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In physics, the degrees of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration or state. It is important in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering, robotics, and other fields.
In quantum mechanics, the motion degrees of freedom are superseded with the concept of wave function, and operators which correspond to other degrees of freedom have discrete spectra. For example, intrinsic angular momentum operator (which corresponds to the rotational freedom) for an electron or photon has only two eigenvalues .
When degrees of freedom is used instead of dimension, this usually means that the manifold or variety that models the system is only implicitly defined. See: See: Degrees of freedom (mechanics) , number of independent motions that are allowed to the body or, in case of a mechanism made of several bodies, number of possible independent relative ...
Degrees of freedom (mechanics) – Number of independent parameters needed to define the state of a mechanical system; Degrees of freedom problem – Multiple ways for multi-joint objects to realize a movement; Euler angles – Description of the orientation of a rigid body
In other words, a rotation formalism captures only the rotational part of a motion, that contains three degrees of freedom, and ignores the translational part, that contains another three. When representing a rotation as numbers in a computer, some people prefer the quaternion representation or the axis+angle representation, because they avoid ...
There is one for each degree of freedom, so the number of generalized coordinates equals the number of degrees of freedom, n. A degree of freedom corresponds to one quantity that changes the configuration of the system, for example the angle of a pendulum, or the arc length traversed by a bead along a wire. If it is possible to find from the ...
An example of a simple open chain is a serial robot manipulator. These robotic systems are constructed from a series of links connected by six one degree-of-freedom revolute or prismatic joints, so the system has six degrees of freedom. An example of a simple closed chain is the RSSR spatial four-bar linkage.
In the case of planar motion, a body has only three degrees of freedom with only one rotational and two translational degrees of freedom. The degrees of freedom in planar motion can be easily demonstrated using a computer mouse. The degrees of freedom are: left-right, forward-backward and the rotation about the vertical axis.