Degrees of freedom (engineering)

From Freepedia

In mechanical engineering, aeronautical engineering and robotics, degrees of freedom (DOF) describes flexibility of motion. A mechanism or linkage that has complete freedom of motion (even if only in a limited area, or envelope) has six degrees of freedom. Three modes are translation - the ability to move in each of three dimensions.

Three are rotation, or the ability to change angle around three perpendicular axes.


To put it in simpler terms, each of the following is one degree of freedom:

  1. Moving up and down (heaving);
  2. moving left and right (swaying);
  3. moving forward and back (surging);
  4. tilting up and down (pitching);
  5. turning left and right (yawing);
  6. tilting side to side (rolling).

See also: Euler angles.

In robotics, degrees of freedom is often used to describe the number of directions that a robot can pivot or move a joint. A human arm is considered to have 7 DOF. A shoulder gives pitch, yaw and roll, an elbow allows for pitch, and a wrist allows for pitch, yaw and roll. Only 3 of those movements would be necessary to move the hand to any point in space, but people would lack the ability to grasp things from different angles or directions.



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