Six Degrees of Freedom
The six degrees of freedom (6DOF) is a representation of how an object moves through 3D space by either translating linearly or rotating axially. A single degree of freedom on an object is controlled by the up/down (Z), forward/back (X), left/right (Y), pitch, roll, or yaw.
Six Degrees of Freedom - Translation
Three of the 6DOF are controlled through translation. As you recall, a translation is any movement along the X, Y, and Z axes. A linear translation’s degrees of freedom are controlled by defining the origin (like the base or the tool head of the robotic arm) and should all be perpendicular to one another respectively.
Translation does not affect an object’s rotation. In theory, the object could be rotating in space and not have any translation, like a wheel spinning on a stationary axle.
Six Degrees of Freedom - Rotation
The remaining three 6DOF are controlled through axial rotation. Typically, the three rotational degrees of freedom, Pitch (P), Roll (R), and Yaw (Y), will rotate around the center of the object’s origin. The rotational degrees of freedom are controlled by either a level plane or by a line. Similar to the three linear translation degrees of freedom, the rotational degrees of freedom are perpendicular to one another. The rotational degrees of freedom will be considered at the center axis of the linear degrees of freedom. XYZ linearly are respective to PRY rotationally.