Six degrees of freedom

"Six axis" redirects here. For the PlayStation 3 video game console controller, see Sixaxis.
The six degrees of freedom: forward/back, up/down, left/right, pitch, yaw, roll

Six degrees of freedom (6DoF) refers to the freedom of movement of a rigid body in three-dimensional space. Specifically, the body is free to change position as forward/backward (surge), up/down (heave), left/right (sway) translation in three perpendicular axes, combined with changes in orientation through rotation about three perpendicular axes, often termed pitch, yaw, and roll.


Serial and parallel manipulator systems are generally designed to position an end-effector with six degrees of freedom, 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 and inverse kinematics.

Robot arms are described by their degrees of freedom. This number typically refers to the number of single-axis rotational joints in the arm, where 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.[1]

In 2007, Dean Kamen, inventor of the Segway, unveiled a prototype robotic arm with 14 degrees of freedom for DARPA. Humanoid robots 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 and neck.[2]


The term is important in mechanical systems, 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 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 magnetic fields generated by either a cubic transmitter or a flat transmitter and is available for integration and manufacturability by medical OEMs.[3]

An example of six degree of freedom movement is the motion of a ship at sea. It is described as :[4]


  1. Moving forward and backward on the X-axis. (Surging)
  2. Moving left and right on the Y-axis. (Swaying)
  3. Moving up and down on the Z-axis. (Heaving)


  1. Tilting side to side on the X-axis. (Rolling)
  2. Tilting forward and backward on the Y-axis. (Pitching)
  3. Turning left and right on the Z-axis. (Yawing)
See also: Euler angles

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 (human) or a robotical entity (computer).

1- Direct type : Involved a degree can be commanded directly without particularly conditions and described as a normal operation. (An aileron on a basic airplane)

2- Semi-direct type : Involved a degree can be commanded when some specific conditions are met. (Reverse thrust on an aircraft)

3- 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 operates in space, the craft is described as fully-direct-six because its six degrees can be commanded. However, when the Space Shuttle is in the earth's atmosphere for its return, the fully-direct-six degrees are not longer applicable for many technical reasons.

Game controllers

Six degrees of freedom also refers to movement in video game-play.

First-person shooter (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, and to a lesser extent, Homeworld and Zone Of The Enders 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 Shattered Horizon, the Descent franchise, Retrovirus (PC game), Miner Wars, Space Engineers, Forsaken and now Overload, from the creators of Descent. The space MMO Vendetta Online also features 6 degrees of freedom.

Motion tracking devices such as TrackIR are used for 6DoF head tracking. This device often finds its places in flight simulators 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, a motion controller for PC, tracks position and rotation of two wired nunchucks, providing six degrees of freedom on each hand.

The SpaceOrb 360 is a 6DOF computer input device released in 1996 originally manufactured and sold by the SpaceTec IMC company (first bought by Labtec, which itself was later bought by Logitech).

See also


  1. Paul, Richard P., Robot Manipulators: Mathematics, Programming, and Control, MIT Press, 1981.
  2. Craig, John J., Introduction to Robotics: Mechanics and Control, Addison-Wesley, 1986.
  3. Medical News Today. Ascension Develops World's Smallest Six Degrees-of-Freedom Sensor For Emerging Medical Procedures. 25 Aug 2008
  4. Summary of ship movement Archived November 25, 2011, at the Wayback Machine.
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