DoF a pair is defined as number of independent relative motions both translation and rotational to define its position.
DOF = 6 – No of restrains
What is 6DOF?
Six-degrees-of-freedom (6DOF) means you can move six ways; forward/backward, left/right, up/down; these movements are linear, determine your position and are measured in feet, inches, meters etc. You can also turn, plus bend forward/backward or side to side; these movements are angular, determine your orientation and are measured in degrees.
When you measure something you first need to measure it from something else; that “something else” is called the reference point or reference frame and is considered the (0, 0, 0) point. You can measure any other point from that point by going forward, sideways and up; or, of course backwards, sideways and down and in any order. As I said earlier, these movements are measured in feet, inches, meters, etc. These three-dimensions account for three of the 6DOF we are discussing.
Once you have moved to that position by moving in three-dimensions, you can change your orientation and bend forward, sideways or turn; orientation is measured in degrees. These are another three degrees of freedom. So the three position movements and the three angle movements make up the 6DOF.