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SIX DEGREES OF FREEDOM

SIX DEGREES OF FREEDOM(6DOF)





The six degrees of freedom: forward/back, up/down, left/right, yaw, pitch, roll
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, up/down , left/right  translation in three perpendicular axes combined with changes  in orientation  through  rotation about three perpendicular axes, often termed yaw , pitch, and roll. 


 Six degree of freedom consists of the following movement:
  • Translation – Moving along the different axes X, Y and Z
    • Moving up and down along the Y axis is called heaving.
    • Moving forwards and backwards along the X axis is called surging.
    • Moving left and right along the Z axis is called swaying.

  • Rotation – Turning in order to face a different axis
    • Moving between X and Y is called pitch.
    • Moving between X and Z is called yaw.
    • Moving between Z and Y is called roll.




A example of an object that has 6DOF is an airplane. It can move freely in three-dimensional space, with the two horizontal axes as X and Z while the vertical axis is Y. If it needs to face up or down, it needs to change the orientation of its nose from horizontal X to Y which is called pitch. If the plane needs to turn from the X axis to the Z axis without changing the orientation of its body, it can do a yaw by using its rudder so the wings remain horizontal while the nose starts to point to the Z axis. Since it is often assumed that the X orientation is always where the nose is facing with regards to the plane, moving the plane from X to Y will make it roll, hence the term. The pilot can then combine any of these parameters of movement to execute maneuvers.

{\displaystyle M=3(N-1-j)+\sum _{i=1}^{j}\ f_{i},}


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