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Six degrees of freedom (6DOF), or sometimes six degrees of movement, refers to the six mechanical degrees of freedom of movement of a
rigid body In physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible, when a deforming pressure or deforming force is applied on it. The distance between any two given points on a rigid body rema ...
in
three-dimensional space In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values ('' coordinates'') are required to determine the position of a point. Most commonly, it is the three- ...
. Specifically, the body is free to change
position Position often refers to: * Position (geometry), the spatial location (rather than orientation) of an entity * Position, a job or occupation Position may also refer to: Games and recreation * Position (poker), location relative to the dealer * ...
as forward/backward (surge), up/down (heave), left/right (sway)
translation Translation is the communication of the semantics, meaning of a #Source and target languages, source-language text by means of an Dynamic and formal equivalence, equivalent #Source and target languages, target-language text. The English la ...
in three
perpendicular In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', � ...
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 * Axis (disambiguation) An axis (: axes) may refer to: Mathematics ...
, combined with changes in
orientation Orientation may refer to: Positioning in physical space * Map orientation, the relationship between directions on a map and compass directions * Orientation (housing), the position of a building with respect to the sun, a concept in building des ...
through
rotation Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersect ...
about three perpendicular axes, often termed yaw (normal axis), pitch (transverse axis), and roll (longitudinal axis). Three degrees of freedom (3DOF), a term often used in the context of
virtual reality Virtual reality (VR) is a Simulation, simulated experience that employs 3D near-eye displays and pose tracking to give the user an immersive feel of a virtual world. Applications of virtual reality include entertainment (particularly video gam ...
, typically refers to tracking of rotational motion only: pitch, yaw, and roll.


Robotics

Serial and
parallel manipulator A parallel manipulator is a mechanical system that uses several computer-controlled serial chains to support a single platform, or end-effector. Perhaps, the best known parallel manipulator is formed from six linear actuators that support a mo ...
systems are generally designed to position an
end-effector An end effector is the device at the end of a robotic arm, designed to interact with the environment. The exact nature of this device depends on the application of the robot. In the strict definition, which originates from serial robotic manipu ...
with six
degrees of freedom In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...
, consisting of three in translation and three in orientation. This provides a direct relationship between actuator positions and the configuration of the manipulator defined by its
forward Forward is a relative direction, the opposite of backward. Forward may also refer to: People *Forward (surname) Sports * Forward (association football) * Forward (basketball), including: ** Point forward ** Power forward (basketball) ** Smal ...
and
inverse kinematics In computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a g ...
.
Robot A robot is a machine—especially one Computer program, programmable by a computer—capable of carrying out a complex series of actions Automation, automatically. A robot can be guided by an external control device, or the robot control, co ...
arms are described by their
degrees of freedom In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...
. This is a practical metric, in contrast to the abstract definition of degrees of freedom which measures the aggregate positioning capability of a system. In 2007,
Dean Kamen Dean Lawrence Kamen (; born April 5, 1951) is an American engineer, inventor, and businessman. He is known for his invention of the Segway PT, Segway and iBOT, as well as founding the non-profit organization For Inspiration and Recognition of Sc ...
, inventor of the
Segway A Segway is a two-wheeled, self-balancing personal transporter device invented by Dean Kamen. The name is a registered trademark of Segway Inc. It was brought to market in 2001 as the Segway HT, and then subsequently as the Segway PT. ''HT ...
, unveiled a prototype robotic arm with 14 degrees of freedom for
DARPA The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the Adva ...
.
Humanoid robot A humanoid robot is a robot resembling the human body in shape. The design may be for functional purposes, such as interacting with human tools and environments and working alongside humans, for experimental purposes, such as the study of bipeda ...
s typically have 30 or more degrees of freedom, with six degrees of freedom per arm, five or six in each leg, and several more in
torso The torso or trunk is an anatomical terminology, anatomical term for the central part, or the core (anatomy), core, of the body (biology), body of many animals (including human beings), from which the head, neck, limb (anatomy), limbs, tail an ...
and
neck The neck is the part of the body in many vertebrates that connects the head to the torso. It supports the weight of the head and protects the nerves that transmit sensory and motor information between the brain and the rest of the body. Addition ...
.


Engineering

The term is important in
mechanical systems A machine is a physical system that uses Power (physics), power to apply forces and control Motion, movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natura ...
, especially biomechanical systems, for analyzing and measuring properties of these types of systems that need to account for all six degrees of freedom. Measurement of the six degrees of freedom is accomplished today through both AC and DC magnetic or electromagnetic fields in sensors that transmit positional and angular data to a processing unit. The data is made relevant through software that integrates the data based on the needs and programming of the users. The six degrees of freedom of a mobile unit are divided in two motional classes as described below. Translational envelopes: #Moving forward and backward on the X-axis. (Surge) #Moving left and right on the Y-axis. (Sway) #Moving up and down on the Z-axis. (Heave) Rotational envelopes: #Tilting side to side on the X-axis. (
Roll Roll may refer to: Physics and engineering * Rolling, a motion of two objects with respect to each-other such that the two stay in contact without sliding * Roll angle (or roll rotation), one of the 3 angular degrees of freedom of any stiff bo ...
) #Tilting forward and backward on the Y-axis. ( Pitch) #Turning left and right on the Z-axis. ( Yaw) In terms of a headset, such as the kind used for
virtual reality Virtual reality (VR) is a Simulation, simulated experience that employs 3D near-eye displays and pose tracking to give the user an immersive feel of a virtual world. Applications of virtual reality include entertainment (particularly video gam ...
, rotational envelopes can also be thought of in the following terms: *Pitch:
Nodding A nod of the head is a gesture in which the head is tilted in alternating up and down arcs along the sagittal plane. In many cultures, it is most commonly, but not universally, used to indicate agreement, acceptance, or acknowledgement. To in ...
"yes" *Yaw: Shaking "no" *Roll: Bobbling from side to side


Operational envelope types

There are three types of operational envelope in the Six degrees of freedom. These types are ''Direct'', ''Semi-direct'' (conditional) and ''Non-direct,'' all regardless of the time remaining for the execution of the maneuver, the energy remaining to execute the maneuver and finally, if the motion is commanded via a biological entity (e.g. human), a robotical entity (e.g. computer) or both. #''Direct type'': Involved a degree can be commanded directly without particularly conditions and described as a normal operation. (An
aileron An aileron (French for "little wing" or "fin") is a hinged flight control surface usually forming part of the trailing edge of each wing of a fixed-wing aircraft. Ailerons are used in pairs to control the aircraft in roll (or movement aroun ...
on a basic airplane) #''Semi-direct type'': Involved a degree can be commanded when some specific conditions are met. (
Reverse thrust Reverse or reversing may refer to: Arts and media *Reverse (Eldritch album), ''Reverse'' (Eldritch album), 2001 *Reverse (2009 film), ''Reverse'' (2009 film), a Polish comedy-drama film *Reverse (2019 film), ''Reverse'' (2019 film), an Iranian cr ...
on an aircraft) #''Non-direct type'': Involved a degree when is achieved via the interaction with its environment and cannot be commanded. (Pitching motion of a vessel at sea) Transitional type also exists in some vehicles. For example, when the
Space Shuttle The Space Shuttle is a retired, partially reusable launch system, reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. ...
operated in
low Earth orbit A low Earth orbit (LEO) is an geocentric orbit, orbit around Earth with a orbital period, period of 128 minutes or less (making at least 11.25 orbits per day) and an orbital eccentricity, eccentricity less than 0.25. Most of the artificial object ...
, the craft was described as fully-direct-six because in the vacuum of space, its six degrees could be commanded via
reaction wheels A reaction wheel (RW) is an electric motor attached to a flywheel, which, when its rotation speed is changed, causes a counter-rotation proportionately through conservation of angular momentum. A reaction wheel can rotate only around its center ...
and RCS thrusters. However, when the Space Shuttle was descending through the Earth's atmosphere for its return, the fully-direct-six degrees were no longer applicable as it was gliding through the air using its wings and control surfaces.


Game controllers

''Six degrees of freedom'' also refers to movement in video game-play.
First-person shooter A first-person shooter (FPS) is a video game genre, video game centered on gun fighting and other weapon-based combat seen from a First person (video games), first-person perspective, with the player experiencing the action directly through t ...
(FPS) games generally provide five degrees of freedom: forwards/backwards, slide left/right, up/down (jump/crouch/lie), yaw (turn left/right), and pitch (look up/down). If the game allows leaning control, then some consider it a sixth DOF; however, this may not be completely accurate, as a lean is a limited partial rotation. The term ''6DOF'' has sometimes been used to describe games which allow freedom of movement, but do not necessarily meet the full 6DOF criteria. For example, ''
Dead Space 2 ''Dead Space 2'' is a 2011 survival horror game developed by Visceral Games and published by Electronic Arts. It was released for PlayStation 3, Windows, and Xbox 360 in January. The second mainline entry in the ''Dead Space'' series, set on the ...
'', and to a lesser extent, ''
Homeworld ''Homeworld'' is a real-time strategy video game developed by Relic Entertainment and published by Sierra Studios on September 28, 1999, for Windows. Set in space, the science fiction game follows the Kushan exiles of the planet Kharak after t ...
'' and ''
Zone Of The Enders ''Zone of the Enders'' is a video game franchise created by Hideo Kojima and Konami that focuses around combat in space with mecha called Orbital Frames. The original ''Zone of the Enders'' was released for the PlayStation 2 in March 2001. A se ...
'' allow freedom of movement. Some examples of true 6DOF games, which allow independent control of all three movement axes and all three rotational axes, include ''
Elite Dangerous ''Elite Dangerous'' is an online game, online space flight simulation game developed and published by Frontier Developments. The player commands a spaceship and explores a realistic 1:1 Scale (ratio), scale, open-world representation of the Mi ...
'', ''
Shattered Horizon ''Shattered Horizon'' is a 2009 first-person shooter video game developed and published by Futuremark Games Studio. The game was released on November 4, 2009 exclusively on Microsoft Windows via Steam. Gameplay ''Shattered Horizon'' is a firs ...
'', the ''
Descent Descent may refer to: As a noun Genealogy and inheritance * Common descent, concept in evolutionary biology * Kinship, one of the major concepts of cultural anthropology **Pedigree chart or family tree **Ancestry **Lineal descendant **Heritage ** ...
'' franchise, the
Everspace ''Everspace'' is a 3D space shooter with roguelike elements, developed and published by German studio Rockfish Games. It was released in 2017, while the sequel, '' Everspace 2'' was released in 2023. Gameplay ''Everspace'' is a space combat ...
franchise, ''
Retrovirus A retrovirus is a type of virus that inserts a DNA copy of its RNA genome into the DNA of a host cell that it invades, thus changing the genome of that cell. After invading a host cell's cytoplasm, the virus uses its own reverse transcriptase e ...
'', '' Miner Wars'', ''
Space Engineers ''Space Engineers'' is a voxel-based sandbox game, developed and published by Czech independent developer Keen Software House. In 2013, the initial developmental release of the game joined the Steam early access program. During the following y ...
'', '' Forsaken'' and '' Overload'' (from the same creators of ''Descent''). The space MMO '' Vendetta Online'' also features 6 degrees of freedom. Motion tracking hardware devices such as TrackIR and software-based apps lik
Eyeware Beam
are used for 6DOF head tracking. This device often finds its places in
flight simulators A flight simulator is a device that artificially re-creates aircraft flight and the environment in which it flies, for pilot training, design, or other purposes. It includes replicating the equations that govern how aircraft fly, how they rea ...
and other vehicle simulators that require looking around the cockpit to locate enemies or simply avoiding accidents in-game. The acronym 3DOF, meaning movement in the three dimensions but not rotation, is sometimes encountered. The
Razer Hydra The Razer Hydra (previously known as Sixense TrueMotion) is a motion and orientation detection game controller developed by Sixense Entertainment, a company founded in 2007, in partnership with Razer USA. It uses a weak magnetic field to detect t ...
, a motion controller for PC, tracks position and rotation of two wired nunchucks, providing six degrees of freedom on each hand. The
SpaceOrb 360 The SpaceOrb 360 is a 6DOF computer input device that is designed to be operated with two hands. Each of the 6 axes have 10-bit precision each when measuring the amount of force or torque applied. It has two right-index-finger buttons and four rig ...
is a 6DOF computer input device released in 1996 originally manufactured and sold by the SpaceTec IMC company (first bought by
Labtec Labtec Enterprises Inc. was an American manufacturer of computer accessories active as an independent company from 1980 to 2001. They were best known for their budget range of peripherals such as keyboards, mice, microphones, speakers and webca ...
, which itself was later bought by
Logitech Logitech International S.A. ( ) is a Swiss multinational manufacturer of computer peripherals and software. Headquartered in Lausanne, Switzerland, the company has offices throughout Europe, Asia, Oceania, and the Americas. It is a component of ...
). They now offer the
3Dconnexion 3Dconnexion is a German manufacturer of human interface devices for manipulating and navigating computer-generated 3D imagery. These devices are often referred to as 3D motion controllers, 3D navigation devices, 6DOF devices (six degrees of ...
range of 6DOF controllers, primarily targeting the professional
CAD Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve c ...
industry. The controllers sold with HTC VIVE provide 6DOF information by the lighthouse, which adopts Time of Flight (TOF) technology to determine the position of controllers.


See also

* * * * * *


References

{{DEFAULTSORT:Six Degrees Of Freedom Mechanics Biomedical engineering Robot kinematics Virtual reality Augmented reality Mixed reality