Six degrees of freedom

# Six degrees of freedom

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Six degrees of freedom (6DoF) refers to motion of a rigid body
Rigid body
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...

in three-dimensional space
Three-dimensional space
Three-dimensional space is a geometric 3-parameters model of the physical universe in which we live. These three dimensions are commonly called length, width, and depth , although any three directions can be chosen, provided that they do not lie in the same plane.In physics and mathematics, a...

, namely the ability to move forward/backward, up/down, left/right (translation
Translation (physics)
In physics, translation is movement that changes the position of an object, as opposed to rotation. For example, according to Whittaker:...

in three perpendicular
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...

axes) combined with rotation
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

about three perpendicular axes (pitch, yaw, roll
Flight dynamics
Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of mass, known as pitch, roll and yaw .Aerospace engineers develop control systems for...

). As the movement along each of the three axes is independent of each other and independent of the rotation about any of these axes, the motion indeed has six degrees of freedom
Degrees of freedom (physics and chemistry)
A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...

. Notice that the initial conditions for a rigid body include also the derivatives of these variables (velocity and angular velocity), being therefore a 12-DOF system.

## Robotics

Robot
Robot
A robot is a mechanical or virtual intelligent agent that can perform tasks automatically or with guidance, typically by remote control. In practice a robot is usually an electro-mechanical machine that is guided by computer and electronic programming. Robots can be autonomous, semi-autonomous or...

arms are often categorized by their degrees of freedom (typically achieving more than six degrees of freedom). This number typically refers to the number of single-axis rotational joints in the arm, where a higher number indicates an increased flexibility in positioning a tool. This is a practical metric, in contrast to the abstract definition of degrees of freedom which measures the aggregate positioning capability of a system. Dean Kamen
Dean Kamen
Dean L. Kamen is an American entrepreneur and inventor from New Hampshire.Born in Rockville Centre, New York, he attended Worcester Polytechnic Institute, but dropped out before graduating after five years of private advanced research for drug infusion pump AutoSyringe...

, inventor of the Segway
Segway PT
The Segway PT is a two-wheeled, self-balancing transportation machine invented by Dean Kamen. It is produced by Segway Inc. of New Hampshire, USA. The name "Segway" is a homophone of "segue" while "PT" denotes personal transporter....

, recently unveiled a prototype robotic arm with 21 degrees of freedom for DARPA. Humanoid robot
Humanoid robot
A humanoid robot or an anthropomorphic robot is a robot with its overall appearance, based on that of the human body, allowing interaction with made-for-human tools or environments. In general humanoid robots have a torso with a head, two arms and two legs, although some forms of humanoid robots...

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
Torso
Trunk or torso is an anatomical term for the central part of the many animal bodies from which extend the neck and limbs. The trunk includes the thorax and abdomen.-Major organs:...

and neck
Neck
The neck is the part of the body, on many terrestrial or secondarily aquatic vertebrates, that distinguishes the head from the torso or trunk. The adjective signifying "of the neck" is cervical .-Boner anatomy: The cervical spine:The cervical portion of the human spine comprises seven boney...

.

## Engineering

The term is important in mechanical systems, especially biomechanical systems
Biomechanics
Biomechanics is the application of mechanical principles to biological systems, such as humans, animals, plants, organs, and cells. Perhaps one of the best definitions was provided by Herbert Hatze in 1974: "Biomechanics is the study of the structure and function of biological systems by means of...

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 are made relevant through software that integrate the data based on the needs and programming of the users.

Ascension Technology Corporation has recently created a 6DoF device small enough to fit in a biopsy needle, allowing physicians to better research at minute levels. The new sensor passively senses pulsed DC
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...

magnetic fields generated by either a cubic transmitter or a flat transmitter and is available for integration and manufacturability by medical OEMs
Original Equipment Manufacturer
An original equipment manufacturer, or OEM, manufactures products or components that are purchased by a company and retailed under that purchasing company's brand name. OEM refers to the company that originally manufactured the product. When referring to automotive parts, OEM designates a...

.

## Other uses

Six degrees of freedom is also used in game-play.

First-person shooter
First-person shooter
First-person shooter is a video game genre that centers the gameplay on gun and projectile weapon-based combat through first-person perspective; i.e., the player experiences the action through the eyes of a protagonist. Generally speaking, the first-person shooter shares common traits with other...

(FPS) games generally provide five degrees of freedom: forwards/backwards, slide left/right, up/down (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, 6DoF has been used to describe some space combat
Space flight simulator game
A space flight simulator game is a genre of simulation video games that lets players experience space flight. Highly realistic examples lacking any sort of combat include Orbiter and Microsoft Space Simulator...

games like Namco
Namco
is a Japanese corporation best known as a former video game developer and publisher. Following a merger with Bandai in September 2005, the two companies' game production assets were spun off into Namco Bandai Games on March 31, 2006. Namco Ltd. was re-established to continue domestic operation of...

's Star Luster
Star Luster
is a first-person shooter and space combat simulator video game developed and published by Namco in 1985 only in Japan. It is an arcade-style combat-dedicated, sci-fi flight simulator that was first released for the Nintendo Famicom. That same year, Nintendo adapted the title for play in the arcade...

, Bandai
Bandai
is a Japanese toy making and video game company, as well as the producer of a large number of plastic model kits. It is the world's third-largest producer of toys . Some ex-Bandai group companies produce anime and tokusatsu programs...

's Kidou Senshi Z-Gundam: Hot Scramble
Kidou Senshi Z-Gundam: Hot Scramble
KidÅ Senshi Z-Gundam: Hot Scramble was released on the Nintendo Family Computer console in 1986 by Bandai. The title translates to Mobile Suit Z-Gundam: Hot Scramble and is based on the first Gundam sequel series, Mobile Suit Zeta Gundam...

, and Arysis Software's Star Cruiser, where players or vehicles are free to move in any 3-dimensional direction, but may not have all three rotational axes. Dead Space 2
Dead Space 2 is a survival horror third-person shooter video game developed by Visceral Games and published by Electronic Arts for Microsoft Windows, PlayStation 3 and Xbox 360. It is the sequel to Dead Space. Unlike its predecessor, Dead Space 2 has a multiplayer mode. A Collector's Edition is...

, and to a lesser extent, Homeworld
Homeworld
Homeworld is a real-time strategy computer game released on September 28, 1999, developed by Relic Entertainment and published by Sierra Entertainment. It was the first fully three-dimensional RTS. In 2003, Relic released the source code for Homeworld...

and Zone Of The Enders
Zone of the Enders (series)
, commonly referred to by the acronym Z.O.E., is a franchise created by Hideo Kojima, owned by the video game publisher Konami, and expanded on by the animation studio Sunrise...

similarly 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 Futuremark Games Studio's Shattered Horizon
Shattered Horizon
Shattered Horizon is a first-person shooter video game developed and published by Futuremark Games Studio. The game was released on the Steam digital distribution service on 4 November 2009. On 19 November 2009, Futuremark Games Studio and Steam released three Guest Passes each to owners of the game...

, Descent
Descent (video game)
Descent is a 3D first-person shooter video game developed by Parallax Software and released by Interplay Entertainment Corp. in 1995. The game features six degrees of freedom gameplay and garnered several expansion packs...

and its sequels, and Miner Wars
Miner Wars
Miner Wars is an upcoming Six degrees of freedom space simulation video game franchise. The first installation, Miner Wars 2081 is currently in development by Keen Software House a...

.

The acronym 3DoF, meaning movement in the three dimensions but not rotation, is sometimes encountered.

The game controller of the PlayStation 3
PlayStation 3
The is the third home video game console produced by Sony Computer Entertainment and the successor to the PlayStation 2 as part of the PlayStation series. The PlayStation 3 competes with Microsoft's Xbox 360 and Nintendo's Wii as part of the seventh generation of video game consoles...

contains a "Sixaxis
Sixaxis
The Sixaxis Wireless Controller was the official gamepad for the Sony PlayStation 3 from launch until 2008 when it was succeeded by the DualShock 3....

" feature, which makes use of the six degrees of freedom. The Sixense TrueMotion
Sixense TrueMotion
The Razer Hydra is a motion and orientation detection game controller developed by Sixense Entertainment, a company founded in 2007, in partnership with Razer USA...

is similar but for the PC.