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A universal joint (also called a universal coupling or U-joint) is a
joint A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw ...
or
coupling A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. The primary purpose of couplings is to join two pieces of rotating equipment while permitting some degree of misalignment or end mov ...
connecting rigid shafts whose
axes Axes, plural of ''axe'' and of ''axis'', may refer to * ''Axes'' (album), a 2005 rock album by the British band Electrelane * a possibly still empty plot (graphics) See also *Axess (disambiguation) *Axxess (disambiguation) Axxess may refer to: ...
are inclined to each other. It is commonly used in shafts that transmit
rotary motion Rotation around a fixed axis is a special case of rotational motion. The fixed-axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rota ...
. It consists of a pair of
hinge A hinge is a mechanical bearing that connects two solid objects, typically allowing only a limited angle of rotation between them. Two objects connected by an ideal hinge rotate relative to each other about a fixed axis of rotation: all other ...
s located close together, oriented at 90° to each other, connected by a cross shaft. The universal joint is not a
constant-velocity joint Constant-velocity joints (also known as homokinetic or CV joints) are mechanical joints which allow a drive shaft to transmit power through a variable angle, at constant rotational speed, without an appreciable increase in friction or Backlash (e ...
. U-joints are also sometimes called by various
eponym An eponym is a person, a place, or a thing after whom or which someone or something is, or is believed to be, named. The adjectives which are derived from the word eponym include ''eponymous'' and ''eponymic''. Usage of the word The term ''epon ...
ous names, as follows: * Cardan joint, after
Gerolamo Cardano Gerolamo Cardano (; also Girolamo or Geronimo; french: link=no, Jérôme Cardan; la, Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged through those of mathematician, ...
, a polymath of the 16th century who contributed to knowledge of various clever mechanisms, including
gimbal A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of ...
s * Hooke joint or Hooke's joint, after
Robert Hooke Robert Hooke FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that ...
, a polymath of the 17th century who contributed to knowledge of various clever mechanisms * Spicer joint, after
Clarence W. Spicer Clarence Winfred Spicer (November 30, 1875 – November 21, 1939) was an American automotive engineer and inventor, best known for the first practical design and use of the universal joint in automotive applications. Early life and education ...
and the
Spicer Manufacturing Company Spicer Manufacturing Company was an American manufacturer of automotive parts, including the Spicer joint, invented by Clarence W. Spicer. History Starting in April 1904, Spicer's patented joint was initially manufactured through an arrangement ...
, who manufactured U joints * Hardy Spicer joint, after the
Hardy Spicer Hardy Spicer is a brand of automotive transmission or driveline equipment best known for its mechanical constant velocity universal joint originally manufactured in Britain by Hardy employing patents belonging to US-based Spicer Manufacturing. Har ...
brand, a successor to the Spicer brand


History

The main concept of the universal joint is based on the design of
gimbal A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of ...
s, which have been in use since antiquity. One anticipation of the universal joint was its use by the ancient Greeks on
ballistae The ballista (Latin, from Greek βαλλίστρα ''ballistra'' and that from βάλλω ''ballō'', "throw"), plural ballistae, sometimes called bolt thrower, was an ancient missile weapon that launched either bolts or stones at a distant ta ...
. In Europe the universal joint is often called the Cardano joint (and a
drive shaft A drive shaft, driveshaft, driving shaft, tailshaft (Australian English), propeller shaft (prop shaft), or Cardan shaft (after Girolamo Cardano) is a component for transmitting mechanical power (physics), power and torque and rotation, usually ...
that uses the joints, a Cardan shaft), after the Italian mathematician
Gerolamo Cardano Gerolamo Cardano (; also Girolamo or Geronimo; french: link=no, Jérôme Cardan; la, Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged through those of mathematician, ...
, who was an early writer on gimbals, although his writings mentioned only gimbal mountings, not universal joints. The mechanism was later described in ''Technica curiosa sive mirabilia artis'' (1664) by
Gaspar Schott Gaspar Schott (German: ''Kaspar'' (or ''Caspar'') ''Schott''; Latin: ''Gaspar Schottus''; 5 February 1608 – 22 May 1666) was a German Jesuit and scientist, specializing in the fields of physics, mathematics and natural philosophy, and known fo ...
, who mistakenly claimed that it was a
constant-velocity joint Constant-velocity joints (also known as homokinetic or CV joints) are mechanical joints which allow a drive shaft to transmit power through a variable angle, at constant rotational speed, without an appreciable increase in friction or Backlash (e ...
.Mills, Allan, "Robert Hooke's 'universal joint' and its application to sundials and the sundial-clock", ''Notes & Records of the Royal Society'', 2007, accesse
online
2010-06-16
Shortly afterward, between 1667 and 1675,
Robert Hooke Robert Hooke FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that ...
analysed the joint and found that its speed of rotation was nonuniform, but that this property could be used to track the motion of the shadow on the face of a sundial. In fact, the component of the
equation of time In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in ...
which accounts for the tilt of the equatorial plane relative to the ecliptic is entirely analogous to the mathematical description of the universal joint. The first recorded use of the term ''universal joint'' for this device was by Hooke in 1676, in his book ''Helioscopes''. He published a description in 1678,Review of Ferdinand Berthoud's Treatise on Marine Clocks, Appendix Art. VIII
The Monthly Review or Literary Journal
Vol. L, 1774; see footnote, page 565.
resulting in the use of the term ''Hooke's joint'' in the English-speaking world. In 1683, Hooke proposed a solution to the nonuniform rotary speed of the universal joint: a pair of Hooke's joints 90° out of phase at either end of an intermediate shaft, an arrangement that is now known as a type of
constant-velocity joint Constant-velocity joints (also known as homokinetic or CV joints) are mechanical joints which allow a drive shaft to transmit power through a variable angle, at constant rotational speed, without an appreciable increase in friction or Backlash (e ...
.
Christopher Polhem Christopher Polhammar (18 December 1661 – 30 August 1751) better known as Christopher Polhem (), which he took after his ennoblement in 1716, was a Swedish scientist, inventor and industrialist. He made significant contributions to the economi ...
of Sweden later re-invented the universal joint, giving rise to the name ''Polhemsknut'' ("Polhem knot") in Swedish. In 1841, the English scientist Robert Willis analyzed the motion of the universal joint. By 1845, the French engineer and mathematician
Jean-Victor Poncelet Jean-Victor Poncelet (; 1 July 1788 – 22 December 1867) was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique. He is considered a reviver of projective geometry, and his work ''Tr ...
had analyzed the movement of the universal joint using spherical trigonometry. The term ''universal joint'' was used in the 18th century and was in common use in the 19th century. Edmund Morewood's 1844 patent for a metal coating machine called for a universal joint, by that name, to accommodate small alignment errors between the engine and rolling mill shafts. Ephriam Shay's
locomotive A locomotive or engine is a rail transport vehicle that provides the Power (physics), motive power for a train. If a locomotive is capable of carrying a payload, it is usually rather referred to as a multiple unit, Motor coach (rail), motor ...
patent of 1881, for example, used double universal joints in the locomotive's
drive shaft A drive shaft, driveshaft, driving shaft, tailshaft (Australian English), propeller shaft (prop shaft), or Cardan shaft (after Girolamo Cardano) is a component for transmitting mechanical power (physics), power and torque and rotation, usually ...
. Charles Amidon used a much smaller universal joint in his bit-brace patented 1884.
Beauchamp Tower Beauchamp Tower (13 January 1845 – 31 December 1904) was an English inventor and railway engineer who is chiefly known for his discovery of full-film or hydrodynamic lubrication. Early life Beauchamp Tower was born the son of Robert Beau ...
's spherical, rotary, high speed steam engine used an adaptation of the universal joint circa 1885. The term ''Cardan joint'' appears to be a latecomer to the English language. Many early uses in the 19th century appear in translations from French or are strongly influenced by French usage. Examples include an 1868 report on the ''Exposition Universelle'' of 1867 and an article on the
dynamometer A dynamometer or "dyno" for short, is a device for simultaneously measuring the torque and rotational speed (RPM) of an engine, motor or other rotating prime mover so that its instantaneous power may be calculated, and usually displayed by the ...
translated from French in 1881. In the 20th century,
Clarence W. Spicer Clarence Winfred Spicer (November 30, 1875 – November 21, 1939) was an American automotive engineer and inventor, best known for the first practical design and use of the universal joint in automotive applications. Early life and education ...
and the
Spicer Manufacturing Company Spicer Manufacturing Company was an American manufacturer of automotive parts, including the Spicer joint, invented by Clarence W. Spicer. History Starting in April 1904, Spicer's patented joint was initially manufactured through an arrangement ...
, as well as the
Hardy Spicer Hardy Spicer is a brand of automotive transmission or driveline equipment best known for its mechanical constant velocity universal joint originally manufactured in Britain by Hardy employing patents belonging to US-based Spicer Manufacturing. Har ...
successor brand, helped further popularize universal joints in the automotive,
farm equipment Agricultural machinery relates to the mechanical structures and devices used in farming or other agriculture. There are many types of such equipment, from hand tools and power tools to tractors and the countless kinds of farm implements that the ...
,
heavy equipment Heavy equipment or heavy machinery refers to heavy-duty vehicles specially designed to execute construction tasks, most frequently involving earthwork operations or other large construction tasks. ''Heavy equipment'' usually comprises five e ...
, and
industrial machinery The following outline is provided as an overview of and topical guide to industrial machinery: Essence of industrial machinery * Heavy equipment * Hardware * Industrial process * Machine * Machine tool * Tool Industrial machines * Agricult ...
industries.


Equation of motion

The Cardan joint suffers from one major problem: even when the input drive shaft axle rotates at a constant speed, the output drive shaft axle 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: # \gamma_1 the angle of rotation for axle 1 # \gamma_2 the angle of rotation for axle 2 # \beta the bend angle of the joint, or angle of the axles with respect to each other, with 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 A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...
with unit vectors \hat and \hat 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 (\hat_1 and \hat_2) pointing from the origin towards one of the connection points. As shown in the diagram, \hat_1 is at angle \gamma_1 with respect to its beginning position along the ''x'' axis and \hat_2 is at angle \gamma_2 with respect to its beginning position along the ''y'' axis. \hat_1 is confined to the "red plane" in the diagram and is related to \gamma_1 by: \hat_1 = \left cos\gamma_1\,,\, \sin\gamma_1\,,\,0\right/math> \hat_2 is confined to the "blue plane" in the diagram and is the result of the unit vector on the ''x'' axis \hat = , 0, 0/math> being rotated through
Euler angles The Euler angles are three angles introduced by Leonhard Euler to describe the Orientation (geometry), orientation of a rigid body with respect to a fixed coordinate system.Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189 ...
pi\!/2\,,\, \beta\,,\, \gamma_2 \hat_2 = \left \cos\beta\sin\gamma_2\,,\, \cos\gamma_2\,,\, \sin\beta\sin\gamma_2\right A constraint on the \hat_1 and \hat_2 vectors is that since they are fixed in the
gimbal A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of ...
, they must remain at
right angles In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. T ...
to each other. This is so when their
dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebra ...
equals zero: \hat_1 \cdot \hat_2 = 0 Thus the equation of motion relating the two angular positions is given by: \tan\gamma_1 = \cos\beta\tan\gamma_2\, with a formal solution for \gamma_2 = \tan^\left tan\gamma_1 \sec\beta\right, The solution for \gamma_2 is not unique since the arctangent function is multivalued, however it is required that the solution for \gamma_2 be continuous over the angles of interest. For example, the following explicit solution using the
atan2 In computing and mathematics, the function atan2 is the 2-argument arctangent. By definition, \theta = \operatorname(y, x) is the angle measure (in radians, with -\pi < \theta \leq \pi) between the positive
(y, x) function will be valid for -\pi < \gamma_1 < \pi: \gamma_2 = \operatorname\left(\sin\gamma_1, \cos\beta\, \cos\gamma_1\right) The angles \gamma_1 and \gamma_2 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 \omega_1 = d\gamma_1/dt and \omega_2 = \omega_1\left(\frac\right) As shown in the plots, the angular velocities are not linearly related, but rather are periodic with a period half that of the rotating shafts. The angular velocity equation can again be differentiated to get the relation between the angular accelerations a_1 and a_2 = \frac - \frac


Double Cardan shaft

A configuration known as a double Cardan joint drive shaft partially overcomes the problem of jerky rotation. This configuration uses two U-joints joined by an intermediate shaft, with the second U-joint phased in relation to the first U-joint to cancel the changing angular velocity. In this configuration, the angular velocity of the driven shaft will match that of the driving shaft, provided that both the driving shaft and the driven shaft are at equal angles with respect to the intermediate shaft (but not necessarily in the same plane) and that the two universal joints are 90 degrees out of phase. This assembly is commonly employed in
rear wheel drive Rear-wheel drive (RWD) is a form of engine and transmission layout used in motor vehicles, in which the engine drives the rear wheels only. Until the late 20th century, rear-wheel drive was the most common configuration for cars. Most rear-wheel ...
vehicles, where it is known as a
drive shaft A drive shaft, driveshaft, driving shaft, tailshaft (Australian English), propeller shaft (prop shaft), or Cardan shaft (after Girolamo Cardano) is a component for transmitting mechanical power (physics), power and torque and rotation, usually ...
or propeller (prop) shaft. Even when the driving and driven shafts are at equal angles with respect to the intermediate shaft, if these angles are greater than zero, 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.Electronically-controlled adjustable height bearing support bracket - US Patent 6345680
The intermediate shaft will also have a
sinusoidal A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in m ...
component to its angular velocity, which contributes to vibration and stresses. Mathematically, this can be shown as follows: If \gamma_1\, and \gamma_2\, are the angles for the input and output of the universal joint connecting the drive and the intermediate shafts respectively, and \gamma_3\, and \gamma_4\, are the angles for the input and output of the universal joint connecting the intermediate and the output shafts respectively, and each pair are at angle \beta\, with respect to each other, then: \tan\gamma_2 = \cos\beta\,\tan\gamma_1\qquad \tan\gamma_4 = \cos\beta\,\tan\gamma_3 If the second universal joint is rotated 90 degrees with respect to the first, then Using the fact that \tan(\gamma + \pi/2) = 1/\tan\gamma yields: \tan\gamma_4 = \frac = \frac = \tan\left(\gamma_1 + \frac\right)\, and it is seen that the output drive is just 90 degrees out of phase with the input shaft, yielding a constant-velocity drive. NOTE: The reference for measuring angles of input and output shafts of universal joint are mutually perpendicular axes. So, in absolute sense the forks of the intermediate shaft are parallel to each other. (Since, one fork is acting as input and the other fork is acting as output for shafts and above 90 degree phase difference is mentioned between the forks.)


Double Cardan joint

A double Cardan joint consists of two universal joints mounted back to back with a centre yoke; the centre yoke replaces the intermediate shaft. Provided that the angle between the input shaft and centre yoke is equal to the angle between the centre yoke and the output shaft, the second Cardan joint will cancel the velocity errors introduced by the first Cardan joint and the aligned double Cardan joint will act as a CV joint.


Thompson coupling

A Thompson coupling is a refined version of the double Cardan joint. It offers slightly increased efficiency with the penalty of great increase in complexity.


See also

* Canfield joint *
Constant-velocity joint Constant-velocity joints (also known as homokinetic or CV joints) are mechanical joints which allow a drive shaft to transmit power through a variable angle, at constant rotational speed, without an appreciable increase in friction or Backlash (e ...
*
Elastic coupling A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. The primary purpose of couplings is to join two pieces of rotating equipment while permitting some degree of misalignment or end mov ...
*
Gear coupling A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. The primary purpose of couplings is to join two pieces of rotating equipment while permitting some degree of misalignment or end mov ...
*
Hotchkiss drive The Hotchkiss drive is a shaft drive form of power transmission. It was the dominant means for front-engine, rear-wheel drive layout cars in the 20th century. The name comes from the French automobile manufacturer Hotchkiss, although other makers, ...
*
Rag joint A rag joint refers to certain flexible joints (flexure bearings) found on automobiles and other machines. They are typically found on steering column shafts that connect the steering wheel to the steering gear input shaft, usually at the steeri ...
* Twin Spring Coupling joint


Notes


References


''Theory of Machines 3''
from National University of Ireland


External links

*

' by Sándor Kabai,
Wolfram Demonstrations Project The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields. It is hos ...
. *
DIY: Replacing Universal Joints
' at About.com.
Thompson Couplings Limited
explanation of the Thompson coupling.
Universal Joint Failure - Custom Solutions Address Common Problems
*Universal Joint Phasing
The Concept and Importance of Drive Shaft Phasing and Alignment


by ABC Television (''The New Inventors'', broadcast Feb 2007). * (constant-velocity coupling).
About universal joints
at McMaster Carr.
Cardan Shaft
at McMaster Carr. {{DEFAULTSORT:Universal Joint Rotating shaft couplings Mechanisms (engineering) Automotive transmission technologies Articles containing video clips