Now we take three large degree wheels similar to the kind used for camshaft timing and fix one to the gearbox yoke, one to the driveshaft, and one to the pinion york so the angle of rotation of each component can be compared as the driveline revolves through one complete revolution. For the first part of our demonstration, the gearbox, driveshaft and pinion are all in a straight line. The Gearbox output is slowly rotated, and readings taken off the three degree wheels. Not suprisingly all the degree wheels register exactly the same reading throughout the full rotation indicating the whole assembly is turning in unison.

For the second test the differential is lowered so the driveshaft falls down 5 degrees but the pinion and driveshaft remain in a straight line. There is nothing magic about the 5 degrees, it just happens to be a convenient angle. The gearbox output shaft is rotated, and all three degree wheel readings recorded.

Rotation in degrees
Gear box shaft	0.0	45.0	90.0	135.0	180.0	225.0	270.0	315.0	360
Driveshaft	0.0	45.1	90.0	134.9	180.0	225.1	270.0	314.9	360
Pinion	0.0	45.1	90.9	134.9	180.0	225.1	270.0	314.9	360

Now, Instead of the whole driveline turning in unison, the section after the first U-Joint creeps ahead then falls behind, twice during a full revolution.

Consider the effect on a vehicle powering along in direct gear at an engine speed of 1500 rpm(First, confirm with you calculator that 1500 rpm equals 25 rev. per second.). Flywheel inertia will prevent the engine adjusting its speed 50 times per second, and the vehicle certainly can not respond so quickly. The variation is made up by taking up slack in the driveline, twisting the shaft and axles, and movement of components on their flexible mounts. Passengers in the vehicle feel a vibration at double the driveshaft speed.

What can be done to improve the situation? The problem was caused by the phase change introduced by the first U-Joint, can we use the second U-Joint to cancel it out? An obvious starting point is to make both U-Joint angles equal to see if the phase change doubles in magnitude or cancels out.

For the next test, adjust the pinion height so the angles of both U-Joints are equal. The gearbox and pinion are now parallel but not in line. Rotate the gearbox shaft and read off the angles again.

Rotation in degrees
Gearbox Shaft	0.0	45.0	90.0	135.0	180.0	225.0	270.0	315.0	360
Driveshaft	0.0	45.1	90.0	134.9	180.0	225.1	270.0	314.9	360
Pinion	0.0	45.0	90.0	135.0	180.0	225.0	270.0	315.0	360

We can now see the driveshaft speed still flucuates, but the gearbox and pinion remain in phase throughout the full revolution. As the flywheel effect of the shaft is relatively small, the transmission of power is virtually vibration free, providing two criteria are met.

1. The angle of both U-Joints must be equal. This is generally achieved by making the engine and pinion parallel. For example the gearbox and pinion may both be horizontal but at different heights. A really thorough investigation also shows that if the angles are equal but opposite, phase correction still exists, but this is generally only of interest in shaft-driven machinery, or trucks with extremely high lift. In such an exmple the engine could be horizontal, the drive sloping down at 5 degrees, and the pinion pointing up at 10 degrees.
   
2. The driveshaft must be assembled with the two yokes in correct alignment. This is easy to draw, but not so easy to describe. Imagine for a moment a bare driveshaft without without U-Joints fitted. Slide into the eyes of the yokes 2 bars which are a snug fit. Look along the shaft from one end, and the two bars must be parallel. Driveshaft manufacturers have jigs to insure the components are held accurately during welding, so unless a one piece shaft has been brutalised and twisted this should not be an issue. However real care must be exercised when assembling a shaft which incorporates a slip joint. A frequent cause of driveline vibration is assembling a slip joint without ensuring the yokes are parallel. Ever one spline out can cause problems. Driveshafts can be easily checked in the car using a magnetic level. Attach the level to the machined face on the outside of the front yoke, then rotate the shaft until the face is vertical. Lock the shaft so it can not turn, then attach the level to the outside face of the rear yoke and confirm it is also vertical.

Now, where does offseting the pinion down come in this? When power is applied the reaction against the axle torque will tend to lift the pinion as the springs and mounts flex. Setting the static pinion angle about 1 degree low will result in the gearbox and the pinion coming close to parallel when power is being applied. Degree shims can be added later to fine tune any errors.

What about Brinelling the joints? If a joint is dead straight, the rollers will always bear against the same place on the cross shaft and cup, resulting in localized wear. To spread the wear over the full surface of the joint would require the rollers to traverse a full roller diameter during each shaft revolution, but this is not practical as it necessitates a U-Joint angle in excess od 4 degrees. An angle of around 2-3 degrees seems to provide a good compromise.