bring the car to a full stop. Once the car has stopped you can continue without a problem. Over the past six months, the car has had this problem about five times. The car drives great the rest of the time without any problems. I had a garage look at the car and they could not find a problem.
The stearing wheel will start to shake very badly. It will not stop until you on 2003 Toyota Camry
You need to be more specific as to what is going on when the steering wheel starts the shaking. Over a bump, certain speed, accel, decel, after turn, as turning, etc. Be specific. If it does it every Sunday at 2 p.m. over the railroad tracks in the rain when accelerate we need to know. That was an exaggerated example of course. Kind of like when you tell your doctor you have a pain every time you lift your arm but is ok if you swing it. Kay????
The steering wheel will start shaking back and forth ( it has the same feel as putting on brakes with a very badly warped rotor). I was driving the car at about 60 mph on a smooth 4 lane road when the steering wheel started to shake back and forth. The shaking continued until I came to a complete stop ( it will not stop shaking until you come to a complete stop). I looked around the car at all tires and did not see any tire problems so I got back in the car and continued on a two trip with no other problems. Since the first time, I have had the problem about 4 more times over a six month period. I have had the alignment checked and the tires are close to new. Also, I put it on a rack and had a shop check for any broken or loose parts in the front suspension.
Now we are talking. Finally the info that should have been supplied when first posted. I had same problem once and found a bent wheel that would cause intermittent shakes at speed like yours. Have the wheels all checked on the balancer for bent. I know you said the tires are all fairly new but I can assure you that when spin balanced the tech is not looking at the wheel inside the cover while it spins. He is likely picking his nose till balancer stops. Also, have the tires rotated to see if the shake moved because it could be a slipped belt in a fairly new tire that only shows at speed or certain tire temp. Have another shop check for suspension bushing probs. In Oregon we have Les Schwab tire stores here that say they check the front ends/suspensions of vehicles when installing tires but I used to work at a brake/suspension shop that found so many probs after a vehicle had been taken to one of the Schwab stores and the customer was still experiencing probs.