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 connecting rigid
shaft
Shaft may refer to:
Rotating machine elements
* Shaft (mechanical engineering), a rotating machine element used to transmit power
* Line shaft, a power transmission system
* Drive shaft, a shaft for transferring torque
* Axle, a shaft around whi ...
s whose
axes are inclined to each other. It is commonly used in shafts that transmit
rotary motion. It consists of a pair of
hinges 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 play. Th ...
.
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 h ...
, a polymath of the 17th century who contributed to knowledge of various clever mechanisms
* Spicer joint, after
Clarence W. Spicer and the
Spicer Manufacturing Company, who manufactured U joints
* Hardy Spicer joint, after the
Hardy Spicer 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. In Europe the universal joint is often called the Cardano joint (and a
drive shaft 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, 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 play. Th ...
.
[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 h ...
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 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 play. Th ...
.
Christopher Polhem 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 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 patent of 1881, for example, used double universal joints in the locomotive's
drive shaft. Charles Amidon used a much smaller universal joint in his
bit-brace patented 1884.
Beauchamp Tower'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
French (french: français(e), link=no) may refer to:
* Something of, from, or related to France
** French language, which originated in France, and its various dialects and accents
** French people, a nation and ethnic group identified with Franc ...
or are strongly influenced by French usage. Examples include an 1868 report on the
''Exposition Universelle'' of 1867 and an article on the
dynamometer translated from French in 1881.
In the 20th century,
Clarence W. Spicer and the
Spicer Manufacturing Company, as well as the
Hardy Spicer successor brand, helped further popularize universal joints in the
automotive,
farm equipment,
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 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:
#
the angle of rotation for axle 1
#
the angle of rotation for axle 2
#
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 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: