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In physics and chemistry, a degree of freedom is an independent physical parameter in the chosen parameterization of a physical system.More formally, given a parameterization of a physical system, the number of degrees of freedom is the smallest number of parameters whose values need to be known in order to always be possible to determine the values of all parameters in the chosen ...
In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation : its two coordinates ; a non-infinitesimal object on the plane might have additional degrees of freedoms related to its orientation .
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.
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 constraints as many independent variables as there are degrees of freedom, these can be used as generalized coordinates. [ 5 ]
For simple systems, there may be as few as one or two degrees of freedom. One degree of freedom occurs when one has an autonomous ordinary differential equation in a single variable, d y / d t = f ( y ) , {\displaystyle dy/dt=f(y),} with the resulting one-dimensional system being called a phase line , and the qualitative behaviour of the system ...
The number of degrees of freedom F (also called the variance) is the number of independent intensive properties, i.e., the largest number of thermodynamic parameters such as temperature or pressure that can be varied simultaneously and independently of each other. [5] An example of a one-component system (C = 1) is a pure chemical
A configuration of the rigid body is defined by six parameters, three from and three from (), and is said to have six degrees of freedom. In this case, the configuration space Q = R 3 × S O ( 3 ) {\displaystyle Q=\mathbb {R} ^{3}\times \mathrm {SO} (3)} is six-dimensional, and a point q ∈ Q {\displaystyle q\in Q} is just a point in that space.
For example, 18 coordinates and 17 constraints could be used to describe the motion of the slider-crank with rigid bodies. However, as there is only one degree of freedom, the equation of motion could be also represented by means of one equation and one degree of freedom, using e.g. the angle of the driving link as degree of freedom.