# Universal joint

A universal joint, U joint or Cardan joint is a joint in a rigid rod that allows the rod to 'bend' in any direction. It consists of a pair of ordinary hinges located close together, but oriented at 90° relative to each other.

Universal joints are common wherever a driveshaft needs to turn a corner; a driveshaft with a universal joint can freely rotate through the universal joint, and no gears are required to couple the two ends. The most obvious example of this application of a universal joint is in the driveshafts of automobiles, a technology known as the Hotchkiss drive.

However, when the two shafts are at an angle other than 180°, the driven shaft does not rotate with the same speed as the drive shaft; the more the angle goes toward 90° the jerkier the movement gets (clearly, when the angle β = 90° the shafts would even lock).

The angular speed ω2 of the driven shaft, as a function of angular speed of the driving shaft ω1, is found using:

[itex]\omega_2 = \frac{\omega_1\cos(\beta)}{1-\sin(\beta)\sin^2(\phi_1)}[itex]

and the angular acceleration,

[itex]\alpha_2 = \frac{\omega_1^2\sin^2(\beta)\cos(\beta)\sin(2\phi_1)}{1-\sin^2(\beta)\sin^2(\phi_1)}[itex]
Missing image
UJgraph.jpg
Angular speed ω2 of driven shaft for different angles β

To prevent the jerky rotation of the axle or driven shaft there usually are two U-joints in a three part shaft assembly. The second U-joint will convert the jerky movement back to an even, uniform speed of the third shaft - if both the driving and the driven shaft are parallel.

## CV joint

Missing image
Homokinetic-joint.jpg
homokinetic joint

Another way to prevent jerky movement is to use a Constant Velocity (CV) or 'homokinetic' joint ('homo' meaning 'same', 'kinetic' meaning 'movement' or motion).
A homokinetic joint has the same function as a U joint but is constructed with a cage and steel balls moving in grooves, inside a 'dome' (see picture).

1. driveshaft from the transmission,
2. steel balls (in this case 6) in a 'cage'. The balls run in grooves in the dome.
3. cage, splined to the driveshaft
4. spherical 'dome' and outer driveshaft, part of the hub of the wheel.

For a CV joint ω2 = ω1 for any angle β.

## History

The concept of the universal joint is based on the design of gimbals, which have been in use since antiquity. The first person known to have suggested its use for transmitting motive power was Gerolamo Cardano, an Italian mathematician, in 1545, although it is unclear whether he produced a working model. In Europe, the device is often called the Cardan joint or Cardan shaft. Robert Hooke produced a working universal joint in 1676, giving rise to an alternative name, the Hooke's joint. It was the American car manufacturer Henry Ford who gave it the name universal joint.de:Kreuzgelenk nl:Cardanische ophanging pl:Sprzęgło wychylne

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