Universal joint

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A universal joint

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.

1 History
2 Angular speed
3 Double cardan
4 See also
5 References
6 External links

[edit] History

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. Though the first use of the name universal joint is sometimes attributed to American car manufacturer Henry Ford, the term appeared in patent documents as early as 1884 when Charles H. Amidon was awarded United States Letters Patent No. 298,542 for a bit brace.

[edit] Angular speed


Angular output shaft speed $\omega_2\,$ for different angles $\beta\,$ of the input shaft	Output shaft angle for different angles $\beta\,$ 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 $\beta\,$ = 90° the shafts would even lock).This happens primarily because the plane containing the four arms of the centre piece constantly changes the angle it makes with the axis of each rotating shaft. 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 $\omega_2\,$ of the driven shaft, as a function of the angular speed of the driving shaft $\omega_1\,$ and the angle of the driving shaft $\phi_1\,$ , is found using:

Universal joints in a driveshaft

$\omega_2 = \frac{\omega_1\cos\beta}{1-\sin^2\beta\sin^2\phi_1}$

and the angular acceleration,

$\alpha_2 =\frac{\alpha_1\cos\beta}{1-\sin^2\beta\sin^2\phi_1}- \frac{\omega_1^2\sin^2\beta\cos\beta\sin 2\phi_1}{(1-\sin^2\beta\sin^2\phi_1)^2}$

[edit] Double cardan

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, provided both the driving and the driven shaft are parallel and the two universal joints are correctly aligned with each other - usually $\beta\,\le$ 45°. This assembly is commonly employed in rear wheel drive vehicles.

Even when the driving and driven shafts are parallel, if $\beta\,>$ 0°, oscillating moments are applied to the three shafts as they rotate. These tend to bend them in a direction perpendicular to the common plane of the shafts. This applies forces to the support bearings and can cause "launch shudder" in rear wheel drive vehicles.^[1] The intermediate shaft will also maintain a sinusoidal angular velocity, which contributes to vibration and stresses.

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 greater vibrations and mechanical 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.