What you described is rarely caused by problems with the steering linkage. Look at the shock absorbers for signs of oil leaking from on top where the shafts come out. Next, check the tires for a broken belt. Most of the time you can verify a broken belt by observing the steering wheel moving left and right a little as you go very slowly through a parking lot. Bulges on the tread surface of a tire are the common things people look for but there are other ways a broken belt can show up. To do a proper inspection, the truck should be on a hoist and running in gear.
Normally worn suspension parts won't cause a shaking either unless something like a worn ball joint is allowing the wheels to sit out of proper alignment. That can result in the two front tires steering in slightly different directions. They'll walk away from each other or toward each other, then, when the sidewalls can't flex any more, the tread will pop back and start all over. You'll see evidence of that in the tire wear patterns.
The best approach is to have the truck inspected at a tire and alignment shop. They'll also measure the suspension ride height. If that is wrong, typically due to sagged springs, it will change the geometry of the control arms and they'll go through the wrong arcs. That will cause excessive tire wear even when the alignment computer says all the adjustments are perfect. Those settings only pertain to a vehicle that is standing still on the hoist, not one that is moving up and down as it goes down the road.
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Thursday, May 28th, 2015 AT 4:11 PM