Vibration is, by nature, a cyclical failure. When something vibrates, it accelerates in one direction, stops, goes back the other way and does it again. To track down the source of any vibration, you need to take a close look at the parts that control the cyclical motion of the wheels and of the steering system. Vibration while turning is never a good sign, and is generally a precursor of failure to come. Don't let these types of issues go, or you could wind up with your tires pointing in the wrong direction relative to gravity or to each other.
Wheel bearings are the first components after your tires to take the force of road impacts and steering loads, and will exhibit a number of fairly typical symptoms before failing. Vibration, grumbling and grinding are some of the typical signs of extreme bearing wear, and will generally get louder or quieter depending upon which direction you turn the wheel while driving down the road. A bad driver-side bearing will get louder when you turn right; a bad passenger side bearing will vibrate more when you turn left. Bearing noise almost always intensifies with speed.
Your vehicle's steering end links not only tell the wheels which way to point, they also dictate the wheels' "toe." Toe-in or toe-out refers to the tires' relative angle to each other. Toe-in means the front of the tires are closer together than the back, and toe-out means that the backs of the tires are closer together than the fronts. Extremely worn steering end links or a busted steering linkage may allow one tire to wobble back and forth due to changes in toe. If you've ever seen an old shopping cart's caster wheel wobbling back and forth as you push the cart, then you've seen the effect that toe and caster-angle changes can have on a vehicle.
Ball joints join the wheels to the control arms, and bushings join the control arms to the chassis. Worn or broken ball joints will allow the wheel to oscillate back in forth as its ball joint ends flop around in the steering spindle or control arms. Bushings are rubber or polyurethane sleeves that surround the control arms' through-bolts as they pass through the chassis mounts. Normally, the bushings would only act as a barrier to absorb minor vibrations working their way up through the suspension; extremely worn or damaged bushings, however, will allow the control arms to squirm around and change suspension alignment. Either of these could result in vibration when turning.
Inner and outer constant velocity joints will typically grind or vibrate just before or during failure, and will tend to do so when the vehicle's wheels turn one way or the other. A constant velocity joint works something like the ball-and-socket joints in your shoulders and hips, and allow the suspension to move and the wheels to turn without snapping the axle shafts. A CV joint normally exists in a state of careful balance, but excess clearances resulting from wear will throw the joint out of balance and result in grinding or vibration when turning.
If your steering wheel vibrates while the vehicle is stationary, then there's almost certainly a problem in your power steering system. You could have a malfunctioning bypass valve in the power steering pump; if this valve bounces open and closed too quickly while turning, the rapid increase and decrease in steering effort may manifest as vibration. The same goes for your power steering rack, especially if it vibrates more when turning one direction than it does in the other. You may also want to check the brackets securing your pump's pressure line; a loose hose can violently vibrate against the pump, frame or engine components.
