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A universal joint, U joint, Cardan joint, Hardy-Spicer joint, or Hooke's joint is a joint in a rigid rod that allows the rod to 'bend' in any direction, and is commonly used in shafts that transmit rotary motion. It consists of a pair of ordinary hinges located close together, but oriented at 90° relative to each other.

Contents 1 History 2 Angular speed 3 Double cardan 4 CV joint 5 See also 6 References

The concept of the universal joint is based on the design of gimbals, which have been in use since antiquity. One anticipation of the universal joint was its use by the Ancient Greeks on ballistae. 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. Christopher Polhem later reinvented it and it was called "Polhem knot". 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.

Angular output shaft speed for different angles of the input shaft	Output shaft angle for different angles of the input shaft

When the two shafts are at an angle other than 180° (straight), the driven shaft does not rotate with constant angular speed in relation to the drive shaft; the more the angle goes toward 90° the jerkier the movement gets (clearly, when the angle = 90° the shafts would even lock). However, the overall average speed of the driven shaft remains the same as that of driving shaft, and so speed ratio of the driven to the driving shaft on average is 1:1 over multiple rotations.

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

and the angular acceleration,

A configuration known as a double cardan joint drive shaft partially overcomes the problem of jerky rotation. In this configuration, two U-joints are utilised where the second U-joint is phased in relation to the first U-joint in order cancel the changing angular velocity, and an intermediate shaft connects the two U-joints. In this configuration, the assembly will result in an almost constant velocity providing both the driving and the driven shaft are parallel and the two universal joints are correctly aligned with each other - usually 45°. This assembly is commonly employed in rear wheel drive vehicles.

In practice, it is often impossible to maintain a strict geometric relationship between the driving and driven shafts, and the intermediate shaft, giving rise to vibrations and mechanical stresses. Under all geometric conditions, the intermediate shaft will maintain a sinusoidal angular velocity, which contributes to vibration and stresses. The stresses can be reduced by the use of a smaller and lighter intermediate shaft, ensuring the driven and driving shafts share as close to the same angle in relation to the intermediate shaft, and reducing the angle of the joints.

Joints have been developed utilizing a floating intermediate shaft and centering elements to maintain equal angles between the driven and driving shafts, and the intermediate shaft. This overcomes the problem of differential angles between the input and output shafts.

A recent innovation, the Thompson coupling is a further development of the double cardan joint, which doesn't rely on friction or sliding elements to maintain a strict geometric relationship within the joint, and which is capable of transmitting torque under axial and radial loads with low frictional losses.

Main article: Constant-velocity joint

Another way to prevent jerky movement is to use a constant-velocity joint (CV joint) 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 for any angle .

• Gear coupling
• Thompson coupling
• Rag joint
• Elastic coupling

• Theory of Machines 3 from National University of Ireland