse when going around a curve. But since it doesn’t seem safe to drive, I dropped by a local shop for a diagnosis. Their thought was that I had a caliper sticking, since it pulled to the left when they test drove it and applied the brakes, and maybe rotors since the vibration indicated warped rotors. Since I hadn’t mentioned shaking during braking, I paid the diagnostic and moved on. Upon leaving, the shaking started up again going around the first curve, at about 35-40 mph. Shortly after that I took it to a dry, flat, unbusy stretch of road, and applied the brakes at about 60 mph, and brought it to a stop in it’s lane with my hands off the wheel; no pull either way. Now I have it up on stands, and have visually and physically checked the parts I know and recognize, ie ball joints, tie rods, wheel bearings, etc. I don’t know how to inspect gear box, or steering shaft issues, but steering wheel play is minimal. I’m not interested in letting my local shop do trial and error fixes on this old truck (270K miles) to the tune of upwards of a thousand bucks. Ideas?

check tire treads for slight bulges, you may have a busted band somewhere. they cah be hard to detect sometimes

Rotate the tires and see if the problem moves. Bad tire or bent rim could cause your problem.

With 270k on the clock most any component could be worn. If rotating the tires doesn’t change anything I’d find a trusted mechanic to go over it. It might take some significant pushing and pulling to figure out what’s worn.