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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 drive shaft needs to turn a corner; a drive shaft 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 drive shaft of automobiles.

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:
ω₂ = ω₁ · COS β/(1-SIN² β · SIN² φ₁)

and the angular acceleration α₂ of the driven shaft is:
α₂ = ω₁² · SIN² β · COS β · SIN 2· φ₁/(1-SIN² β · SIN² φ₁)

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.

1 CV 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. drive shaft 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.

2 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 Girolamo 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 HookeRobert Hooke ( July 18, 1635 March 3, 1703) was one of the greatest experimental scientists of the seventeenth century, and hence one of the key figures in the scientific revolution. Born in Freshwater, on the Isle of Wight, Hooke received his early educa produced a working universal joint in 1676Events January 29 Feodor III becomes Tsar of Russia First measurement of the speed of light, by Ole Romer Bacon's Rebellion Year in topic 1676 in literature 1676 in music 1676 in science Births May 8 Frederick I of Sweden Deaths July 22 Pope Clement X 167, giving rise to an alternative name, the Hooke's joint. It was the American car manufacturer Henry FordThis article is about the founder of the Ford Motor Company; for articles on other people named Henry Ford, see Henry Ford (disambiguation). Henry Ford ( July 30, 1863 April 7, 1947) was the founder of the Ford Motor Company and one of the first to apply who gave it the name universal joint.