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Universal joint
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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 hinges located close together, orientated at 90° to each other, connected by a cross shaft.
main concept of the universal joint is based on the design of gimbals, which have been in use since antiquity.
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Encyclopedia
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 hinges located close together, orientated at 90° to each other, connected by a cross shaft.
History
The main 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.
Equation of motion
The Cardan joint suffers from one major problem: even when the drive shaft rotates at a constant speed, the driven shaft rotates at a variable speed, thus causing vibration and wear. The variation in the speed of the driven shaft depends on the configuration of the joint, which is specified by three variables:
- The angle of rotation of axle 1
- The angle of rotation of axle 2
- The angle of the axles with respect to each other, zero being parallel, or straight through.
These variables are illustrated in the diagram on the right. Also shown are a set of fixed coordinate axes with unit vectors and and the planes of rotation of each axle. These planes of rotation are perpendicular to the axes of rotation and do not move as the axles rotate. The two axles are joined by a gimbal which is not shown. However, axle 1 attaches to the gimbal at the red points on the red plane of rotation in the diagram, and axle 2 attaches at the blue points on the blue plane. Coordinate systems fixed with respect to the rotating axles are defined as having their x-axis unit vectors ( and ) pointing from the origin towards one of the connection points. As shown in the diagram, is at angle with respect to its beginning position along the x axis and is at angle with respect to its beginning position along the y axis.
is confined to the "red plane" in the diagram and is related to by:
is confined to the "blue plane" in the diagram and is the result of the unit vector on the x axis being rotated through Euler angles ]:
A constraint on the and vectors is that since they are fixed in the gimbal, they must remain at right angles to each other:
Thus the equation of motion relating the two angular positions is given by:
The angles and in a rotating joint will be functions of time. Differentiating the equation of motion with respect to time and using the equation of motion itself to eliminate a variable yields the relationship between the angular velocities and :
| | Angular output shaft speed for different angles of the input shaft | Output shaft angle for different angles of the input shaft |
As shown in the plots, the angular velocities are not linearly related, but rather are periodic with a period twice that of the rotating shafts. The angular velocity equation can again be differentiated to get the relation between the angular accelerations and :
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 to 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 90°. This assembly is commonly employed in rear wheel drive vehicles, where it is known as a drive shaft or propeller (prop) shaft.
Even when the driving and driven shafts are parallel, if 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. The intermediate shaft will also maintain a sinusoidal angular velocity, which contributes to vibration and stresses.
Double Cardan joints are similar to drive shafts, except that the length of the intermediate shaft is shortened as much as is practical, effectively allowing the two Hooke's joints to be mounted back to back. This provides true constant velocity operation at low speeds, but the torque required to accelerate the internals of the joint does provide some additional vibration at higher speeds. DCJs are typically used in steering columns, as they eliminate the need to correctly phase the universal joints at the ends of the intermediate shaft (IS), which eases packaging of the IS around the other components in the engine bay of the car. They are also used to replace Rzeppa-style constant-velocity joints in applications where high articulation angles, or impulsive torque loads are common, such as the driveshafts and halfshafts of rugged four wheel drive vehicles. In practice, it can be difficult 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 shorter and lighter intermediate shaft, and 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. Double Cardan 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.
Thompson Coupling
The Thompson coupling is a constant velocity universal joint that can be loaded axially, and maintain constant velocity over a range of input and output shaft angles, with low friction and vibration. It consists of two cardan joints assembled within each other, which are geometrically constrained to maintain constant velocity at all input and output shaft angles. The geometric configuration also maintains constant velocity of the intermediate coupling, or coupling yoke, that joins the pair of cardan joints, which eliminates the induced shear stresses and vibration inherent in traditional double cardan shafts .
The use of cardan joints within the Thompson Coupling reduces the wear, heat and friction which is present in Rzeppa type constant velocity joints - cardan joints utilise roller bearings running circumferentially, whereas Rzeppa constant velocity joints use balls which roll and slide axially along grooves.
The novel feature of the coupling is the method to geometrically constrain the pair of cardan joints within the assembly, using a spherical four bar linkage, and it is the first coupling to have this combination of properties.
The coupling has earned its inventor the Australian Society for Engineering in Agriculture Engineering Award.
See also
External links
- by Sándor Kabai, Wolfram Demonstrations Project.
- , About.com.
- - Explanation of the Thompson coupling
- ABC Television - The New Inventors - broadcast Feb 2007
- Video on Youtube: http://www.youtube.com/watch?v=xgQgm3GwaFs
- Video on Youtube: http://www.youtube.com/watch?v=Dh5C4e4exhM
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