Degrees of freedom (mechanics)

In physics, the degrees of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration or state.

An automobile with highly stiff suspension can be considered to be a rigid body traveling on a plane (a flat, two-dimensional space).

The exact constraint mechanical design method manages the degrees of freedom to neither underconstrain nor overconstrain a device.

Applying this definition, we have: A single rigid body has at most six degrees of freedom (6 DOF) 3T3R consisting of three translations 3T and three rotations 3R.

[3][4] Consider a system of n rigid bodies moving in space has 6n degrees of freedom measured relative to a fixed frame.

Here the term degrees of freedom is used to describe the number of parameters needed to specify the spatial pose of a linkage.

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.

Although keep in mind that it is not redundant in the human arm because the two DOFs; wrist and shoulder, that represent the same movement; roll, supply each other since they can't do a full 360.

A fixed-wing aircraft, with 3–4 control DOFs (forward motion, roll, pitch, and to a limited extent, yaw) in a 3-D space, is also non-holonomic, as it cannot move directly up/down or left/right.

A summary of formulas and methods for computing the degrees-of-freedom in mechanical systems has been given by Pennestri, Cavacece, and Vita.

[5] In electrical engineering degrees of freedom is often used to describe the number of directions in which a phased array antenna can form either beams or nulls.