U-joints are not used with front-wheel drive (FWD) because they produce cyclic vibrations when operated at more than a few degrees off-center. A U-joint will cause a change in speed between the driving and driven shafts whenever the joint operates at an angle. As the operating angle of the joint increases, the speed (velocity) of the driven shaft starts to vary during each revolution. And the greater the operating angle, the greater the variation in speed of the driven shaft.
The driven shaft still turns at the same number of revolutions per minute as the shaft that's driving it, but because of the geometry of the U-joint the speed of the driven shaft alternately increases (accelerates) and decreases (decelerates) four times every revolution -- which causes the vibrations we're talking about.
This isn't a concern in a rear-wheel drive application because the U-joints on the ends of the driveshaft are positioned 180 degrees to one another to cancel out vibrations. What's more, both U-joints always operate at the same angle. But in a front-wheel drive application, the outer joint may have to operate at an angle of up to 45 degrees when the wheels are steered. This is too much of a difference between the inner and outer joints angles for U-joints to handle. So constant velocity (CV) joints are required.
Unlike a U-joint, a CV joint always drives the output shaft at the same speed as the input shaft regardless of the operating angle of the joint. Therefore, it doesn't make any difference if the inner and outer joints operate at different angles.
In a U-joint, the four-point center cross attaches at two points on either yoke. When the joint is bent, two of the arms on the center cross travel in one elliptical path while the other two arms follow a different elliptical path. This is what causes the speed variations that result in vibration. It's hard to visualize, but that's what happens.
CV joints handle joint angularity differently. The six balls inside a "Rzeppa" style CV joint are positioned so they always travel in a circular path exactly half way between the joint angle. A circular path keeps velocity constant while an elliptical path causes changes in velocity. So that's the inside scoop on why U-joints won't work in FWD applications.