Six degrees of freedom

For the episode, seeThe Twilight Zone (2019 TV series).

"Six axis" redirects here. For the video game console controller, seeSixaxis.

Not to be confused withSix degrees of separation.

The six degrees of freedom: forward/back, up/down, left/right, yaw, pitch, roll

Six degrees of freedom(6DOF), or sometimessix degrees of movement,refers to the sixmechanical degrees of freedomof movement of arigid bodyinthree-dimensional space.Specifically, the body is free to changepositionas forward/backward (surge), up/down (heave), left/right (sway)translationin threeperpendicularaxes,combined with changes inorientationthroughrotationabout 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 ofvirtual reality,typically refers to tracking of rotational motion only: pitch, yaw, and roll.

Robotics

Serialandparallel manipulatorsystems are generally designed to position anend-effectorwith sixdegrees 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 itsforwardandinverse kinematics.

Robotarms are described by theirdegrees of freedom.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,inventor of theSegway,unveiled a prototype robotic armwith 14 degrees of freedom forDARPA.Humanoid robotstypically have 30 or more degrees of freedom, with six degrees of freedom per arm, five or six in each leg, and several more intorsoandneck.

Engineering

The term is important inmechanical systems,especiallybiomechanical 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.

Mnemonics to remember angle names

The six degrees of freedom of a mobile unit are divided in two motional classes as described below.

Translational envelopes:

1. Moving forward and backward on the X-axis. (Surge)
2. Moving left and right on the Y-axis. (Sway)
3. Moving up and down on the Z-axis. (Heave)

Rotational envelopes:

1. Tilting side to side on the X-axis. (Roll)
2. Tilting forward and backward on the Y-axis. (Pitch)
3. Turning left and right on the Z-axis. (Yaw)

In terms of aheadset,such as the kind used forvirtual reality,rotational envelopes can also be thought of in the following terms:

• Pitch:Nodding"yes"
• Yaw:Shaking"no"
• Roll:Bobblingfrom side to side

Operational envelope types

There are three types of operational envelope in the Six degrees of freedom. These types areDirect,Semi-direct(conditional) andNon-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.

1. Direct type:Involved a degree can be commanded directly without particularly conditions and described as a normal operation. (Anaileronon a basic airplane)
2. Semi-direct type:Involved a degree can be commanded when some specific conditions are met. (Reverse thruston 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 avesselat sea)

Transitional type also exists in some vehicles. For example, when theSpace Shuttleoperated inlow Earth orbit,the craft was described as fully-direct-six because in the vacuum of space, its six degrees could be commanded viareaction wheelsandRCS 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 wasgliding through the air using its wings and control surfaces.

Game controllers

Six degrees of freedomalso 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 term6DOFhas 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,HomeworldandZone Of The Endersallow freedom of movement.

Some examples of true 6DOF games, which allow independent control of all three movement axes and all three rotational axes, includeElite Dangerous,Shattered Horizon,theDescentfranchise, theEverspacefranchise,Retrovirus,Miner Wars,Space Engineers,ForsakenandOverload(from the same creators ofDescent). The space MMOVendetta Onlinealso features 6 degrees of freedom.

Motion tracking hardware devices such asTrackIRand software-based apps likeEyeware Beamare used for 6DOF head tracking. This device often finds its places inflight simulatorsand other vehicle simulators that require looking around the cockpit to locate enemies or simply avoiding accidents in-game.

The acronym3DOF,meaning movement in the three dimensions but not rotation, is sometimes encountered.

TheRazer Hydra,a motion controller for PC, tracks position and rotation of two wirednunchucks,providing six degrees of freedom on each hand.

TheSpaceOrb 360is a 6DOF computer input device released in 1996 originally manufactured and sold by the SpaceTec IMC company (first bought byLabtec,which itself was later bought byLogitech). They now offer the3Dconnexionrange of 6DOF controllers, primarily targeting the professionalCADindustry.

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

• Degrees of freedom (mechanics)– Number of independent parameters needed to define the state of a mechanical system
• Degrees of freedom problem– Multiple ways for multi-joint objects to realize a movement
• Euler angles– Description of the orientation of a rigid body
• Geometric terms of location– Directions or positions relative to the shape and position of an object
• Ship motions– Terms connected to the six degrees of freedom of motion
• Aircraft principal axes– Principal directions in aviation