![Goniometer IMG 4841](https://upload.wikimedia.org/wikipedia/commons/7/70/Goniometer_IMG_4841.jpg)
A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words,
γωνία (''gōnía'') '
angle
In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle.
Angles formed by two ...
' and
μέτρον (''métron'') '
measure
Measure may refer to:
* Measurement, the assignment of a number to a characteristic of an object or event
Law
* Ballot measure, proposed legislation in the United States
* Church of England Measure, legislation of the Church of England
* Mea ...
'.
The first known description of a goniometer, based on the
astrolabe
An astrolabe ( grc, ἀστρολάβος ; ar, ٱلأَسْطُرلاب ; persian, ستارهیاب ) is an ancient astronomical instrument that was a handheld model of the universe. Its various functions also make it an elaborate inclin ...
, was by
Gemma Frisius
Gemma Frisius (; born Jemme Reinerszoon; December 9, 1508 – May 25, 1555) was a Frisian physician, mathematician, cartographer, philosopher, and instrument maker. He created important globes, improved the mathematical instruments of his d ...
in 1538.
Applications
Surveying
Prior to the invention of the
theodolite
A theodolite () is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and i ...
, the goniometer was used in
surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ca ...
. The application of triangulation to
geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
was described in the second (1533) edition of ''Cosmograficus liber'' by Petri Appiani as a 16-page appendix by Frisius entitled ''Libellus de locorum describendorum ratione''.
Communications
The
Bellini–Tosi direction finder
A Bellini–Tosi direction finder (B–T or BTDF) is a type of radio direction finder (RDF), which determines the direction to, or ''bearing'' of, a radio transmitter. Earlier RDF systems used very large rotating loop antennas, which the B–T sy ...
was a type of
radio direction finder
Direction finding (DF), or radio direction finding (RDF), isin accordance with International Telecommunication Union (ITU)defined as radio location that uses the reception of radio waves to determine the direction in which a radio station ...
that was widely used from
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
to
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
. It used the signals from two crossed antennas, or four individual antennas simulating two crossed ones, to re-create the radio signal in a small area between two loops of wire. The operator could then measure the angle to the target radio source by performing direction finding within this small area. The advantage to the Bellini–Tosi system is that the antennas do not move, allowing them to be built at any required size.
The basic technique remains in use, although the equipment has changed dramatically. Goniometers are widely used for military and civil purposes,
e.g. interception of satellite and naval communications on the French warship
Dupuy de Lôme uses multiple goniometers.
Crystallography
In
crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...
, goniometers are used for measuring angles between crystal faces. They are also used in
X-ray diffraction
X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
to rotate the samples. The groundbreaking investigations of physicist
Max von Laue
Max Theodor Felix von Laue (; 9 October 1879 – 24 April 1960) was a German physicist who received the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals.
In addition to his scientific endeavors with cont ...
and colleagues into the
atomic structure of crystals in 1912 involved a goniometer.
Light measurement
Goniophotometer
A Goniophotometer is a device used for measurement of the light emitted from an object at different angles. The use of goniophotometers has been increasing in recent years with the introduction of LED-light sources, which are mostly directed light ...
s measure the spatial distribution of light visible to the human eye (often
luminous intensity
In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. ...
) at specific angular positions, usually covering all spherical angles.
In medicine
A goniometer is used to document initial and subsequent range of motion, at the visits for occupational injuries, and by
disability
Disability is the experience of any condition that makes it more difficult for a person to do certain activities or have equitable access within a given society. Disabilities may be Cognitive disability, cognitive, Developmental disability, dev ...
evaluators to determine a permanent disability. This is to evaluate progress, and also for medico-legal purposes. It is a tool to evaluate
Waddell's signs
Waddell's signs are a group of physical signs, first described in a 1980 article in '' Spine'', and named for the article's principal author, Professor Gordon Waddell (1943–2017), a Scottish Orthopedic Surgeon. Waddell's signs may indicate n ...
(findings that may indicate symptom magnification.)
Rehabilitative therapy
In physical therapy, occupational therapy, and athletic training, a goniometer measures
range of motion
Range of motion (or ROM), is the linear or angular distance that a moving object may normally travel while properly attached to another. It is also called range of travel (or ROT), particularly when talking about mechanical devices and in mechanic ...
of limbs and joints of the body. These measurements help accurately track progress in a rehabilitation program. When a patient has decreased range of motion, a therapist assesses the joint before performing an intervention, and continues to use the tool to monitor progress. The therapist can take these range of motion measurements at any joint. They typically require knowledge about the anatomy of the body, particularly bony landmarks. For example, when measuring the knee joint, the therapist places the axis (point of rotation) on the lateral
epicondyle
An epicondyle () is a rounded eminence on a bone that lies upon a condyle ('' epi-'', "upon" + ''condyle'', from a root meaning "knuckle" or "rounded articular area"). There are various epicondyles in the human skeleton, each named by its anatomic ...
of the femur, and lines up the stationary arm with the
greater trochanter
The greater trochanter of the femur is a large, irregular, quadrilateral eminence and a part of the skeletal system.
It is directed lateral and medially and slightly posterior. In the adult it is about 2–4 cm lower than the femoral head.Stan ...
of the
femur
The femur (; ), or thigh bone, is the proximal bone of the hindlimb in tetrapod vertebrates. The head of the femur articulates with the acetabulum in the pelvic bone forming the hip joint, while the distal part of the femur articulates with ...
. Finally, the therapist lines up the moveable arm of the goniometer with the lateral
malleolus
A malleolus is the bony prominence on each side of the human ankle.
Each leg is supported by two bones, the tibia on the inner side (medial) of the leg and the fibula on the outer side (lateral) of the leg. The medial malleolus is the promine ...
of the
fibula
The fibula or calf bone is a leg bone on the lateral side of the tibia, to which it is connected above and below. It is the smaller of the two bones and, in proportion to its length, the most slender of all the long bones. Its upper extremity is ...
, and records a measurement using the degree scale on the circular portion of the tool. Reading
accuracy
Accuracy and precision are two measures of ''observational error''.
''Accuracy'' is how close a given set of measurements (observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each other ...
is sometimes a problem with goniometers. Issues with the intra-measure (between measures) and inter-tester (between clinicians)
reliability
Reliability, reliable, or unreliable may refer to:
Science, technology, and mathematics Computing
* Data reliability (disambiguation), a property of some disk arrays in computer storage
* High availability
* Reliability (computer networking), a ...
may increase as the experience of the examiner decreases. Some studies suggest that these errors can be anywhere between 5 and 10 degrees.
These goniometers come in different forms that some argue increase reliability. The universal standard goniometer is a plastic or metal tool with 1 degree increments. The arms are usually not longer than 12-inches, so it can be hard to accurately pinpoint the exact landmark for measurement. The telescopic-armed goniometer is more reliable—with a plastic circular axis like a classic goniometer, but with arms that extend to as long as two feet in either direction.
More recently in the twenty-first century,
smartphone
A smartphone is a portable computer device that combines mobile telephone and computing functions into one unit. They are distinguished from feature phones by their stronger hardware capabilities and extensive mobile operating systems, whic ...
application developers have created mobile applications that provide the functions of a goniometer. These applications (such as Knee Goniometer and Goniometer Pro) use the accelerometers in phones to calculate joint angles. Recent research supports these applications and their devices as reliable and valid tools with as much accuracy as a universal goniometer.
Modern rehabilitative therapy motion capture systems perform goniometry at the very least measuring active range of motion.
While in some cases accuracy may be inferior to a goniometer, measuring angles with a motion capture system is superior at measuring during dynamic, as opposed to static situations. Furthermore, using a traditional goniometer takes valuable time. In the clinical context, performing manual measurements takes valuable time and may not be practical.
Surface science
Contact angle goniometer
![Contact angle measurement with Attension Theta](https://upload.wikimedia.org/wikipedia/commons/0/0b/Contact_angle_measurement_with_Attension_Theta.png)
In
surface science
Surface science is the study of physical and chemical phenomena that occur at the interface of two phases, including solid–liquid interfaces, solid–gas interfaces, solid–vacuum interfaces, and liquid–gas interfaces. It includes the fiel ...
, an instrument called a contact angle goniometer or
tensiometer
Tensiometer may refer to one of a number of devices. The two most common are:
* Tensiometer (surface tension) an instrument used to measure the surface tension of liquids
*Tensiometer (soil science)
A tensiometer in soil science is a measur ...
measures the static
contact angle
The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liq ...
, advancing and receding contact angles, and sometimes surface tension. The first contact angle goniometer was designed by
William Zisman
Dr. William Albert Zisman (1905–1986)Dr. William A. Zisman: A Retrospective, Labstracts, July 6, 2009, p3 was an American chemist and geophysicist.
Life and career
He was born in Albany, NY and spent his youth in Providence, RI up to the age o ...
of the
United States Naval Research Laboratory
The United States Naval Research Laboratory (NRL) is the corporate research laboratory for the United States Navy and the United States Marine Corps. It was founded in 1923 and conducts basic scientific research, applied research, technological ...
in
Washington, D.C.
)
, image_skyline =
, image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, ...
and manufactured by ramé-hart (now ramé-hart instrument company), New Jersey, USA. The original manual contact angle goniometer used an eyepiece with a microscope. Today's contact angle goniometer uses a camera and software to capture and analyze the drop shape, and is better suited for dynamic and advanced studies.
Surface tension
Contact angle
The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liq ...
goniometers (q.v.)can also determine the
surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...
for any liquid in gas or the
interfacial tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to ...
between any two liquids. If the difference in densities between the two fluids is known, the surface tension or interfacial tension can be calculated by the pendant drop method. An advanced instrument often called a goniometer / tensiometer includes software tools that measure
surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...
and
interfacial tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to ...
using the pendant drop, inverted pendant drop, and sessile drop methods, in addition to
contact angle
The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liq ...
. A
centrifugal adhesion balance relates the contact angles to the adhesion of the drop to the surface. A
gonioreflectometer
A gonioreflectometer is a device for measuring a bidirectional reflectance distribution function (BRDF).
The device consists of a light source illuminating the material to be measured and a sensor that captures light reflected from that material ...
measures the reflectivity of a surface at a number of angles.
Positioning
![Positioning goniometer stage](https://upload.wikimedia.org/wikipedia/commons/9/95/Positioning_goniometer_stage.jpg)
A positioning goniometer or goniometric stage is a device that rotates an object precisely about a fixed axis in space. It is similar to a
linear stage
A linear stage or translation stage is a component of a precise motion system used to restrict an object to a single axis of motion. The term linear slide is often used interchangeably with "linear stage", though technically "linear slide" refer ...
— however, rather than move linearly relative to its base, the stage platform rotates partially about a fixed axis above the mounting surface of the platform. Positioning goniometers typically use a
worm drive
A worm drive is a gear arrangement in which a worm (which is a gear in the form of a screw) meshes with a worm wheel (which is similar in appearance to a spur gear). The two elements are also called the worm screw and worm gear. The terminolo ...
with a partial worm wheel fixed to the underside of the stage platform meshing with a worm in the base. The worm gear may be rotated manually, or by a motor in automated positioning systems.
Knife and blade cutting edge angle measurement
The included cutting angles of all kinds of sharp edge blades are measured using a laser reflecting goniometer. Developed by the
Cutlery and Allied Trades Research Association (CATRA) in the UK, a range of devices can accurately determine the cutting edge profile, including a rounding of the tip to ½°. The included angle of a blade is important in controlling its cutting ability and edge strength—i.e., a low angle makes a thin sharp edge optimized for cutting softer materials, while a large angle makes a thick edge that is less sharp but stronger, which may be better for cutting harder materials.
Doctor blade inspection
Used
doctor blade
In printing the doctor blade (from ''ductor blade'') removes the excess ink from the smooth non-engraved portions of the anilox roll and the land areas of the cell walls. Doctor blades are also used in other printing and coating processes, such as ...
s, from
gravure
Rotogravure (or gravure for short) is a type of intaglio printing process, which involves engraving the image onto an image carrier. In gravure printing, the image is engraved onto a cylinder because, like offset printing and flexography, it ...
and other
printing
Printing is a process for mass reproducing text and images using a master form or template. The earliest non-paper products involving printing include cylinder seals and objects such as the Cyrus Cylinder and the Cylinders of Nabonidus. The ea ...
and
coating
A coating is a covering that is applied to the surface of an object, usually referred to as the Substrate (materials science), substrate. The purpose of applying the coating may be decorative, functional, or both. Coatings may be applied as liquid ...
processes, can be inspected with a goniometer, typically with a built-in light source, to examine the blade edge for wear and correct angles. A difference in angle from that set on the machine may indicate excessive pressure, and a range of angles ("rounding") probably indicates a lack of stiffness, or wear, in the blade holder assembly.
See also
*
*
*
*
References
{{Reflist
External links
Reference for the famous Chain Home British Radar of WWII
Angle measuring instruments
Dimensional instruments
Laboratory equipment
Occupational therapy
Physical therapy
Surface science
Surveying instruments